Summer
2014
Ernest Bevin College
Mr C. Barkley
[GCSE REVISION BOOKELT]
Review of GCSE work from year 10
Grade D questions.
1.1
Here is part of Jo’s electricity bill.
Work out how much Jo has to pay for the units she has used.
£ ..............................................................
(Total for Question 7 is 4 marks)
June 2012 – Unit 2 (Modular)– Higher – Non-Calculator – Q7
1.2
Grant drives a lorry to deliver some equipment from a factory to a hospital.
The distance from the factory to the hospital is 200 miles.
The lorry uses one litre of fuel to go 5 miles.
A litre of fuel for the lorry costs £1.50
Work out the total cost of the fuel the lorry used.
£..............................................
(Total for Question 2 is 3 marks)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q2
2.1
Sandy has a 4-sided spinner.
The sides of the spinner are labelled A, B, C and D.
The spinner is biased.
The table shows the probability that the spinner will land
on A or on B or on C.
Side
Probability
A
B
C
0.15
0.32
0.27
D
(a) Work out the probability that the spinner will land on D.
(2)
Sandy spins the spinner 300 times.
(b) Work out an estimate for the number of times the spinner will land on A.
(2)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q1
2.2
Priya is raising money for a charity by selling tomato plants that she has grown from seeds.
She sells 48 tomato plants for £1.35 each.
Priya keeps 15% of the money she gets to pay for the growbags and seeds that she used.
She sends the rest of the money to the charity.
How much money did she send to the charity?
£ ...............................
(Total for Question 3 is 6 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q3
2.3
Fatima bought 48 teddy bears at £9.55 each.
She sold all the teddy bears for a total of £696.
She sold each teddy bear for the same price.
Work out the profit that Fatima made on the teddy bears.
(Total for Question 5 is 4 marks)
Practice Paper Set A – Unit 2 (Modular) – Higher – Non-calculator – Q5
3.1
Using the information that
170.2 ÷ 4.6 = 37
write down the value of
(a) 1702 ÷ 4.6
(1)
(b) 170.2 ÷ 460
(1)
(c) 3.7 × 4.6
(1)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q7
3.2 Bethanusesthis formula to work out her gas bill
Cost
=
Fixed charge + Cost per unit × units used
Last month the Cost of her gas bill was £165
Her fixed charge was £45
The cost per unit was 50p
How many units did she use?
(Total for Question 2 is 3 marks)
Practice Paper Set A – Unit 2 (Modular) – Higher – Non-calculator – Q2
6.1
Work out
2
3
+
5
8
Give your answer in its simplest form.
(Total for Question 4 is 2 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q4
6.2
Work out
1
3
+
5
7
(Total for Question 1 is 2 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q1
6.3
All of the students in a science class went to one revision class.
1
of the students went to the physics revision class.
6
2
of the students went to the biology revision class.
9
All of the other students went to the chemistry revision class.
What fraction of the students went to the chemistry revision class?
(Total for Question 1 is 3 marks)
Practice Paper Set A – Unit 2 (Modular) – Higher – Non-calculator – Q1
*6.4 Susan has 2 dogs
Each dog is fed 83 kg of dog food each day.
Susan buys dog food in bags that each weigh 14kg.
For how many days can Susan feed the dogs from 1 bag of dog food?
You must show allyour working.
……………….. days
(Total for Question 7 is 5 marks)
Practice Paper Set C – Unit 2 (Modular) – Higher – Non-calculator – Q7
6.5
Work out
3 1

8 3
(Total for Question 3 is 2 marks)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q3
7.1
Work out 15% of £80
(Total for Question 3 is 2 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q3
7.2
Lydia is buying a ring.
The ring costs £60
She pays a deposit of 40%.
Work out how much she pays as the deposit. £ ........................................................
(2)
June 2011 – Unit 2 (Modular) – Higher –Non- Calculator – Q3
7.3
A TV costs £400
Peter pays a deposit of 15%.
How much does Peter still have to pay for the TV?
(Total for Question 5 is 3 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q5
7.4
A shop sells freezers and cookers.
The ratio of the number of freezers sold to the number of cookers sold is 5 : 2
The shop sells a total of 140 freezers and cookers in one week.
*(a) Work out the number of freezers and the number of cookers sold that week.
(3)
Jake buys this freezer in a sale.
The price of the freezer is reduced by 20%.
(b) Work out how much Jake saves.
(2)
(Total for Question 3 is 5 marks)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q3
7.5
There are 200 counters in a bag.
The counters are blue or red or yellow.
35% of the counters are blue.
1
of the counters are red.
5
Work out the number of yellow counters in the bag.
(Total for Question 3 is 4 marks)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q3
7.6
One day a supermarket has 8420 customers.
65% of the customers pay with a debit card.
1
of the customers pay with a credit card.
5
The rest of the customers pay with cash.
Work out how many customers pay with cash.
(Total for Question 2 is 4 marks)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q2
8.1
Graham and Michael share £35 in the ratio 5 : 2
Work out the amount of money that Graham gets.
(Total for Question 3 is 2 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q3
8.2
Grace and Jack share £140 in the ratio 3 : 4
Work out the amount of money that Jack gets.
(Total for Question 1 is 2 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q1
8.3
A pile of sand has a weight of 60 kg.
The sand is put into a small bag, a medium bag and a large bag in the ratio 2 : 3 : 7
Work out the weight of sand in each bag.
small bag .................................kg
medium bag................................. kg
large bag.................................kg
(Total for Question 2 is 3 marks)
November 2011 – Unit 1 (Modular) – Higher – Calculator – Q2
8.4
There are some sweets in a bag.
18 of the sweets are toffees.
12 of the sweets are mints.
(a)
Write down the ratio of the number of toffees to the number of mints.
Give your ratio in its simplest form.
(2)
There are some oranges and apples in a box.
The total number of oranges and apples is 54
The ratio of the number of oranges to the number of apples is 1 : 5
(b)
Work out the number of apples in the box.
(2)
Practice Paper Set C – Unit 1 (Modular) – Higher – Calculator – Q7
*8.5
Mrs Collins is organising a school trip.
120 students are going on the trip.
The ratio of the number of staff to the number of students must be 1 : 15
Mrs Collins books three coaches for the trip.
Each coach has 42 seats.
Are there enough seats for all the students and staff?
You must show all your working.
(Total for Question 2 is 4 marks)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q2
8.6
Ali, Ben and Candice share £300 in the ratio 2 : 3 : 5
How much money does Candice get?
(Total for Question 2 is 2 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q2
8.7
Build-a-mix makes concrete.
1 cubic metre of concrete has a weight of 2400 kg.
15% of the concrete is water.
The rest of the ingredients of concrete are cement, sand and stone.
The weights of these ingredients are in the ratio 1 : 2 : 5
(a) Work out the weight of cement, of sand and of stone in 1 cubic metre of concrete.
cement = .............................................................. kg
sand = .............................................................. kg
stone = .............................................................. kg
(4)
Build-a-mix needs to make 30 cubic metres of concrete.
Build-a-mix has only got 6.5 tonnes of cement.
* (b) Will this be enough cement for Build-a-mix to make 30 cubic metres of concrete?
You must show all of your working.
(3)
June 2011 – Unit 1 (Modular) – Higher – Calculator – Q3
9.1
5 identical calculators cost a total of £31.75
Work out the cost of 7 of these calculators.
(Total for Question 1 is 2 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q1
9.2
Here is a list of ingredients needed to make 12 scones.
Ingredients for 12 scones
220 g self-raising flour
40g butter
150 ml milk
2 tablespoons sugar
Viv is making scones for 15 people.
She is making 2 scones for each person.
Work out the amount of each ingredient she needs.
Self-raisingflour ..............................................................g
Butter ..............................................................g
Milk ..............................................................ml
Tablespoons of sugar ...................................................................
(Total for Question 1 is 3 marks)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q1
9.3
Richard’s car uses 1 litre of petrol every 8 miles.
Petrol costs £1.30 per litre.
Richard drives 240 miles.
Work out the total cost of the petrol the car uses.
£ .............................................
(Total for Question 1 is 3 marks)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q1
9.4
A small photograph has a length of 4 cm and a width of 3 cm.
Shez enlarges the small photograph to make a large photograph.
The large photograph has a width of 15 cm.
Small photograph
Large photograph
The two photographs are similar rectangles.
Work out the length of the large photograph.
(Total for Question 1 is 3 marks)
June 2012 – Unit 3 (Modular)– Higher – Calculator – Q1
9.5
Stacey went to the theatre in Paris.
Her theatre ticket cost €96
The exchange rate was £1 = €1.20
(a) Work out the cost of her theatre ticket in pounds (£).
(2)
Stacey bought a handbag in Paris.
The handbag cost €64.80
In Manchester, the same type of handbag costs £52.50
The exchange rate was £1 = €1.20
*(b) Compare the cost of the handbag in Paris with the cost of the handbag in Manchester.
(3)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q2
9.6
Here are the ingredients needed to make 16 chocolate biscuits.
Chocolate biscuits
Makes 16 chocolate biscuits
100 g
50 g
120 g
15 g
Sabrina has 250 g
300 g
600 g
and 60 g
of butter
of caster sugar
of flour
of cocoa
of butter
of caster sugar
of flour
of cocoa
Work out the greatest number of chocolate biscuits Sabrina can make.
You must show your working.
(Total for Question 5 is 3 marks)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q5
9.7
Lewis has a copper pipe with a length of 150 cm and a mass of 800 grams.
He cuts a piece of the copper pipe with a length of 90 cm.
Work out the mass of this piece of copper pipe.
............................................. grams
(Total for Question 4 is 2 marks)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q4
*10.1
Wheat biscuits of the same size can be bought in large boxes, medium boxes and smallboxes.
A large box costs £3.69 and contains 48 biscuits.
A medium box costs £1.78 and contains 24 biscuits.
A small box costs £1.14 and contains 12 biscuits.
Which size of box is the best value for money?
Explain your answer.
You must show all your working.
(Total for Question 3 is 4 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q3
*10.2
Gordon owns a shop.
Here are the prices of three items in Gordon’s shop and in a Supermarket.
Gordon’s Shop
400 g loaf of bread
1 litre of milk
40 tea bags
Supermarket
£1.22
£0.96
£2.42
400 g loaf of bread
1 litre of milk
40 tea bags
£1.15
£0.86
£2.28
Gordon reduces his prices by 5%.
Will the total cost of these three items be cheaper in Gordon’s shop than in the Supermarket?
(Total for Question 4 is 3 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q4
*10.3 Margaret is in Switzerland.
The local supermarket sells boxes of Reblochon cheese.
Each box of Reblochon cheese costs 3.10 Swiss francs.
It weighs 160 g.
In England, a box of Reblochon cheese costs £13.55 per kg.
The exchange rate is £1 = 1.65 Swiss francs.
Work out whether Reblochon cheese is better value for money in Switzerland or in England.
(Total for Question 5 is 4 marks)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q5
*10.4 Soap powder is sold in three sizes of box.
A 2 kg box of soap powder costs £1.89
A 5 kg box of soap powder costs £4.30
A 9 kg box of soap powder costs £8.46
Which size of box is the best value for money?
Explain your answer.
You must show all your working.
(Total for Question 5 is 4 marks)
June 2012 – Unit 3 (Modular)– Higher – Calculator – Q5
3.92  89.9
0.209
11.1 Work out an estimate for
(Total for Question 5 is 3 marks)
Practice Paper Set C – Unit 2 (Modular) – Higher – Non-calculator – Q5
11.2 Work out an estimate for the value of
89.3  0.51
.
4.8
(Total for Question 8 is 2 marks)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q8
12.1
(a) Simplify 4b × 2c
(1)
(b) Expand 3(2w – 5t)
(2)
(c) Expand and simplify (x + 7)(x – 2)
[Grade C]
(2)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q2
12.2
(a) Simplify 2e – 8f + 6e + 3f
(2)
(b) Factorise 4t + 10
[Grade C]
(1)
(c) Expand and simplify
3 + 2( p – 1)
(2)
(d) Factorise ax+ bx+ ay + by
[Grade B]
(2)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q5
12.3
Here are the first five terms of an arithmetic sequence.
4
11
18
25
32
(a) Write down, in terms of n, an expression for the nth term of this sequence.
(2)
An expression for the nth term of another sequence is 3n2 – 1
(b) Find the fourth term of this sequence.
(2)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q8
12.4 A taxi company uses this formula to calculate taxi fares.
f = 7d2 + 320
wheref is the taxi fare, in pence, and d is the distance travelled, in km.
Aziz uses this taxi company to travel a distance of 8 km.
Work out the taxi fare.
(Total for Question 2 is 3 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q2
12.5 t = x2 – 5y
x=6
y=4
Work out the value of t.
(Total for Question 3 is 2 marks)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q3
13.1 Brian is x years old.
Peter is 4 years older than Brian.
Amy is 2 years younger than Brian.
The total of their ages is 26 years.
Work out the value of x.
(Total for Question 2 is 4 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q2
13.2 Here is a parallelogram.
x cm
The height of the parallelogram is x cm.
The perimeter of the parallelogram is 44 cm.
The length of the parallelogram is three times as long as the height.
The slant length of the parallelogram is 2 cm longer than the height.
Find the area of the parallelogram.
………………… cm2
(Total for Question 3 is 5 marks)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q3
13.3 k = 3e + 5
(a) Work out the value of k when e = –2
(2)
(b) Solve
4y + 3 = 2y + 14
(2)
(c) Solve
3(x – 5) = 21
(2)
–3 <n < 4
nis an integer.
(d) Write down all the possible values of n.
(2)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q5
14.1
Here are the first five terms of an arithmetic sequence.
2
7
12
17
22
(a) (i) Find the next term of this sequence.
(ii) Explain how you found your answer.
(2)
(b) Write down an expression, in terms of n, for the nth term of the sequence.
(2)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q2
14.2
Here are the first four terms of an arithmetic sequence.
5
9
13
17
(a) What is the next term of this sequence?
(1)
(b) Write down an expression, in terms of n, for the nth term of the sequence.
(2)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q1
14.3
Here are some patterns made from sticks.
(a)
Pattern number 1
Complete the table
Pattern number 2
Pattern number
Number of sticks
1
6
2
10
3
14
Pattern number 3
4
5
10
(b)
(c)
(3)
Explain if a complete pattern can be made from 99 sticks.
(2)
Write down an expression, in terms of n, for the number of sticks in Pattern number n.
(2)
Practice Paper Set B – Unit 2 (Modular) – Higher – Non-Calculator – Q1
14.4
Here are the first four terms of an arithmetic sequence.
10
16
22
28
(a) Find the 10th term of this sequence.
(1)
(b) Find an expression, in terms of n, for the nth term of the sequence.
(2)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q5
14.5
Here are the first 5 terms of an arithmetic sequence.
6
10
14
18
22
(a) Write down an expression, in terms of n, for the nth term of this sequence.(2)
The nth term of a different sequence is 2n2 – 4
(b) Find the 3rd term of this sequence.
(2)
June 2011 – Unit 2 (Modular) – Higher –Non- Calculator – Q10
14.6 The first five terms of an arithmetic sequence are
2
6
10
14
18
(a) Write down an expression, in terms of n, for the nth term of this sequence.
(2)
An expression for the nth term of a different sequence is 20 – 5n
(b) Work out the 10th term of this sequence.
(2)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q7
14.7 Here are some patterns made from white centimetre squares and grey centimetre squares.
Pattern 1
Pattern 2
Pattern 3
A Pattern has 20 grey squares.
(a) Work out how many white squares there are in this Pattern.
(2)
(b) Find an expression, in terms of n, for the total number of centimetre squares in
Pattern n.
(2)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q1
15.1 On the grid, draw the graph of y = 2x – 3 for values of x from –2 to 2
(Total for Question 9 is 3 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q9
15.2
On the grid, draw the graph of y = 4x – 2 for values of x from x = – 2 to x = 3
(Total for Question 8 is 3 marks)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q8
15.3 On the grid, draw the graph of y = 2x + 3 for values of x from x = –3 to x = 1
(Total for Question 3 is 3 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q3
15.4 (a) Complete the table of values for y =
x
–2
y
3
1
x+4
2
–1
0
1
2
4
(2)
(b) On the grid, draw the graph of y =
1
x+4
2
(2)
(c) (i)
On the grid, draw the line that is perpendicular to y =
1
x + 4 and passes through the
2
point with coordinates (0, 4)
(ii) Find the equation of this line.
[Grade B]
(3)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q8
*17.1
BDEis an isosceles triangle.
DB = DE.
The straight line ABC is parallel to the straight line DEF.
Work out the size of the angle marked x.
You must give reasons for each stage in your working.
(Total for Question 1 is 4 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q1
17.2
AFB and CHDare parallel lines.
EFD is a straight line.
Work out the size of the angle marked x.
(Total for Question 13 is 3 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q4
17.3
A
B
95º
120º
72º
x
C
ABCD is a quadrilateral
CDE is a straight line.
Find the size of angle x.
D
E
(Total for Question 3 is 3 marks)
Practice Paper Set B – Unit 2 (Modular) – Higher – Non-calculator – Q3
17.4
x
Diagram NOT
accurately drawn
65º
D
E
F
ABCD is a parallelogram.
ABC and DEF are straight lines.
Find the value of the angle marked x.
You must give reasons to explain your answer.
(Total for Question 2 is 4 marks)
Practice Paper Set C – Unit 2 (Modular) – Higher – Non-calculator – Q2
18.1
(a) Reflect shape P in the line x = 3
(2)
(b) Describe fully the single transformation that maps shape A onto shape B.
(3)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q10
18.2
(a) Rotate triangle T 90° clockwise about the point (0, 0).
(2)
(b) Describe fully the single transformation which maps shape P onto shape Q.
(3)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q11
18.3
Describe fully the single transformation which maps triangle A onto triangle B.
(Total for Question 6 is 3 marks)
June 2012 – Unit 3 (Modular)– Higher – Calculator – Q6
18.4
y
6
5
4
3
2
1
6
5
4
3
2
1
O
1
2
3
4
5
6
x
1
P
2
3
4
5
6
(a) Rotate triangle P 180 about the point (1, 1). Label the new triangle A.
6
(b) Translate triangle P by the vector   .Label the new triangle B.
 1 
y
(2)
(2)
5
4
R
3
2
Q
1
O
(c)
1
2
3
4
5
x
Describe the single transformation that moves shape Q to shape R .
(2)
Practice Paper Set A – Unit 3 (Modular)– Higher – Calculator – Q4
18.5
Describe fully the single transformation that maps triangle A onto triangle B.
(Total for Question 7 is 3 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q7
18.6
On the grid, enlarge the shape with scale factor 3, centre A.
(Total for Question 2 is 3 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q2
18.7 Two shapes are shown on the grid.
(a) Describe fully the transformation that maps shape P onto shape Q.
(2)
(b) Rotate triangle A 90° clockwise about the point (0, 2).
Label the new triangle B.
(2)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q1
19.1
The diagram shows the front elevation and the side elevation of a prism.
Front elevation
Side elevation
(a) On the grid, draw a plan of this prism.
(b) In the space below, draw a sketch of this prism.
(2)
(2)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q9
19.2 The diagram shows a solid prism.
2 cm
1 cm
3 cm
4 cm
(a)
On the grid below, draw the front elevation of the prism from the direction of the
arrow.
(2)
(b)
On the grid below, draw the plan of the prism.
(2)
Practice Paper Set C – Unit 3 (Modular) – Higher – Non-Calculator – Q3
19.3 Here are the plan and front elevation of a prism.
The cross section of the shape is represented by the front elevation.
Plan
Front Elevation
(a)
On the grid below draw a side elevation.
(b)
In the space below draw a 3D sketch of the shape.
(2)
(2)
Practice Paper Set A – Unit 2 (Modular) – Higher – Non-Calculator – Q8
19.4 Here is a solid prism.
On the grid, draw an accurate side elevation of the solid prism
from the direction of the arrow.
(Total for Question 10 is 2 marks)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q10
19.5. Here is a box in the shape of a cuboid.
(a) Complete an accurate drawing of the cuboid on the isometric grid.
One edge of the cuboid has been drawn for you.
(2)
The box is made to hold cubes.
Each cube has edges of length 2 cm.
(b) Work out the largest number of cubes that can fit into the box.
(2)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
20.1 Use ruler and compasses construct an angle of 45º at A
You must show all construction lines.
A
(Total for Question 6 is 3 marks)
Practice Paper Set C – Unit 3 (Modular) – Higher –Calculator – Q6
21.1
Work out the area of this triangle.
(3)
June 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q1
21.2 Here is a right-angled triangle.
The shape below is made from 4 of these triangles.
Work out the perimeter of the shape.
............................................. cm
(Total for Question 3 is 3 marks)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q3
22.1
Here is a circle.
8 cm
The radius of the circle is 8 cm.
(a)
Work out the circumference of the circle.
………………. cm
(2)
(b)
Work out the area of the circle.
…………….. cm²
(2)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q1
22.2 Susan has a round cake.
The cake has a diameter of 20 cm.
Susan wants to put a ribbon round the cake.
What is the least length of ribbon she can use?
(Total for Question 3 is 3 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q3
22.3 Here is a circle.
The radius of the circle is 4 cm.
Work out the circumference of the circle.
.............................................. cm
(Total for Question 5 is 2 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q5
*22.4 The diagram shows a flower bed in the shape of a circle.
The flower bed has a diameter of 2.4 m.
Sue is going to put a plastic strip around the edge of the flower bed.
The plastic strip is sold in 2 metre rolls.
How many rolls of plastic strip does Sue need to buy?
You must show all your working.
(Total for Question 4 is 4 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q4
25.1 Ouzma wants to find out the method of transport people use to travel to a shopping centre.
Design a suitable data collection sheet she could use to collect this information.
(Total for Question 3 is 3 marks)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q3
25.2 James wants to find out how long his friends spend using the internet.
He uses this question on his questionnaire.
(a) Write down two things wrong with this question.
(2)
(b) Write a better question for James to use on his questionnaire to find out how long his
friends spend using the internet.
(2)
November 2011 – Unit 1 (Modular) – Higher – Calculator – Q4
25.3 (a) Dan is doing a survey to find out how much time students spend playing sport.
He is going to ask the first 10 boys on the register for his PE class.
This may not produce a good sample for Dan’s survey.
Give two reasons why.
(2)
(b) Design a suitable question for Dan to use on a questionnaire to find out how much time
students spend playing sport.
(2)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q1
26.1
80 children went on a school trip.
35 of the children were boys.
They went to London, York or to a theme park.
10 boys and 15 girls went to London.
5 boys went to York.
25 of the children went to the theme park.
(a) Use this information to complete the two-way table.
Theme
London
York
Park
Total
Boys
Girls
Totals
(3)
One of the 80 children is to be chosen at random.
(b) What is the probability that this child went to London.
(2)
Practice Paper Set C – Unit 1 (Modular) – Higher – Calculator – Q6
26.2 There are a total of 96 children in Years 4, 5 and 6
37 of these children cannot swim.
11 children in Year 4 cannot swim.
21 children in Year 5 can swim.
There are 30 children in Year 6
18 of these 30 children can swim.
(i) Work out the number of children in Year 4 who can swim.
(ii) Work out the total number of children in Year 5
(4)
June 2011 – Unit 1 (Modular) – Higher – Calculator – Q1
26.3 There are 200 students at a college.
Each student studies one of Art, Graphics or Textiles.
Of the 116 female students, 26 study Graphics.
22 male students study Textiles.
A total of 130 students study Art.
The number of students who study Graphics is the same as the number of studentswho study
Textiles.
Work out how many male students study Art.
(Total for Question 6 is 4 marks)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q6
26.4 A teacher asked 30 students if they had a school lunch or a packed lunch or if they went
home for lunch.
17 of the students were boys.
4 of the boys had a packed lunch.
7 girls had a school lunch.
3 of the 5 students who went home were boys.
Work out the number of students who had a packed lunch.
(Total for Question 4 is 4 marks)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q4
26.5 120 children went on a school activities day.
Some children went bowling.
Some children went to the cinema.
The rest of the children went skating.
66 of these children were girls.
28 of the 66 girls went bowling.
36 children went to the cinema.
20 of the children who went to the cinema were girls.
15 boys went skating.
Work out the number of children who went bowling.
(Total for Question 6 is 4 marks)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q6
28.1 A survey was carried out for a magazine.
90 cat owners were asked to write down the make of cat food their cats liked best.
The bar chart shows information about the results.
The information in the bar chart is going to be shown in a pie chart.
Use the information in the bar chart to complete the pie chart.
(Total for Question 4 is 3 marks)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q4
28.2 Each year group in a school raised money for charity.
The incomplete table and pie chart show some information about this.
Complete the table.
Year Group
7
8
9
Amount raised
..........................
£225
..........................
10
£125
11
£162.50
£900
(Total for Question 7 is 3 marks)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q7
29.1
The scatter graph shows information about 8 people.
It shows each person’s height and the circumference of their head.
The table gives this information for 2 other people.
Height (cm)
180
170
Circumference of head (cm)
72
65
(a) On the scatter graph, plot the information from the table.(1)
(b) Describe the correlation. (1)
(c) Draw a line of best fit on your scatter graph.(1)
(d) Estimate the circumference of the head of a person who is 156 cm tall
....................cm(1)
November 2011 – Unit 1 (Modular) – Higher – Calculator – Q5
29.2 The scatter graph shows information about the ages and values of seven Varley motor
scooters.
Another Varley motor scooter is 5 years old.
It has a value of £300
(a) Show this information on the scatter graph.
(1)
(b) Describe the relationship between the age and the value of Varley motor scooters.
(1)
A Varley motor scooter is 4 years old.
(c) Estimate its value.
£..................................................................
(2)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q3
29.3 Some children took part in a piano competition.
Each child was given a mark from Judge A and from Judge B.
The scatter graph below shows some of this information.
(a) Describe the correlation.
(1)
Judge A gives 44 marks to another child.
(b) Use the scatter graph to estimate Judge B’s mark for this child
......... marks
(2)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q5
29.4
A beach cafe sells ice creams. Each day the manager records the number of hours of sunshine
and the number of ice creams sold.
The scatter graph shows this information.
On another day there were 11.5 hours of sunshine and 73 ice creams sold.
(a) Show this information on the scatter graph.
(1)
(b) Describe the relationship between the number of hours of sunshine and the number of ice
creams sold.
(1)
One day had 10 hours of sunshine.
(c) Estimate how many ice creams were sold.
(2)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q2
30.1 The list below shows the weight, in grams, of 15 baskets of strawberries.
193
200
207
211
198
189
218
195
206
189
223
190
207
205
212
Show this information in an ordered stem and leaf diagram.
You must include a key.
(Total for Question 1 is 3 marks)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q1
30.2 Here are the heights, in cm, of 20 sunflower plants.
73
84
78
96
98
84
101
93
71
104
81
92
95
103
100
96
87
91
88
96
(a) Draw an ordered stem and leaf diagram for these heights.
(3)
(b) Find the median height.
............................... cm
(1)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q5
31.1 Marta asked some students how many cans of drink they each drank yesterday.
The table shows her results.
Number of cans
Frequency
0
6
1
9
2
7
3
3
4
2
5
1
Work out the total number of cans these students drank yesterday.
(Total for Question 1 is 2 marks)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q1
31.2 Julie is x years old.
Kevin is x + 3 years old.
Omar is 2x years old.
Write an expression, in terms of x, for the mean of their ages.
(2)
November 2011 – Unit 1 (Modular) – Higher – Calculator – Q3
31.3 Josh asked 30 adults how many cups of coffee they each drank yesterday.
The table shows his results.
Number of cups
Frequency
0
5
1
9
2
7
3
4
4
3
5
2
Work out the mean.
(Total for Question 9 is 3 marks)
Practice Paper Set C – Unit 1 (Modular) – Higher – Calculator – Q9
31.4 There are 15 bags of apples on a market stall.
The mean number of apples in each bag is 9
The table below shows the numbers of apples in 14 of the bags.
Number
of apples
Frequency
7
2
8
3
9
3
10
4
11
2
Calculate the number of apples in the 15th bag.
(Total for Question 6 is 3 marks)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q6
32.1 Josh plays a game with two sets of cards.
Josh takes at random one card from each set.
He adds the numbers on the two cards to get the total score.
(a) Complete the table to show all the possible total scores.
Set A
Set B
1
2
4
5
7
3
4
5
7
8
10
6
7
8
10
8
9
(b) What is the probability that Josh’s total score will be greater than 12?
(1)
(2)
Josh’s year group are raising money for a sponsored skydive.
60 students are each going to play Josh’s card game once.
Each student pays 50p to play the game.
Josh pays £1.50 to any player getting a total of 8
(c) Show that Josh can expect to make a profit of £21 from his game.
(4)
November 2011 – Unit 1 (Modular) – Higher – Calculator – Q8
33.1 Laura has a four-sided spinner.
The spinner is biased.
The table shows each of the probabilities that the spinner will land on 1 or land on 3
The probability that the spinner will land on 2 is equal to the probability that it will land on 4
Number
1
Probability
2
3
0.25
4
0.35
Laura is going to spin the spinner once.
(a) Work out the probability that the spinner will not land on 1
(2)
(b) Work out the probability that the spinner will land on 2
(2)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q1
33.2 Here is a five-sided spinner.
The table shows the probabilities that the spinner will land on 1 or 2 or 3 or 4 or 5
Number
Probability
1
2
3
4
5
0.15
0.20
0.10
0.25
0.30
Pete spins the spinner once.
(a) Work out the probability that the spinner will land on a number greater than 2(2)
Elinor is going to spin the spinner 200 times.
(b) Work out an estimate for the number of times the spinner will land on 5
(2)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q3
33.3 Tim plays a game.
He can win the game or he can lose the game or he can draw the game.
The probability that Tim will win the game is 0.25.
The probability that Tim will lose the game is x.
(a) Give an expression, in terms of x, for the probability that he will draw the game.
(2)
Tim plays the game 240 times.
(b) Work out an estimate for the number of times he will win the game.
(2)
November 2013 – Unit 1 (Modular) – Higher – Calculator – Q2
Grade C questions
1.1
(a) Express 54 as a product of its prime factors.
(2)
(b) Find the Lowest Common Multiple (LCM) of 45 and 54
(2)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q4
1.2
Find the Lowest Common Multiple (LCM) of 8 and 12
(Total for Question 5 is 2 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q5
1.3
(a) Express 48 as a product of its prime factors.
(2)
Buses to Exeter leave a bus station every 20 minutes.
Buses to Plymouth leave the bus station every 16 minutes.
A bus to Exeter and a bus to Plymouth both leave the bus station at 8 a.m.
(b) When will buses to Exeter and Plymouth next leave the bus station at the same time?
(3)
June 2011 – Unit 2 (Modular) – Higher –Non- Calculator – Q3
1.4
Veena bought some food for a barbecue.
She is going to make some hot dogs.
She needs a bread roll and a sausage for each hot dog.
There are 40 bread rolls in a pack.
There are 24 sausages in a pack.
Veena bought exactly the same number of bread rolls and sausages.
(i) How many packs of bread rolls and packs of sausages did she buy?
...……………………………. packs of bread rolls
...…………………………… packs of sausages.
(ii) How many hot dogs can she make?
...……………………………. hot dogs
(Total for Question 4 is 5 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q4
2.1
(a)
4.52
Work out
(2)
(b)
Write as a power of 4
(i)
45 × 47
(ii)
(45)3
(1)
(1)
(c)
1
3n 
9
Find the value of n.
[Grade A]
(1)
Practice Paper Set B – Unit 2 (Modular) – Higher – Non-calculator – Q2
2.2
(a) Simplify
54 × 56
(1)
(b) Simplify
75 ÷ 72
(1)
4.1
(a)
Work out
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q2
2 1

3 4
(2)
(b)
Work out
3
1
2 +5
4
2
(3)
Practice Paper Set A – Unit 2 (Modular) – Higher – Non-calculator – Q6
6.1
Last year, Jora spent
30% of his salary on rent
2
of his salary on entertainment
5
1
of his salary on living expenses.
4
He saved the rest of his salary.
Jora spent £3600 on living expenses.
Work out how much money he saved.
(Total for Question 15 is 5 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q9
6.2
Mrs Jennings shares £770 between her two sons, Pete and Tim.
She shares the money in the ratio of her sons’ ages.
The combined age of her two sons is 66 years.
Pete is 6 years younger than Tim.
Work out how much money each son gets.
You must show all your working.
Pete £ ...............................
Tim £ ...............................
(Total for Question 10 is 5 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q10
*6.3 Edgar had a maths test and a science test.
He got 68% in the maths test.
He got 36 out of 55 in the science test.
Which test did Edgar get the better mark in, maths or science?
(3)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q5
6.4
A company sends every item of mail by second class post.
Each item of mail is either a letter or a packet.
The tables show information about the cost of sending a letter by second class post and the
cost of sending a packet by second class post.
Letter
Weight range
0 – 100 g
Packet
Weight range
0 – 100 g
101 – 250 g
251 – 500 g
501 – 750 g
751 – 1000 g
Second Class
32p
Second Class
£1.17
£1.51
£1.95
£2.36
£2.84
The company sent 420 items by second class post.
The ratio of the number of letters sent to the number of packets sent was 5 : 2
2
of the packets sent were in the weight range 0 – 100 g.
3
The other packets sent were in the weight range 101 – 250 g.
Work out the total cost of sending the 420 items by second class post.
(Total for Question 7 is 5 marks)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q7
6.5
Bill gives away £20 000 to help animals.
He gives 20% of the £20 000 to a donkey sanctuary.
He shares the rest of the £20 000 between a dogs’ home and a cats’ home in the ratio 3 : 2
How much money does Bill give to the cats’ home?
£..............................................
(Total for Question 6 is 4 marks)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
7.1
A cooker costs £650 plus 20% VAT.
(a) Calculate the total cost of the cooker.
(3)
A washing machine has a price of £260
In a sale its price is reduced by £39
(b) Write the reduction as a percentage of the price.
.......................... %
(2)
3 kitchen chairs cost a total of £44.79
(c) Work out the total cost of 8 of these chairs.
(2)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q4
7.2
£500 is invested at a simple interest rate of 3% per year.
After how many years is the total interest £60?
(Total for Question 2 is 3 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q2
7.3
John earns £30 000 each year.
He knows that 20% of his monthly pay is deducted each month.
Work out how much money John has left each month after this deduction.
£ ..............................................................
(3)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
*7.4
Jim buys 6 trays of Cola for £9.99 a tray.
Each tray holds 24 cans of Cola.
Jim goes to the school fete to sell his Cola.
He sells 75 cans at 80p each.
He gives 10 cans to his friends.
He sells the rest at 50p each.
24 cans
£9.99 a tray
What is Jim’s percentage profit or loss?
Give your answer to 1 decimal place.
(Total for Question 9 is 5 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q9
7.5
Petra booked a family holiday.
The total cost of the holiday was £3500 plus VAT at 20%.
Petra paid £900 of the total cost when she booked the holiday.
She paid the rest of the total cost in 6 equal monthly payments.
Work out the amount of each monthly payment.
(Total for Question 7 is 5 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q7
*8.1
Sam is going to paint his garden shed.
The paint is sold in two different shops.
Sam needs 7.5 litres of paint.
Sam wants to buy the cheapest paint.
He is going to buy the paint from one of these shops.
Which shop should he buy the paint from?
You must show your working.
(Total for Question 8 is 4 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q8
*8.2
Debra and Mark are planning to go on a cruise.
They can travel with one of two companies, Caribbean Calypso or Royal European.
The table shows the cost per person to travel with each company.
Type of cabin
Cost per
person
Inside
Outside
Balcony
Suite
Caribbean Calypso
£1136
£1319
£1529
£2329
Royal European
£1043
£1263
£1484
£2147
Caribbean Calypso has a discount of 10% if you book online.
Royal European has a discount of 5% if you book online.
Debra and Mark are going to book a suite for their cruise.
They are going to book online.
Debra and Mark want to pay the lowest possible cost.
Which company should they choose?
You must show all your working.
(2)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q4
*8.3 Jon and Alice are planning a holiday.
They are going to stay at a hotel.
The table shows information about prices at the hotel.
Price per person per night (£)
Dinner(£)
Double room
Single room
per person per day
01 Nov – 29April
59.75
118.00
31.75
30 April – 08 July
74.25
147.00
31.00
09 July – 29 Aug
81.75
161.75
31.00
74.25
147.00
30 Aug – 31 Oct
Saver Prices
5 nights for the price of 4 nights from 1st May to 4th July.
3 nights for the price of 2 nights in November.
31.00
Jon and Alice will stay in a double room.
They will eat dinner at the hotel every day.
They can stay at the hotel for 3 nights in June or 4 nights in November.
Which of these holidays is cheaper?
(Total for Question 8 is 5 marks)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q8
8.4
The table shows the costs, per person, of a holiday at two different hotels.
It shows the cost for 5 nights and the cost for each extra night.
It also shows the discount for each child.
ParkPalace
Dubai Grand
5 nights
extra
night
5 nights
extra
night
01 Jan – 31 Mar
£1169
£150
£849
£86
01 Apr – 09 Apr
£1229
£150
£1219
£95
10 Apr – 15 Jul
£810
£80
£853
£53
16 Jul – 20 Aug
£810
£80
£854
£53
21 Aug – 10 Dec
£810
£80
£869
£94
Date holiday starts
Discount for each child
1
off
5
15% off
There are two adults and two children in the Smith family.
The family want a holiday for 7 nights, starting on 1st August.
One hotel will be cheaper for them than the other hotel.
Work out the cost of the cheaper holiday.
You must show all your working.
(Total for Question 8 is 6 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q8
*8.5 Mr and Mrs Jones are planning a holiday to the Majestic Hotel in the Cape Verde Islands.
The table gives information about the prices of holidays to the Majestic Hotel.
MAJESTIC HOTEL, Cape VerdeIslands
Price per adult
Departures
7 nights
14 nights
1 Jan – 8 Jan
£694
£825
9 Jan – 28 Jan
£679
£804
29 Jan – 5 Feb
£687
£815
6 Feb – 18 Feb
£769
£835
19 Feb – 8 Mar
£714
£817
9 Mar – 31 Mar
£685
£805
1 Apr – 9 Apr
£788
£862
10 Apr – 30 Apr
£748
£802
Price per child: 95% of adult price for 7 nights or 85% of adult price for 14 nights.
Mr and Mrs Jones are thinking about going on holiday
on 20 February for 7 nights
or
on 10 April for 14 nights.
Mr and Mrs Jones have 2 children.
Compare the costs of these two holidays for the Jones family.
(Total for Question 2 is 5 marks)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q2
*8.6 Pete and Sue are going to take their children to France.
They will travel together on the same ferry.
They will travel with one of two ferry companies, Easy Ferry or Seawagon.
The tables give information about the costs for each adult and each child to travel with these
ferry companies.
Easy Ferry
July
August
Date
1 – 10
11 – 21
22 – 31
1 – 10
11 – 21
22 – 31
Adult
£32.00
£36.50
£39.50
£42.25
£42.25
£37.75
Child
£18.00
£20.25
£23.75
£25.85
£25.85
£21.00
Seawagon
July
August
Date
1 – 10
11 – 21
22 – 31
1 – 10
11 – 21
22 – 31
Adult
£33.50
£37.50
£40.25
£43.85
£44.95
£38.50
Child
£17.25
£19.75
£21.85
£24.65
£23.95
£19.95
The table below gives information about the discount they will get from each ferry company
if they book early.
Early booking discount
Easy Ferry
1
off
3
Seawagon
25% off
Pete and Sue have three children.
They will travel on 25 July.
They will book early.
Pete and Sue will travel with the cheaper ferry company.
Which ferry company?
You must show all your working.
(5)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q4
*8.7
Joan is planning a skiing holiday in Hinterglemm for herself and her two children.
They are going skiing for 6 days.
The table shows the costs of ski hire, of boot hire and of buying lift passes in two shops in
Hinterglemm.
All prices are in Euros.
Shop A
Adult
Child
Ski hire
Boot hire
Lift pass
6 days
111
53
236
13 days
168
90
314
6 days
78
52
165
13 days
122
87
210
Ski hire
Boot hire
Lift pass
6 days
108
54
242
13 days
170
89
324
6 days
68
48
160
13 days
118
85
205
Shop B
Adult
Child
Joan will use her own skis and her own boots.
For 6 days she will need
to hire skis for each of her two children
to hire boots for each of her two children
and to buy lift passes for herself and each of her two children.
Shop A gives 5% off the total cost.
Shop B gives 3% off the total cost.
Joan wants to hire the skis and boots and buy the lift passes from the same shop.
She wants to get everything from the cheaper shop.
Which shop is cheaper for Joan?
You must show all your working.
(Total for Question 8 is 5 marks)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q8
*8.8 Ketchup is sold in three different sizes of bottle.
Small bottle
Medium bottle
Large bottle
A small bottle contains 342 g of ketchup and costs 88p.
A medium bottle contains 570 g of ketchup and costs £1.95.
A large bottle contains 1500 g of ketchup and costs £3.99.
Which bottle is the best value for money?
You must show your working.
(Total for Question 9 is 4 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q9
9.1
Work out
1
3
3 4
3
4
(Total for Question 3 is 2 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q3
9.2
Use your calculator to work out
67.92  13.9
3.4  9.8
Write down all the figures from your calculator display.
You must give your answer as a decimal.
(Total for Question 2 is 2 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q2
9.3
Use your calculator to work out
13.7  5.862
2.54  1.96
Write down all the figures on your calculator display.
You must give your answer as a decimal.
(Total for Question 6 is 2 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q6
9.4
(a) Work out the value of
 30
2 .5 2
Give your answer correct to 3 decimal places.
(2)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q9
9.5
Use your calculator to work out
40.96
.
7.1  2.48
Write down all the figures on your calculator display.
You must give your answer as a decimal.
(Total for Question 3 is 2 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q3
10.1 (a) Simplify 3y + 2x – 4 + 5x + 7
(1)
(b) Factorise 2x2 – 4x (2)
(c) Expand and simplify 11 – 3(x + 2)
(2)
(d) Expand and simplify (x – 6)(3x + 7)
[Grade B]
(2)
June 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q2
10.2 (a) Simplify p3 × p5
h7
(b) Simplify 2 (1)
h
(1)
(c) Simplify (x2)3(1)
June 2011 – Unit 2 (Modular) – Higher –Non- Calculator – Q8
10.3 (a) Factorise
10a + 5
(1)
(b) Expand and simplify
5(x + 7) + 3(x – 2)
(c) Factorise completely
3a2b + 6ab2
(2)
[Grade B]
(2)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
10.4
(a) Simplify 5f × 4g
(1)
9a + 3(8 – 2a)(2)
(b) Expand and simplify
(c) Simplify c2 × c6(1)
(d) Simplify (x5)3
(1)
(e) Factorise 7y + 21
10.5 (a) Factorise
(1)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q2
3t + 12
(1)
(b) (i) Expand and simplify
7(2x + 1) + 6(x + 3)
(ii)Show that when x is a whole number
7(2x + 1) + 6(x + 3)
is always a multiple of 5
(3)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q9
11.6 (a) Simplify 2e + 3f – e + 4f
(2)
(b) Expand 5(2c + 3d)
(1)
(c) Here are two straight lines, ABCDE and PQ.
In the diagrams all the lengths are in cm.
AE = 2PQ.
Find an expression, in terms of x, for the length of DE.
Give your answer in its simplest form.
.............................................. cm
(4)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q7
3(2p – 5) = 21
11.1 (a) Solve
p = .............................................
(3)
9x – 11 = 5x + 7
(b) Solve
x = .............................................
(3)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q6
*11.2
The area of this shape is 38 cm².
All the measurements are in cm.
3x + 5
3
8
2x – 3
Find the length of the smallest side.
(Total for Question 8 is 4 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q8
11.3 (a)
Solve
5x + 4 = 2(4x – 3)
x = ……………………..
(3)
(b)
Solve
2x  3 x  4

5
6
2
[Grade A]
x = …………………
(3)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q10
11.4 (a)
Solve
3x – 5 = 7x + 30
(2)
(b)
Solve
20  2 x
 2x  3
5
(3)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q10
11.5 (a) Solve
2x + 3 = x – 4
x = ..............................................
(2)
(b) Solve
4(x – 5) = 14
x = ..............................................
(2)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q12
11.6 Dan has some marbles.
Ellie has twice as many marbles as Dan.
Frank has 15 marbles.
Dan, Ellie and Frank have a total of 63 marbles.
How many marbles does Dan have?
(Total for Question 8 is 3 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q8
*12.1
This formula is used to work out the body mass index, B, for a person of mass M kg and
height H metres.
B=
M
H2
A person with a body mass index between 25 and 30 is overweight.
Arthur has a mass of 96 kg.
He has a height of 2 metres.
Is Arthur overweight?
You must show all your working.
(Total for Question 14 is 3 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
12.2 R = 4(3y – 5)
R = 32
(a)
Work out the value of y.
(2)
F = ma + b
(b)
Make m the subject of the formula.
m = ………………….
(2)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q1
13.1 The equation
x3 + 10x = 23
has a solution between 1 and 2
Use a trial and improvement method to find the solution.
Give your answer correct to one decimal place.
You must show all your working.
(Total for Question 7 is 4 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q7
13.2 The equation
x3 – x = 32
has a solution between 3 and 4
Use a trial and improvement method to find this solution.
Give your solution correct to one decimal place.
You must show all your working.
x = .............................................
(Total for Question 11 is 4 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q11
13.3 The equation x3 + 6x2 = 500 has a solution between 6 and 7
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show all your working.
x = ..............................................
(Total for Question 10 is 4 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q10
13.4 The equation
x3 – 6x = 84
has a solution between 4 and 5.
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show all your working.
(Total for Question 11 is 4 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q11
14.1 3x + 5 > 16
xis an integer.
Find the smallest value of x.
(Total for Question 1 is 5 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q1
14.2 (a)
–5 <n 2
n is an integer
Write down all the possible values of n.
(b)
(2)
Here is an inequality, in x, shown on a number line.
x
–4 –3 –2 –1
0
1
2
3
4
5
Write down the inequality.
(2)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q6
14.3 (a)
–1 <y< 4
On the number line below mark the inequality
y
–4
–3
–2
–1
0
1
2
3
4
5
(1)
(b)
Here is an inequality, in x, shown on a number line.
x
–4 –3 –2 –1
Write down the inequality.
0
1
2
3
4
5
(2)
(c)
Solve the inequality
3t + 5 > 17
(2)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q2
14.4
–4 <n  1
n is an integer.
(a) Write down all the possible values of n.
(2)
(b) Write down the inequalities represented on the number line.
(2)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q4
15.1 The point A has coordinates (3, 8).
The point B has coordinates (7, 5).
M is the midpoint of the line segment AB.
Find the coordinates of M.
(2)
June 2011 – Unit 2 (Modular) – Higher –Non- Calculator – Q7
15.2
Find the coordinates of the midpoint of the line joining the points (1, 2) and (4, 0).
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q3
15.3. The graph shows information about the distances travelled by a car for different amounts of
petrol used.
(a) Find the gradient of the straight line.
(2)
(b) Write down an interpretation of this gradient.
(1)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q8
15.4 The straight line P has been drawn on a grid.
Find the gradient of the line P.
(Total for Question 7 is 2 marks)
June 2013 – Unit 1 (Modular) – Higher – Calculator – Q7
16.1 (a)
y = x² + x – 3
Complete the table of values for
x
–4
y
9
–3
–2
–1
–1
–3
0
1
2
(2)
(b)
On the grid below, draw the graph of y = x² + x – 3 for values of x from –4 to 2
y
10
8
6
4
2
–4
–3
–2
–1
O
1
2
–2
–4
–5
(2)
(c)
x² + x – 3 = 0
……………………….
(2)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q4
Use your graph to find estimates for the solutions of
[Grade B]
16.2 (a) Complete the table of values for y = 2x2 – 1
x
–2
y
7
–1
0
1
2
1
(2)
(b) On the grid below, draw the graph of y = 2x2 – 1 for values of x from x = –2 to x = 2
(2)
(c) Use your graph to write down estimates of the solutions of the equation 2x2 – 1 = 0
[Grade B]
....................................................................
(2)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q11
16.3 (a) Complete the table of values for y = x2 – 4
x
y
–3
–2
–1
0
–3
0
1
2
3
0
5
(2)
(b) On the grid, draw the graph of y = x2 – 4 for x = –3 to x = 3
(2)
(Total for Question 6 is 4 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q6
15.4 Water flows out of a cylindrical tank at a constant rate.
The graph shows how the depth of water in the tank varies with time.
(a) Work out the gradient of the straight line.
(2)
(b) Write down a practical interpretation of the value you worked out in part (a).
(1)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q8
17.1 The graph shows the distance travelled by two trains.
(a) Work out the gradient of the line for train A.
(2)
(b) Which train is travelling at the greater speed?
You must explain your answer.
(1)
(c) After how many minutes has train A gone 10 miles further than train B?
....................................minutes
(1)
November 2011 – Unit 1 (Modular) – Higher – Calculator – Q7
17.2
You can use this formula to change a temperature C, in °C, to a temperature F,in °F.
F = 1.8C + 32
(a) Use the formula to change 20 °C into °F.
............................... °F
(2)
(b) On the grid below, draw a conversion graph that can be used to change between
temperatures in °C and temperatures in °F.
(3)
c)
Use your graph to change 100 °F into °C.
............................... °C
(1)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q7
17.3 You can use the graph opposite to find out how much Lethna has to pay for the units
ofelectricity she has used.
Lethna pays at one rate for the first 100 units of electricity she uses.
She pays at a different rate for all the other units of electricity she uses.
Lethna uses a total of 900 units of electricity.
Work out how much she must pay.
£.........................................................
(Total for Question 5 is 3 marks)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q5
17.4 Water is leaking out of two containers.
The water started to leak out of the containers at the same time.
The straight line P shows information about the amount of water, in litres, in container P.
The straight line Q shows information about the amount of water, in litres, in container Q.
(a) Work out the gradient of line P.
(2)
One container will become empty first.
(b) (i) Which container?
You must explain your answer.
(ii) How much water is then left in the other container?
............................... litres
(2)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q6
*17.5 You can use this graph to convert between litres and gallons.
Jack buys 8 gallons of diesel.He pays £52.
Francoise buys 40 litres of diesel.She pays £58.
Who got the better value for their money, Jack or Francoise?
You must show your working.
(Total for Question 4 is 3 marks)
November 2013 – Unit 1 (Modular) – Higher – Calculator – Q4
*18.1
ABC is parallel to DEF.
EBP is a straight line.
AB = EB.
Angle PBC = 40°.
Angle AED= x°.
Work out the value of x.
Give a reason for each stage of your working.
(5)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q10
19.1 The interior angle of a regular polygon is 160°.
(i) Write down the size of an exterior angle of the polygon.
(ii) Work out the number of sides of the polygon.
(Total for Question 6 is 3 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q6
19.2
The diagram shows 3 sides of a regular polygon.
Each interior angle of the regular polygon is 140°.
Work out the number of sides of the regular polygon.
(Total for Question 6 is 3 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q6
19.3 The diagram shows a regular hexagon and a regular octagon.
x
Find the size of the angle marked x.
You must show all the stages in your working.
Give the reasons for your answer.
(Total for Question 4 is 6 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q4
19.5
ABCDE is a regular pentagon.
ABP is an equilateral triangle.
Work out the size of angle x.
.............................................. °
(Total for Question 8 is 4 marks)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q8
20.1 Jake makes a picture frame from 4 identical pieces of card.
Each piece of card is in the shape of a trapezium.
The outer edge of the frame is a square of side 12 cm.
The inner edge of the frame is a square of side 8 cm.
Work out the area of each piece of card.
.............................................................. cm2
(Total for Question 16 is 4 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q4
20.2 A piece of card is in the shape of a trapezium.
A hole is cut in the card.
The hole is in the shape of a trapezium.
Work out the area of the shaded region.
.............................................................. cm2
(Total for Question 7 is 3 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q7
20.3 Janice cuts a triangle from a rectangular piece of metal.
She uses the rest of the metal to make a name badge.
The rectangle has length 6 cm and width 3 cm.
The right-angled triangle has base 2 cm and height 3 cm.
Work out the area of the name badge.
20.4
(Total for Question 10 is 4 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q10
The diagram shows the plan of the floor of Mrs Phillips’ living room.
Mrs Phillips is going to cover the floor with floor boards.
One pack of floor boards will cover 2.5 m2.
How many packs of floor boards does she need?
You must show your working.
(4)
June 2011 – Unit 2 (Modular) – Higher – Non-Calculator - Q6
20.5
The diagram shows a wall in Neil’s house.
Neil is going to cover the wall completely with tiles.
Each tile has a width of 30 cm and a height of 40 cm.
The tiles are sold in packs.
There are 6 tiles in each pack.
Each pack costs £15
Work out the least amount of money Neil needs to pay for the tiles.
You must show all your working.
£ .............................................
(Total for Question 6 is 4 marks)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
20.6
Mrs Kunal’s garden is in the shape of a rectangle.
Part of the garden is a patio in the shape of a triangle.
The rest of the garden is grass.
Mrs Kunal wants to spread fertiliser over all her grass.
One box of fertiliser is enough for 32 m2 of grass.
How many boxes of fertiliser will she need?
You must show your working.
(Total for Question 8 is 4 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q8
*20.7 Amy has a field in the shape of a trapezium.
200 m
Diagram NOT
accurately drawn
125 m
100 m
275 m
She wants to sell the field.
Farmer Boyce offers her £1 per m²
Farmer Giles offers her £24 000
Which is the better offer?
You must show all your working.
(Total for Question 7 is 4 marks)
Practice Paper Set A – Unit 2 (Modular) – Higher – Non-calculator – Q7
*20.8
Kevin wants to tile two walls in his bathroom.
3.6 m
1.8 m
2.4 m
Tile
12 cm
15 cm
One wall is a rectangle with length 3.6 m by 2.4 m.
The other wall is a rectangle with length 2.1 m by 2.4 m.
The tiles that Kevin wants to use are 12 cm wide and 15 cm high.
There are 40 tiles in each box.
How many boxes of tiles does Kevin need to buy?
(Total for Question 6 is 6 marks)
Practice Paper Set B – Unit 2 (Modular) – Higher – Non-calculator – Q6
20.9 (b) Change 4.5 km2 to m2.
.............................................. m2
(2)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q9
21.
The diagram shows the region inside a running track.
This region is in the shape of a rectangle with a semi-circle at both ends.
The rectangle has a length of 105 m.
It has a width of 64 m.
The semi-circles each have a diameter of 64 m.
The groundsman is going to cover this region with grass seed.
One sack of grass seed will cover 250 m2.
How many sacks of grass seed does the groundsman need?
You must show all your working.
(Total for Question 9 is 4 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q9
22.1
Calculate the length of AB.
Give your answer correct to 1 decimal place.
............................................. cm
(Total for Question 7 is 3 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q7
22.2 The diagram shows the marking on a school playing field.
The diagram shows a rectangle and its diagonals.
Work out the total length of the four sides of the rectangle and its diagonals.
(Total for Question 9 is 5 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q9
*23.1 Marc drives a truck.
The truck pulls a container.
The container is a cuboid 10 m by 4 m by 5 m.
Diagram NOT
accurately drawn
Marc fills the container with boxes.
Each box is a cuboid 50 cm by 40 cm by 20 cm.
Show that Marc can put no more than 5000 boxes into the container.
(Total for Question 4 is 4 marks)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q4
23.2 The diagram shows a prism.
Work out the volume of the prism.
........................................cm3
(Total for Question 8 is 4 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q8
23.3
Work out the total surface area of this triangular prism.
(Total for Question 5 is 4 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q5
23.4 This diagram, drawn on a centimetre grid, is an accurate net of a triangular prism.
Work out the volume of the prism.
(Total for Question 7 is 4 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q7
23.5 The diagram shows an L-shaped prism.
Calculate the volume of the prism.
............................................. cm3
(Total for Question 9 is 3 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q9
23.6
Terry fills a carton with boxes.
Each box is a cube of side 10 cm.
The carton is a cuboid with
length 60 cm
width 50 cm
height 30 cm
Work out the number of boxes Terry needs to fill one carton completely.
(Total for Question 7 is 3 marks)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q7
23.7
Work out the volume of the triangular prism.
.............................................. cm3
(Total for Question 9 is 2 marks)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q9
23.8 Here is the cross section of a steel girder.
The cross section has two lines of symmetry.
The girder is a prism.
The length of the girder is 200 cm.
Work out the volume of the girder.
.............................................. cm3
(Total for Question 11 is 5 marks)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q11
24.1 The diagram shows an accurate scale drawing of two towns, Middleton and Newtown.
Scale: 1 cm to 2 km
A new shopping centre is going to be built.
The shopping centre will be
less than 12 km from Middleton and
less than 15 km from Newtown.
On the diagram, shade the region where the shopping centre can be built.
(Total for Question 6 is 3 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q6
24.2 The diagram represents a triangular garden ABC.
The scale of the diagram is 1 cm represents 1 m.
A tree is to be planted in the garden so that it is
nearer to AB than to AC,
within 5 m of point A.
On the diagram, shade the region where the tree may be planted.
B
A
C
(Total 3 marks)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q7
24.3 Here is a scale drawing of Gilda’s garden.
Scale: 1 cm represents 1 m
Gilda is going to plant an elm tree in the garden.
She must plant the elm tree at least 4 metres from the oak tree.
On the diagram, show by shading the region where Gilda can plant the elm tree.
(Total for Question 3 is 2 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q3
24.4 The map shows the positions of two schools, Alford and Bancroft.
Scale 1 cm represents 1 km
A new school is going to be built.
The new school will be less than 5 kilometres from Alford.
It will be nearer to Bancroft than to Alford.
Shade the region on the map where the new school can be built.
(Total for Question 7 is 3 marks)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q7
25.1
Caroline is driving her car in France.
She sees this road sign.
Caroline is going to Rennes on the N12
She stops driving 10 miles from the road sign.
Work out how much further Caroline has to drive to get to Rennes
..............................................................
(Total for Question 7 is 3 marks)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q7
25.2 Here is a list of ingredients for making apple crumble for 2 people.
Apple Crumble
for 2 people
10 ounces apples
4 ounces flour
2 ounces sugar
1 ounce butter
1 tablespoon water
1 teaspoon baking powder
1 ounce = 28 grams
1 tablespoon = 15 ml
1 teaspoon = 5 ml
Anne is going to make apple crumble for 5 people.
(a) Work out how much flour she needs.
Give your answer in grams.
............................................. grams
(3)
David is making an apple crumble.
He uses 140 grams of butter.
(b) Work out how many people he is making apple crumble for.
(2)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q2
25.3. Jonty is going to completely fill an empty tank with water.
The tank holds 2 m3.
How many litres of water does he need?
……………………. litres
(Total for Question 8 is 3 marks)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q8
*25.4 Rodney bought some old railway track at an auction.
Each piece of track was 20 metres long.
Each piece of track weighed 40 kg per metre length.
Rodney has a lorry that can carry a maximum of 45 tonnes.
What is the maximum number of railway tracks that Rodney can fit onto the lorry?
(Total for Question 10 is 6 marks)
Practice Paper Set B – Unit 2 (Modular) – Higher – Non-Calculator – Q10
25.5 Sam has a swimming pool.
There are 60 000 litres of water in the swimming pool.
Sam wants to put chlorine powder in the water.
She needs 0.75 mg of chlorine powder for each litre of water.
Work out the total amount of chlorine powder Sam needs.
Give your answer in grams.
........................................ g
(Total for Question 11 is 3 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q11
26.1 The diagram shows the position of town A.
Town B is 64 km from town A on a bearing of 070°.
Mark the position of town B, with a cross (×).
Use a scale of 1 cm represents 10 km.
(Total for Question 5 is 2 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q5
26.2
N
A
Diagram NOT
accurately drawn
63º
138º
P
B
Work out the bearing of
(i)
B from P,
…………………º
(ii)
P from A.
………………….º
(Total for Question 7 is 4 marks)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q7
26.3 The diagram shows the position of two ports, P and Q.
A ship sails from port P to port Q.
Scale: 1 cm represents 20 km
(a)
Find the bearing of port P from port Q
(1)
(b)
Work out the real distance between port P and port Q.
Use the scale 1 cm represents 20 km.
.................................. km(2)
Port R is 120 km on a bearing of 120 from port Q.
(c)
On the diagram, mark port R with a cross ().
Label it R.
(2)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q3
26.4 The diagram shows the position of two boats, B and C.
Boat T is on a bearing of 060° from boat B.
Boat T is on a bearing of 285° from boat C.
In the space above, draw an accurate diagram to show the position of boat T.
Mark the position of boat T with a cross (×).
Label it T.
(Total for Question 6 is 3 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q6
27.1
Mr Smith drives 24 miles to work.
On Monday his journey to work takes 30 minutes.
On Tuesday the average speed of his journey to work is 56 km/h.
Did Mr Smith drive more quickly to work on Monday or Tuesday?
You must show all your working.
(4)
June 2011 – Unit 2 (Modular) – Higher –Non- Calculator – Q9
27.2 A plane takes 30 seconds to fly a distance of 8 kilometres.
Work out the average speed of the plane, in miles per hour.
.............................................................. miles per hour
(Total for Question 9 is 3 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q9
*27.3 Lisa cycles to work.
The travel graph shows information about her journey to work on Tuesday.
Martin also cycles to work.
On Tuesday his average speed was 16 km per hour.
Who has the greater average speed, Lisa or Martin?
You must show all your working.
(Total for Question 9 is 4 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q9
28.1 Dishwasher tablets are sold in two sizes of box.
A small box contains 15 tablets and costs £3.95
A large box contains 22 tablets and costs £6.15
*(a) Which size of box gives the better value for money?
You must show all your working. (4)
The weight of the large box is 357 grams, to the nearest gram.
(b) (i) What is the minimum possible weight of the box?
........................................ grams
(ii) What is the maximum possible weight of the box?
........................................ grams (2)
November 2011 – Unit 1 (Modular) – Higher – Calculator – Q6
28.2 Sonia measures the length of her pencil case as 15cm to the nearest cm.
(a)
Write down the greatest length this could be.
………….………….cm
(1)
(b)
Write down the least length this could be.
……………………..
(1)
Practice Paper Set A – Unit 1 (Modular) – Higher – Calculator – Q8
28.3 A piece of wood has a length of 65 centimetres to the nearest centimetre.
(a) What is the least possible length of the piece of wood?
.............................................. cm
(1)
(b) What is the greatest possible length of the piece of wood?
.............................................. cm
(1)
March 2013 – Unit 1 (Modular) – Higher – Calculator – Q7
29.1 Gulam and Alexi measured the heights of some wild grasses.
Here are their results
Height (h cm)
(a)
Frequency
0h5
3
5  h  10
6
10  h  15
5
15  h  20
7
20  h  25
3
25  h  30
1
On the grid below draw a frequency polygon to show this information.
10
8
frequency
6
4
2
0
0
5
10
15
height (cm)
20
25
30
(2)
(b)
In which group does the median height lie?
…………………………
(1)
Practice Paper Set C – Unit 1 (Modular) – Higher – Calculator – Q8
29.2 Helen went on 35 flights in a hot air balloon last year.
The table gives some information about the length of time, t minutes, of each flight.
Length of time (t minutes)
Frequency
0 <t ≤ 10
6
10 <t ≤ 20
9
20 <t ≤ 30
8
30 <t ≤ 40
7
40 <t ≤ 50
5
On the grid below, draw a frequency polygon for this information.
(Total for Question 5 is 2 marks)
June 2013 – Unit 1 (Modular) – Higher – Calculator – Q5
31.1 The table gives information about the speeds of 75 cars on a road.
Speed (s km/h)
Frequency
30 s < 40
7
40 s < 50
22
50 s < 60
34
60 s < 70
12
Work out an estimate for the mean speed.
....................................................... km/h(4)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q6
31.2 Faisel weighed 50 pumpkins.
The grouped frequency table gives some information about the weights of the pumpkins.
Weight (w kilograms)
Frequency
0 <w 4
11
4<w 8
23
8<w  12
14
12<w  16
2
Work out an estimate for the mean weight.
............................................. kg
(4)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q3
31.3
The table shows information about midday temperatures.
Temperature (t °C)
10 t <15
15 t <20
20 t <25
25 t <30
30 t <35
35 t <40
Number of days
6
4
24
44
10
4
(a) Write down the modal class interval.
(1)
(b) Work out an estimate for the mean midday temperature.
Give your answer correct to 3 significant figures
.............................................................. °C
(4)
(c) On the grid opposite, draw a cumulative frequency graph for the information from the table
about the midday temperatures.[Grade B]
d) Find estimates for the median and the interquartile range of these midday temperatures.
[Grade B]
Median .............................................................. °C
Interquartile range .............................................................. °C
(3)
June 2011 – Unit 1 (Modular) – Higher – Calculator – Q8
32.1 23 girls have a mean height of 153 cm.
17 boys have a mean height of 165 cm.
Work out the mean height of all 40 children.
.............................................................. cm (3)
June 2012 – Unit 1 (Modular)– Higher – Calculator – Q8
32.2 5 female giraffes have a mean weight of x kg.
7 male giraffes have a mean weight of y kg.
Write down an expression, in terms of x and y, for the mean weight of all 12 giraffes.
(Total for Question 10 is 2 marks)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q10
32.3 Susie has to deliver some packages and some parcels.
The total number of packages is 4 times the number of parcels.
The total number of packages and parcels is 40
Each parcel has a weight of 1.5 kg.
The total weight of the packages and parcels is 37.6 kg.
Each of the packages has the same weight.
Work out the weight of each package.
(Total for Question 10 is 4 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q10
32.4 Daniela works in a shop.
Daniela served 50 customers in the morning.
She served 75 customers in the afternoon.
The mean time to serve 50 customers in the morning was 48.7 seconds.
The mean time to serve all 125 customers was 50.2 seconds.
(a) Work out the mean time to serve the 75 customers in the afternoon.
.............................................................. seconds (3)
For the 75 customers served in the afternoon
the least time was 18 seconds
the greatest time was 96 seconds
the median time was 56 seconds
the lower quartile was 32 seconds
the upper quartile was 72 seconds
(b) On the grid, draw a box plot for this information.
[Grade B]
(3)
March 2012 – Unit 1 (Modular)– Higher – Calculator - Q10
32.5 The table gives information about the time it took each of 80 children to do a jigsaw
puzzle.
Number of children
Mean time (minutes)
32
32.4
Boys
48
Girls
Work out the mean time for all 80 children.
28.4
.............................................. minutes
(Total for Question 10 is 3 marks)
November 2013 – Unit 1 (Modular) – Higher – Calculator – Q10
*33.1 Zoe recorded the heart rates, in beats per minute, of each of 15 people.
Zoe then asked the 15 people to walk up some stairs.
She recorded their heart rates again.
She showed her results in a back-to-back stem and leaf diagram.
Compare the heart rates of the people before they walked up the stairswith their heart rates
after they walked up the stairs.
(Total for Question 4 is 6 marks)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q4
33.2 Jamal plays 15 games of ten-pin bowling.
Here are his scores.
72
59
75
66
79
75
66
63
89
76
65
79
77
71
83
(a) Draw an ordered stem and leaf diagram to show Jamal’s scores.
(3)
Gill plays 15 games of ten-pin bowling.
The table gives some information about her scores.
Highest score
95
Lowest score
75
Mean score
80
*(b) Compare the distribution of Jamal’s scores and the distribution of Gill’s scores.
(5)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q5
33.3
There are 25 students in a class.
12 of the students are girls.
Here are the heights, in cm, of the 12 girls.
160
173
148
154
152
164
179
164
162
174
168
170
(a) Show this information in an ordered stem and leaf diagram.
(3)
There are 13 boys in the class.
Here are the heights, in cm, of the 13 boys.
157
159
162
166
168
169
170
173
174
176
176
181
184
* (b) Compare the heights of the boys with the heights of the girls. (3)
June 2011 – Unit 1 (Modular)– Higher – Calculator – Q4
34.1 The probability that a seed will grow into a flower is 0.85
Loren plants 800 seeds.
Work out an estimate for the number of these seeds that will grow into flowers.
(Total for Question 5 is 2 marks)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q5
34.2 Here is a four-sided spinner.
The sides of the spinner are labelled A, B, C and D.
The table shows the probability that the spinner will land on A or on B or on D.
Letter
Probability
A
B
0.12
0.39
Amber spins the spinner once.
(a) Work out the probability that the spinner will land on C.
C
D
0.18
(2)
Lucy is going to spin the spinner 50 times.
(b) Work out an estimate for the number of times the spinner will land on A. (2)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q2
34.3 Denzil has a 4-sided spinner.
The sides of the spinner are numbered 1, 2, 3 and 4
The spinner is biased.
The table shows each of the probabilities that the spinner will land on 1, on 3 and on 4
The probability that the spinner will land on 3 is x.
Number
Probability
1
0.3
2
3
4
x
0.1
(a) Find an expression, in terms of x, for the probability that the spinner will land on 2.
Give your answer in its simplest form.
(2)
Denzil spins the spinner 300 times.
(b) Write down an expression, in terms of x, for the number of times the spinner is likely to
land on 3.
(1)
June 2011 – Unit 1 (Modular) – Higher – Calculator – Q5
34.4 The probability that a pea plant will grow from a seed is 93%.
Sarah plants 800 seeds.
Work out an estimate for the number of seeds that will grow into pea plants.
(Total for Question 2 is 2 marks)
March 2013 – Unit 1 (Modular) – Higher – Calculator – Q2
Grade B questions
1.1
Jozef invests £1700 for 2 years at 4% per annum compound interest.
Work out the value of his investment at the end of 2 years.
£ .............................................
(Total for Question 11 is 3 marks)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q11
1.2
Danny bought a car for £10 000
The value of the car depreciated by 20% in the first year.
Then the value of the car depreciated by 10% in the second year.
Work out the value of Danny’s car at the end of two years.
(Total for Question 11 is 3 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q11
1.3
Neil invested £500 on 1st January 2000 at a fixed compound interest rate of R% each year.
The value V, in pounds, of this investment after n years is given by the formula
V = 500 × (1.025)n
(a) Write down the value of R.
(1)
(b) Use your calculator to find the value of Neil’s investment at the end of 12 years.
£ .............................................
(2)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q16
1.4
Charlie invests £1200 at 3.5% per annum compound interest.
Work out the value of Charlie’s investment after 3 years.
£ ..............................................................(3)
June 2011 – Unit 1 (Modular)– Higher – Calculator – Q7
1.5
Aminata invested £2500 for n years in a savings account.
She was paid 3% per annum compound interest.
At the end of n years, Aminata has £2813.77 in the savings account.
Work out the value of n.
(Total for Question 13 is 2 marks)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q13
1.6
Jodi bought a car for £12 000
She bought the car 3 years ago.
The car depreciated at a rate of 10% each year.
(a)
How much is the car worth now?
(3)
Mia also bought a car for £12 000
Her car also depreciated at 10% a year.
(b)
After how many years will her car be worth £6000?
…………….. years
(3)
Practice Paper Set B – Unit 1 (Modular) – Higher – Calculator – Q9
*1.7
Jim buys 6 trays of Cola for £9.99 a tray.
Each tray holds 24 cans of Cola.
Jim goes to the school fete to sell his Cola.
He sells 75 cans at 80p each.
He gives 10 cans to his friends.
He sells the rest at 50p each.
24 cans
£9.99 a tray
What is Jim’s percentage profit or loss?
Give your answer to 1 decimal place.
(Total for Question 9 is 5 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q9
*1.8
Here are two schemes for investing £2500 for 2 years.
Scheme A
gives 4% simple interest each year.
Scheme B
gives 3.9% compound interest each year.
Which scheme gives the most total interest over 2 years?
You must show all your working.
(Total for Question 13 is 4 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q13
1.9
Martin bought a computer for £1200
At the end of each year the value of the computer is depreciated by 20%.
After how many years will the value of the computer be £491.52?
You must show your working.
(Total for Question 11 is 3 marks)
March 2013 – Unit 1 (Modular) – Higher – Calculator – Q11
1.10 Becky buys a new car for £20 000.
The value of this car will depreciate
by 15% at the end of the first year
then by 10% at the end of every year after the first year.
After how many years will the car have a value of less than £15 000?
You must show all your working.
(Total for Question 10 is 4 marks)
June 2013 – Unit 1 (Modular) – Higher – Calculator – Q10
*1.11 Ella wants to invest £6000 in a savings account for 2 years.
She finds information about savings accounts at two different banks.
Northway Bank
Portland Bank
Compound interest
Compound interest
of
of
3.8% per annum
5% per annum in year 1
3.2% per annum in year 2
Ella wants to choose the bank that pays the greater total amount of interest for
the 2 years.
Which bank should she choose?
You must show all your working.
(Total for Question 15 is 4 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q2
2.1
Mr and Mrs Adams sold their house for £168 000.
They made a profit of 12% on the price they paid for the house.
Calculate how much they paid for the house.
£ .............................................
(Total for Question 13 is 3 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q13
2.2
A holiday costs £840 plus 20% VAT.
(a) Calculate the total cost of the holiday.
(3)
In a sale, normal prices are reduced by 45%.
The sale price of another holiday is £462
(b) Work out the normal price of this holiday.
(3)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q16
2.3
Sally buys a car for £4900
She saves 30% on the original price of the car.
£ ……………..
(Total for Question 14 is 3 marks)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q14
What was the original price of the car?
2.4
(a)
Ben bought a car for £12 000.
Each year the car depreciated by 10%.
Work out its value two years after he bought it.
(3)
(b)
Susie also bought a car two years ago.
It too depreciated by 10% each year.
The car is now worth £8100
Work out the original cost of Susie’s car.
(3)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q12
3.1
(a) Write 125 000 in standard form.
(1)
–4
(b) Write 8 × 10 as an ordinary number.
(1)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q10
3.2
(a) Write 60 800 000 in standard form.
(1)
(b) Write 1.7 × 10–4 as an ordinary number.
(1)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q11
3.3
(a) Write 55 000 in standard form.
(1)
(b) Work out (3.6 × 109) × (5 × 10–4)
Write your answer as an ordinary number.
(2)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q17
3.4
Work out (2.5 × 109)  (5 × 103).
Give your answer in standard form.
(Total for Question 13 is 2 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q13
3.5
3.6
3.7
An object is travelling at a speed of 2650 metres per second.
How many seconds will the object take to travel a distance of 3.45 × 1010 metres?
Give your answer in standard form, correct to 2 significant figures.
(Total for Question 12 is 3 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q12
Work out 5.6 × 108 × 3 × 10–5
Give your answer in standard form.
(Total for Question 14 is 2 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q14
Light travels at 186 000 miles per second.
A light year is the distance light can travel in a year of 365 14 days.
How many miles are there in one light year?
Give your answer in standard form.
………………………. miles
(Total for Question 10 is 3 marks)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q10
3.8
A spaceship travelled for 6  102 hours at a speed of 8  104 km/h.
(a)
Calculate the distance travelled by the spaceship.
Give your answer in standard form.
……………………. km(3)
One month an aircraft travelled 2.4  105 km.
The next month the aircraft travelled 3.7  104 km.
(b)
Calculate the total distance travelled by the aircraft in the two months.
Give your answer as an ordinary number.
………………… km
(2)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q10
3.9
Write these numbers in order of size.
Start with the smallest number.
–2.5 × 10–4
0.0052 × 106
(Total for Question 12 is 3 marks)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q12
4.2 × 105
30 × 10–6
13 × 104
4 109  3.2 107
1.6 106
Give your answer in standard form.
3.10 Work out
(Total for Question 16 is 2 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q16
4.1
(a) Simplify m0
(1)
6 –1 3
(b) Simplify (2x y )
(2)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q12
4.2
(a) Expand 3(x + 2)
3
(2)
2
(b) Factorise completely 12x y – 18 xy
(2)
(c) Expand and simplify (2x – 3)(x + 4)
4 3
(2)
3 2
(d) Simplify 5x y × 2x y
(2)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q11
4.3
(x + 5)(x – 8)
(a) Expand and simplify
(b) Factorise
(2)
x2 – 16
(1)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q12
4.4
(a) Factorise fully 20w2y + 24wy3
(2)
(b) Factorise m2 + 3m – 40
(2)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q10
4.5
(a) Factorise x2 + 5x + 4
(2)
(3x – 1)(2x + 5)
(b) Expand and simplify
(2)
(c) Write as a single fraction
1
1
1
+
–
2x
5x
3x
[Grade A]
(2)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q14
4.6
Simplify fully
(x + 5)2 – (x – 5)2
(Total for Question 12 is 2 marks)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q12
4.7
(a) Factorise fully
6ab + 10ac
(2)
(b) Expand and simplify
(x – 5)(x + 7)
(2)
2m 2t 6
m 4t 2
Give your answer in its simplest form.
(c) Simplify
(2)
(d) Factorise
y2 – 16
(1)
(e) Simplify
(h2)–3
(1)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q12
5.1
(a) Make t the subject of the formula
2(a + t) = 5t + 7
t = ......................................................
(3)
(b) Solve the simultaneous equations
3x – 4y = 8
9x + 5y = –1.5
x = ........................................
y = ........................................
(3)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q16
5.2
Solve the simultaneous equations.
3x + 2y = 8
6x – 5y = 34
x = ..............................................
y = ..............................................
.(Total for Question 15 is 3 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q15
5.3
Bob and Sallybuy some fruit.
Bob buys
5 oranges and 2 bananas for £2.00
Sally buys
2 oranges and 3 bananas for £1.35
Work out the cost of
(i)
one orange
(ii)
one banana
(Total for Question 14 is 5 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q14
5.4
Solve
5x + 2y = 8
2x – 4y = 8
(Total for Question 16 is 3 marks)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q16
5.5
Solve the simultaneous equations
3x – 2y = 7
7x + 2y = 13
(Total for Question 14 is 3 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q14
5.6
Solve the simultaneous equations
3x + 10y = 7
x – 4y = 6
(Total for Question 13 is 3 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q13
5.7
Solve the simultaneous equations
4x – 5y = 33
3x + y
=1
(Total for Question 14 is 3 marks)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q14
6.1
(a) Solve 7(x – 4) = 35
–3 n < 4
n is an integer.
(b) Write down the possible values of n.
(2)
(2)
(c) Solve the inequality 5x + 3 > 3x – 11
(2)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q4
7.1
Make m the subject of the formula
6m2 = k
m = .............................................
(Total for Question 15 is 2 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q15
7.2
(a) Make t the subject of the formula
2(a + t) = 5t + 7
t = ......................................................
(3)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q16a
7.3
Make t the subject of the formula 3t + b = a2
t = ..............................................
(Total for Question 7 is 2 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q7
7.4
The diagram shows a solid triangular prism.
All the measurements are in centimetres.
The volume of the prism is V cm3.
Find a formula for V in terms of x.
Give your answer in simplified form.
(Total for Question 11 is 3 marks)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q11
7.5
(a) Solve 4(y – 7) = 13.
y = ..............................................
(2)
(b) Make t the subject of the formula P = 4t – 3.
(2)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q10
8.1
(a) On the grid, draw the graph of y = 4x + 2 from x = –1 to x = 3
(b) (i) Write down the equation of a straight line that is parallel to y = 4x + 2
(ii) Write down the gradient of a straight line that is perpendicular to y = 4x + 2(2)
June 2011 – Unit 2 (Modular)– Higher –Non- Calculator – Q5
8.2
This graph can be used to convert between degrees Celsius (C) and degreesFahrenheit (F).
Find the values of m and k such that
F = mC + k
m = ..............................................................
k = ..............................................................
(3)
June 2011 – Unit 1 (Modular)– Higher – Calculator – Q9
8.3
Here are the graphs of 6 straight lines.
Match each of the graphs A, B, C, D, E and F to the equations in the table.
Equation
y=
1
x+2
2
1
y = 2x –
y=– x+2
2
2
y = –2x – 2
y = 2x + 2
1
y=– x–2
2
Graph
(Total for Question 12 is 3 marks)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q12
8.4
Here are the equations of 5 straight lines.
P
y = 2x + 5
Q
1
S
y= – x+6
T
2
y = – 2x + 5
1
y= x+1
2
R
y= x+5
Write down the letter of the line that is parallel to
y=x–5
Write down the letter of the line that is perpendicular to
y = 2x – 1
Find the coordinates of the point where the line y = 2x + 5 cuts the
(i) y axis,
(ii)x axis.
(a)
(b)
(c)
(1)
(1)
(2)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q13
9.1
(a)
y = x2 – 3x – 1
Complete the table of values for
–2
x
y
–1
0
1
3
–1
–3
2
3
4
–1
(2)
2
On the grid draw the graph of y = x – 3x – 1 for values of x from –2 to 4
y
(b)
10
8
6
4
2
x
–3
–2
–1
O
1
2
3
4
–2
(c)
Solve the equation
–4
x2 – 3x = 4
(2)
(2)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q11
9.2
On the grid, draw the graph of y = x2 – 2x – 5 for –1 x  5
(Total for Question 12 is 4 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q12
9.3
(a) Complete this table of values for y = x3 + 2x – 1
x
y
–2
–1
–4
0
1
2
11
(2)
(b) On the grid, draw the graph of y = x3 + 2x – 1
(2)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q12
9.4
(a) Complete the table of values for y = x2 – 5x + 3.
x
y
–1
0
1
3
–1
2
3
–3
4
5
3
(2)
(b) On the grid below, draw the graph of y = x2 – 5x + 3 for values of x from x = –1
to x = 5.
(2)
2
(c) Find estimates of the solutions of the equation x – 5x + 3 = 0.
x = ..............................................
or x = ..............................................
(2)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q9
10.1 The diagram shows a cuboid drawn on a 3-D coordinate grid.
The vertex N of the cuboid has coordinates (6, 2, 4).
(a) What are the coordinates of the vertex R?
( ................ , ................ , ................ )
(1)
(b) What are the coordinates of the midpoint of the line segment RN ?
( ................ , ................ , ................ )
(2)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q13
10.2
The diagram shows a cuboid drawn on a 3-D grid.
Three of the vertices of the cuboid are
P (3, 2, 0)
Q (3, 0, 0)
R (3, 0, 4)
(a) Label the vertex Q with a cross (×).
(1)
The vertex S is shown on the diagram.
(b) Write down the coordinates of the vertex S.
(................................ , ................................. , ................................)
(1)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q12
10.3 AB is a line segment.
A is the point (2, 5, 6).
The midpoint of the line AB has coordinates (–1, –4, 2).
Find the coordinates of point B.
(........................ , ........................ , ........................ )
(Total for Question 10 is 2 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q10
10.4 The diagram shows a cuboid on a 3-D grid.
The coordinates of the vertex M are (5, 3, 2).
Work out the coordinates of the midpoint of LN.
(.................. , .................. , ..................)
(Total for Question 14 is 2 marks)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q14
11.1
The diagram shows a regular decagon.
Work out the size of angle x.
(4)
June 2011 – Unit 2 (Modular)– Higher –Non- Calculator – Q11
11.2
ABCDEFGH is a regular octagon.
PAE is a straight line.
Angle PAB = y°
Work out the value of y.
(Total for Question 9 is 4 marks)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q9
11.3
ABCDE and AFGCH are regular pentagons.
The two pentagons are the same size.
Work out the size of angle EAH.
You must show how you got your answer.
(Total for Question 10 is 4 marks)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q10
11.4
A, B, C and D are four vertices of a regular 10-sided polygon.
Angle BCX = 90°.
Work out the size of angle DCX.
(Total for Question 10 is 3 marks)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q10
*12.1
T and R are two points on a circle centre O.
PT and PR are the tangents to the circle from P.
Angle TPO = 20°.
Work out the size of angle TOR.
You must give reasons for each stage of your working.
(Total for Question 15 is 4 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q15
12.2
S and T are points on the circumference of a circle, centre O.
PT and PS are tangents.
Angle TPO = 24°.
Work out the size of angle SOT.
(3)
March 2012 – Unit 2 (Modular)– Higher – Non-Calculator – Q12
*12.3
A, B, C and D are points on the circumference of a circle.
EDF is a tangent to the circle.
AB = AD.
Angle ADE = 54°.
Work out the size of angle BCD.
You must give a reason for each stage in your working.
(Total for Question 20 is 5 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q20
B
*12.4
E
A
O
27°
C
Diagram NOT
accurately drawn
F
In the diagram ABC are points on the circle centre O.
Angle ACB = 27
FE is a tangent to the circle at point C.
(i)
Calculate the size of angle BAC.
Give reasons for your answer.
(ii)
Calculate the size of angle BCE.
Give reasons for your answer.
(Total for Question 15 is 4 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q15
*12.5
B
Diagram NOT
accurately drawn
35º
A
O
D
C
The diagram shows a circle, centre O.
AC is a diameter
Angle BAC = 35º
D is the point on AC such that angle BDA is a right angle
(a)
Work out the size of angle BCA. Give reasons for your answer.
(b)
Calculate the size of angle BOA. Give reasons for your answer.
(2)
(2)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q14
*12.6
A, B and C are three points on a circle.
DBE is a tangent to the circle.
AB is parallel to CD.
BC is a diameter.
Angle ABC = 27°.
Find the size of angle CDB.
Give reasons for your answer.
(Total for Question 14 is 4 marks)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q14
13.1
O
40
Diagram NOT
accurately drawn
9 cm
The diagram shows a sector of a circle centre O.
The radius of the circle is 9 cm.
The angle at the centre of the circle is 40.
Find the perimeter of the sector.
Give your answer correct to 2 decimal places.
…………………. cm
(Total for Question 16 is 4 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q16
14.1
Triangle A is reflected in the x-axis to give triangle B.
Triangle B is then reflected in the line x = 1 to give triangle C.
Describe fully the single transformation that maps triangle A onto triangle C.
(Total for Question 14 is 3 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q14
15.1
P
10 cm
Diagram NOT
accurately drawn
A
3 cm
2 cm
C
B
12 cm
Q
ACQ and BCP are straight lines.
AB is parallel to PQ.
AB = 2 cm.
AC = 3 cm.
CQ = 12 cm.
CP = 10 cm.
(a) Work out the length of PQ.
………….. cm
(2)
(b) Work out the length of BP.
…………… cm
(3)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q12
15.2 ABC is a triangle.
D is a point on AB and E is a point on AC.
DE is parallel to BC.
AD = 4 cm, DB = 6 cm, DE = 5 cm, AE = 5.8 cm.
Calculate the perimeter of the trapezium DBCE.
.............................................. cm
(Total for Question 13 is 4 marks)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q13
16.1 The diagram shows a right-angled triangle.
Angle ACB = 90°.
AB = 12.4 cm.
CB = 9.7 cm.
Work out the value of x.
Give your answer correct to 1 decimal place.
(Total for Question 13 is 3 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q13
16.2
ABCD is a parallelogram.
DC = 5 cm
Angle ADB = 36°
Calculate the length of AD.
Give your answer correct to 3 significant figures.
............................................. cm
(Total for Question 14 is 4 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q14
16.3 LMN is an equilateral triangle.
Work out the height of triangle LMN.
Give your answer correct to 3 significant figures.
.............................................. cm
(Total for Question 17 is 3 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q17
16.4 Here is an isosceles triangle.
10 cm
50°
Find the area of the triangle.
Give your answer correct to 3 significant figures.
………………. cm2
(Total for Question 13 is 6 marks)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q13
16.5 GHJ is a right-angled triangle.
(a) Calculate the length of GJ.
Give your answer correct to one decimal place.
.............................................. cm
(1)
LMN is a different right-angled triangle.
(b) Calculate the size of the angle marked x.
Give your answer correct to one decimal place.
..............................................°(3)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q10
16.6
DEF is a right-angled triangle.
DE = 86 mm.
EF = 37 mm.
Calculate the size of the angle marked y.
Give your answer correct to 1 decimal place.
(Total for Question 11 is 3 marks)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q11
17.1
Judy drives at an average speed of 80 km per hour for 2 hours 45 minutes.
Work out the number of miles Judy drives.
...........................miles
(Total for Question 16 is 3 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q16
17.2
Matt decides to make a bell.
He mixes copper and tin to make the metal for the bell.
No metal is gained or lost in the process.
He has 270 kg of copper and 0.01 m3 of tin.
The density of copper is 9000 kg per m3.
The density of tin is 7300 kg per m3.
Work out the density of the metal in the bell.
(Total for Question 12 is 6 marks)
Practice Paper Set C – Unit 2 (Modular) – Higher – Non-Calculator – Q12
17.3
A water trough is in the shape of a prism.
Hamish fills the trough completely.
Water leaks from the bottom of the trough at a constant rate.
2 hours later, the level of the water has fallen by 20 cm.
Water continues to leak from the trough at the same rate.
How many more minutes will it take for the trough to empty completely?
(Total for Question 11 is 6 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q11
17.4 The distance from Caxby to Drone is 45 miles.
The distance from Drone to Elton is 20 miles.
Colin drives from Caxby to Drone.
Then he drives from Drone to Elton.
Colin drives from Caxby to Drone at an average speed of 30 mph.
He drives from Drone to Elton at an average speed of 40 mph.
Work out Colin’s average speed for the whole journey from Caxby to Elton.
.............................................. mph
(Total for Question 11 is 3 marks)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q11
18.1 Nathan is doing a survey about DVDs.
He writes a questionnaire.
Nathan decides to hand out his questionnaire to the women who are inside a DVD store.
His sample is biased.
(a) Give two possible reasons why.
(2)
This is one of the questions on Nathan’s questionnaire.
(b) Write down two things wrong with this question.
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q9
18.2
The table below shows the population of each of three villages.
Village
Ashley
Brigby
Irton
Population
243
370
127
Mr Akhtar carries out a survey of the people living in these three villages.
He uses a sample stratified by village population.
There are 50 people from Brigby in his sample.
Work out the number of people from Irton in his sample.
(Total for Question 13 is 2 marks)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q13
18.3 Raul is the manager of a restaurant.
He wants to find out how often local people eat in a restaurant.
Raul is going to carry out a survey using a questionnaire.
(a) Design a suitable question for Raul to use on his questionnaire.
(2)
(b) The two-way table shows information about the ages of the customers in Raul’s
restaurant one evening.
Age (years)
Total
0–16
17–30
31–60
over 60
Male
8
10
17
20
55
Female
7
9
22
34
72
Total
15
19
39
54
127
Raul carries out his survey using only these customers.
He uses a sample of 50 of these customers stratified by gender and by age.
Calculate the number of males aged 17–30 in his sample.
(2)
Raul’s survey is biased.
(c) Give two possible reasons why.
(2)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q11
18.4 A factory makes 600 laptops.
Mrs Green is responsible for checking these laptops.
She is going to take a random sample of 80 of the laptops.
(a) Describe a method she could use to select the sample.
(1)
Mrs Green finds that 3 of the 80 laptops are faulty.
b) Work out an estimate for how many of the 600 laptops are faulty.
(2)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q11
18.5 There are N beads in a jar.
40 of these beads are black.
Julie takes at random a sample of 50 beads from the jar.
5 of the beads in her sample are black.
Work out an estimate for the value of N.
(2)
June 2012 – Unit 1 (Modular)– Higher – Calculator – Q11
18.6 The table gives information about the number of students at a school.
Year 9
Year 10
Year 11
Total
244
315
181
740
Priya is going to survey 60 of the students in the school.
She is going to use a sample stratified by year group.
(a) Work out the number of year 9, year 10 and year 11 students Priya should have in her
sample.
You must show all your working.
Year 9 .............................................
Year 10 .............................................
Year 11 .............................................(3)
Priya is going to use a random sample to select the students.
(b) (i) Explain what is meant by a random sample.
(ii) Describe how Priya could take a random sample.
(2)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q13
*18.7 A farmer wants to estimate the number of rabbits on his farm.
On Monday he catches 120 rabbits.
He puts a tag on each rabbit.
He then lets the rabbits run away.
On Tuesday the farmer catches 70 rabbits.
15 of these rabbits have a tag on them.
Work out an estimate for the total number of rabbits on the farm.
You must write down any assumptions you have made.
(Total for Question 14 is 4 marks)
November 2011 – Unit 1 (Modular)–Higher – Calculator – Q14
18.8 Simon is designing a questionnaire for people who visit his sports club.
He wants to find out how often people visit his sports club.
(a) Design a suitable question he could use.
(2)
Simon asks 10 of his friends who visit his sports club to do his questionnaire.
This may not be a suitable sample.
(b) Give one reason why.
(1)
There are 365 runners in Simon’s sports club.
The table gives information about these runners.
Age (in years)
Number of male runners
Number of female runners
10 – 19
35
36
20 – 29
52
48
30 – 39
45
32
40 – 49
37
29
50 – 69
20
31
Simon surveys the runners in his sports club.
He uses a sample of 50 runners stratified by gender and by age.
(c) Work out the number of male runners with an age 30 – 39 years he should have in his
sample.
(2)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q10
19.1 The table shows information about the lengths, in seconds, of 40 TV adverts.
Time (T seconds)
Frequency
10 <T 20
4
20 <T 30
7
30 <T 40
13
40 <T 50
12
4
50 <T 60
(a) Complete the cumulative frequency table for this information.
Time (T seconds)
10 <T 20
Cumulative
frequency
4
10 <T 30
10 <T 40
10 <T 50
10 <T 60
(1)
(b) On the grid, draw a cumulative frequency graph for your table.
(2)
(c) Use your graph to find an estimate for the median length of these TV adverts.
.............................................................. seconds
(1)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q7
19.2 The table shows some information about the weights, in grams, of 60 eggs.
Weight(wgrams)
Frequency
00<w300
0
30<w500
14
50<w600
16
60<w700
21
9
70<w100
(a) Calculate an estimate for the mean weight of an egg.
(b) Complete the cumulative frequency table.
Cumulative
Weight(wgrams)
frequency
0
0<w300
(4)
0<w500
0<w600
0<w700
0<w100
(1)
(c) On the grid, draw a cumulative frequency graph for your table
(2)
(d) Use your graph to find an estimate for the number of eggs with a weight greater than63 grams. (2)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q10
19.3 The cumulative frequency graph shows information about the heights of some
hollyhockplants.
(a) Find an estimate for the median height. ............................................................. cm (1)
(b) Work out an estimate for the interquartile range.............................................. cm
(2)
(c) Find an estimate for the number of hollyhock plants taller than 90 cm.
(2)
March 2012 – Unit 1 (Modular)–Higher – Calculator – Q8
19.4 The table gives some information about the weights of 60 babies.
Lowest
2.0 kg
Highest
6.5 kg
Lower quartile
2.8 kg
Upper quartile
4.2 kg
Median
3.0 kg
(a) Draw a box plot to show this information.
(2)
There are 60 babies.
(b) Work out an estimate for the number of these babies with a weight greater than 2.8 kg. (2)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q9
19.5 The cumulative frequency graph shows information about the speeds of 60 carson a
motorway one Sunday morning.
(a) Use the graph to find an estimate for the median speed.
....................... km/h(1)
The speed limit on this motorway is 130 km/h.
The traffic police say that more than 20% of cars travelling on the motorway break thespeed
limit.
(b) Comment on what the traffic police say.
(3)
For these 60 cars
the minimum speed was 97 km/h
and
the maximum speed was 138 km/h.
(c) Use the cumulative frequency graph and the information above to draw a box
plotshowing information about the speeds of the cars.
(3)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q9
19.6 Here are the ages, in years, of 15 women at West Ribble Tennis Club.
16, 18, 18, 20, 25, 25, 27, 28, 30, 35, 38, 42, 45, 46, 50
(a) On the grid, draw a box plot for this information.
(3)
The box plot below shows the distribution of the ages of the men atWest Ribble Tennis Club.
* (b) Use the box plots to compare the distributions of the ages of these women and
thedistributions of the ages of these men.
(2)
November 2011 – Unit 1 (Modular)–Higher – Calculator – Q10
19.7 Mrs Angus’s class did a maths test.
The cumulative frequency graph shows information about their marks.
(a) Use the cumulative frequency graph to find
(i) the median,
(ii) the interquartile range.
(3)
Mr Wilson’s class did the same maths test.
The box plot shows information about their marks.
*(b) Compare the interquartile range of the marks of Mr Wilson’s class with theinterquartile
range of the marks of Mrs Angus’s class.
(2)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q14
*19.8 There are two trays of plants in a greenhouse.
The first tray of plants was given fertiliser.
The second tray of plants was not given fertiliser.
On Monday the heights of the plants were measured in centimetres.
The boxes show some information about the heights of the plants.
Heights of the plants given fertiliser
22
29
30
35
37
40
44
48
48
54
56
59
66
72
47
Information about the heights of plants
not given fertiliser
Smallest
Largest
Median
18
64
44
Lower quartile
Upper quartile
26
47
Compare the distribution of the heights of the plants given fertiliser to
the distribution of the heights of the plants not given fertiliser.
(Total for Question 9 is 4 marks)
March 2013 – Unit 1 (Modular) – Higher – Calculator – Q9
19.9 Jodie picks all the apples from her 56 apple trees.
For each tree she records the total weight of its apples.
The table shows some information about these total weights in kg.
least weight
greatest weight
median
lower quartile
upper quartile
25
55
40
35
45
(a) Work out how many of Jodie’s apple trees have a total weight of apples of less than
45 kg.
(2)
(b) On the grid, draw a box plot for the information in the table.
(2)
Tom has 59 apple trees.
The box plot shows the distribution of the total weights of the apples Tom picks from
each of his apple trees.
*(c) Compare the distribution of the weights of apples Jodie picks with the distribution of
the weights of apples Tom picks.
(2)
June 2013 – Unit 1 (Modular) – Higher – Calculator – Q11
20.1 Mary plays a game of throwing a ball at a target.
The table shows information about the probability of each possible score.
Score
Probability
0
1
2
3
4
5
0.09
x
0.18
0.16
0.21
0.30
Mary is 3 times as likely to score 2 points than to score 1 point.
(a) Work out the value of x.
(3)
Mary plays the game twice.
(b) Work out the probability of Mary scoring a total of 8
(3)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q9
20.2 There are 4 banana smoothies and 3 apple smoothies in a box.
Jenny takes at random 1 smoothie from the box.
She writes down its flavour, and puts it back in the box.
Jenny then takes at random a second smoothie from the box.
(a) Complete the probability tree diagram.
(2)
(b) Work out the probability that both smoothies are apple flavour.(2)
November 2011 – Unit 1 (Modular)–Higher – Calculator – Q13
20.3 Martin and Luke are students in the same maths class.
The probability that Martin will bring a calculator to a lesson is 0.8
The probability that Luke will bring a calculator to a lesson is 0.6
(a) Complete the probability tree diagram.
(2)
(b) Work out the probability that both Martin and Luke will not bring a calculator to
alesson.
(2)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q11
20.4. In a newsagent’s shop, the probability that any customer buys a newspaper is 0.6
In the same shop, the probability that any customer buys a magazine is 0.3
(a) Complete the probability tree diagram.
(2)
(b) Work out the probability that a customer will buy either a newspaper or a magazinebut
not both.
(3)
March 2012 – Unit 1 (Modular)–Higher – Calculator – Q9
20.5
Sally has a fair 4-sided spinner numbered 1, 3, 5 and 7
and a fair 6-sided die.
7
5
1
3
6
35
He spins the spinner once and rolls the die once.
To get the score he adds the numbers together.
(a)
Work out the probability that the score will be 3
(2)
(b)
Work out the probability the score will be less than 5.
(3)
Practice Paper Set B – Unit 1 (Modular)–Higher – Calculator – Q13
Grade A questions
1.1
(a) Find the value of 50
(b) Find the value of 27
(1)
1
3
(c) Find the value of 2
(1)
–3
(1)
March 2012 – Unit 2 (Modular)– Higher – Non-Calculator – Q11
1.2
Write down the value of
(i) 70
(ii) 5–1
1
(iii) 9 2
(Total for Question 12 is 3 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q12
1
1.3
(a) Write down the value of 27 3
(b) Find the value of 25
1.4
1

2
(1)
(2)
June 2011 – Unit 2 (Modular)– Higher –Non- Calculator- Q15
Write down the value of
(i) 4–2
1
(ii) 64 3
(Total for Question 13 is 2 marks)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q13
1.5
(a)
Simplify
x0
(1)
(b)
Simplify
  32 
y 




4
(2)
(Total for Question 14 is 3 marks)
Practice Paper Set B – Unit 2 (Modular)– Higher – Non-Calculator – Q14
2.1
Express
̇ as a fraction in its simplest form.
(3)
March 2012 – Unit 2 (Modular)– Higher – Non-Calculator – Q14
 
2.2
Write the recurring decimal 0.0 2 5 as a fraction.
(Total for Question 13 is 3 marks)
Practice Paper Set B – Unit 2 (Modular)– Higher – Non-Calculator – Q13
3.1
Rationalise the denominator
3
(Total for Question 13 is 2 marks)
7
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q13
3.2
(a) Rationalise the denominator of
15
5
(1 + 3)2can be written in the form a + b3, where aandb are integers.
(2)
(b) Work out the value of a and the value of b.
(2)
March 2012 – Unit 2 (Modular)– Higher – Non-Calculator – Q16
3.3
3.4
(a) Express 5 27 in the form n 3 , where n is a positive integer.(2)
21
(b) Rationalise the denominator of
(2)
3
June 2011 – Unit 2 (Modular)– Higher –Non- Calculator – Q14
(a) Write down the value of 10–1.
(1)
2
(b) Find the value of 27 3 .
(2)
(c) Write
75 in the form k 3 , where k is an integer.
(2)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q17
3.5
The perimeter of a square is √120 cm.
Work out the area of the square.
Give your answer in its simplest form.
.............................................. cm2
(Total for Question 13 is 3 marks)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q13
5.1
y is directly proportional to x.
When x = 600, y = 10
(a) Find a formula for y in terms of x.
y = ........................................(3)
(b) Calculate the value of y when x = 540
y = ........................................(1)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q13
6.1
(a) Factorise
e2 – 100
(b) Factorise
2x2 – 7x – 15
(c) Simplify
( g  7)
( g  7) 3
(1)
(2)
9
(1)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q12
6.2
Solve 5x2 – 3x– 7 = 0
Give your solutions correct to 3 significant figures.
(Total for Question 19 is 3 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q19
6.3
Solve 3x² + 2x – 1 = 0
(Total for Question 19 is 3 marks)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q19
6.4
Solve 2x2 + 5x – 3 = 0
(Total for Question 20 is 3 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q20
6.5
Solve 5x2 + 6x – 2 = 0
Give your solutions correct to 2 decimal places.
(Total for Question 18 is 3 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q18
6.6
8.1
Solve, by factorising, the equation 8x2 –30x – 27 = 0.
[Grade A* due to “8”]
(Total for Question 20 is 3 marks)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q20
Prove that (n – 1)2 + n2 + (n + 1)2 = 3n2 + 2
(2)
June 2011 – Unit 2 (Modular)– Higher –Non- Calculator – Q12
*8.2
The diagram shows a pentagon.
All measurements are in centimetres.
Show that the area of this pentagon can be written as 5x2 + x – 6
(Total for Question 14 is 4 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q14
*8.3
The diagram shows a triangle inside a rectangle.
All measurements are given in centimetres.
Show that the total area, in cm2, of the shaded regions is 18x – 30
(4)
March 2012 – Unit 2 (Modular)– Higher – Non-Calculator – Q13
8.4
Make x the subject of
4x – 3 = 2(x + y)
x = ..............................................
(Total for Question 17 is 3 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q17
*9.1 Explain why any straight line that passes through the point (1, 2) must intersect the curvewith
equation x2 +y2 = 16 at two points.
y
5
(1,2)
x
–5
O
5
–5
(Total for Question 17 is 3 marks)
Practice Paper Set A – Unit 3 (Modular)– Higher – Calculator – Q17
9.2
Here are three graphs.
Here are four equations of graphs.
y = x3
y = x2 + 4
y=
1
x
y = 2x
Match each to the correct equation.
A and y= ..............................................
B and y= ..............................................
C and y= ..............................................
(Total for Question 14 is 3 marks)
March 2013 – Unit 1 (Modular) – Higher – Calculator – Q14
10.1 (a) Write down the equation of a straight line that is parallel to y = 5x + 6
(1)
(b) Find an equation of the line that is perpendicular to the line y = 5x + 6 and passesthrough
the point (–2, 5).
(3)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q13
10.2
In the diagram
A is the point (–2, 0)
B is the point (0, 4)
C is the point (5, –1)
Find an equation of the line that passes through C and is perpendicular to AB.
(Total for Question 16 is 4 marks)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q16
10.3 Find an equation of the straight line that is perpendicular to the straight line x + 2y = 5 and
that passes through the point (3, 7).
(Total for Question 17 is 4 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q17
10.4
A straight line, L, is perpendicular to the line with equation y = 1 – 3x.
The point with coordinates (6, 3) is on the line L.
Find an equation of the line L.
(3)
March 2012 – Unit 2 (Modular)– Higher – Non-Calculator – Q15
10.5
In the diagram,
the points A, B and C lie on the straight line y = 2x – 1
The coordinates of Aare (2, 3).
The coordinates of B are (5, 9).
Given that AC = 3AB, find the coordinates of C.
(Total for Question 18 is 3 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q2
11.1
(a)
-2 <x 1
x is an integer.
Write down all the possible values of x.
(2)
(b)
-2 <x 1
y> -2
x and y are integers.
y<x + 1
On the grid below mark with a cross (×), each of the six points which
satisfiesall these 3 inequalities.
y
5
4
3
2
1
-5
-4
-3
-2
-1
O
1
2
3
4
5
x
-1
-2
-3
-4
(3)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q11
11.2 (a) Given that
x is an integer such that –2 <x  3
yis an integer such that –1 y < 5
andy = x
write down the possible values of x.
(2)
(b) On the grid below, show by shading the region defined by the inequalities
y> 1
y < 2x – 2
y<6–x
x> 0
Mark this region with the letter R.
(4)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q14
11.3 On the grid below, show by shading, the region defined by the inequalities
x> –1
x + y< 6
y> 2
Mark this region with the letter R.
(Total for Question 12 is 4 marks)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q12
13.1
AC = 9.2 m
BC = 14.6 m
Angle ACB = 64°
(a) Calculate the area of the triangle ABC.
Give your answer correct to 3 significant figures.
............................................. m2(2)
(b) Calculate the length of AB.
Give your answer correct to 3 significant figures.
............................................. m(3)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q19
14.1 Ella is designing a glass in the shape of a cylinder.
1
The glass must hold a minimum of
litre of liquid.
2
The glass must have a diameter of 8 cm.
Calculate the minimum height of the glass.
............................................. cm
(Total for Question 12 is 5 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q12
14.2 Here is a vase in the shape of a cylinder.
The vase has a radius of 5 cm.
There are 1000 cm3 of water in the vase.
Work out the depth of the water in the vase.
Give your answer correct to 1 decimal place.
.............................................. cm
(Total for Question 16 is 3 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q16
14.3 Jane has a flower bed in the shape of an equilateral triangle.
The perimeter of the flower bed is 15 metres.
(a) Work out the area of the flower bed.
Give your answer correct to 1 decimal place.
.............................................. m2
(3)
Jane has some containers in the shape of hemispheres with diameter 35 cm.
Jane is going to fill the containers completely with compost.
She has 80 litres of compost.
1 litre = 1000 cm3.
(b) Work out how many containers Jane can fill completely with compost.
(4)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q16
15.1
Ali has two solid cones made from the same type of metal.
The two solid cones are mathematically similar.
The base of cone A is a circle with diameter 80 cm.
The base of cone B is a circle with diameter 160 cm.
Ali uses 80 mlof paint to paint cone A.
Ali is going to paint cone B.
(a) Work out how much paint, in ml, he will need.
The volume of cone A is 171 700 cm3.
........................................ ml
(2)
(b) Work out the volume of cone B.
........................................ cm3
(3)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q17
15.2 Kalinda has two solid cylinders made of the same material.
The cylinders are mathematically similar.
Cylinder A has a diameter of 6 cm.
Cylinder B has a diameter of 18 cm.
Cylinder A has a mass of 80 g.
Work out the mass of cylinder B.
............................................... g
(Total for Question 18 is 2 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q18
15.3 The volumes of two mathematically similar solids are in the ratio 27 : 125
The surface area of the smaller solid is 36cm2.
Work out the surface area of the larger solid.
……………….. cm²
(Total for Question 15 is 3 marks)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q15
16.1
During one week in January, the flights from an airport were delayed.
The table shows information about the flight delays on Monday.
Delay (t hours)
Frequency
4
0 <t  2
60
2 <t_ 7
40
7 <t  11
6
11 <t  13
(a) Draw a histogram for the information given in the table.
(3)
The histogram below shows information about the flight delays on Tuesday.
12 flights were delayed for up to 2 hours.
Avi says
“A greater number of flights were delayed for more than 7 hours on Monday than for
more than 7 hours on Tuesday.”
(b) Is Avi correct?
You must explain your answer.
(2)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q15
16.2 The incomplete frequency table and histogram give some information about the heights,
in centimetres, of some tomato plants.
Height(hcm)
Frequency
00<h10
10<h25
30
25<h30
30<h50
50
50<h60
20
(a) Use the information in the histogram to complete the table.
(2)
(b) Use the information in the table to complete the histogram.
(2)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q14
16.3 The table gives some information about the distances, in miles, that some men travelled to
work.
Distance (d
miles)
0 <d  5
Frequency
15
5 <d  10
17
10 <d  20
10
20 <d  30
6
30 <d  50
2
(a) Draw a histogram for the information in the table.
(3)
The histogram below shows information about the distances, in miles, that some women
travelled to work.
xwomen travelled between 10 and 20 miles to work.
(b) Find an expression, in terms of x, for the total number of women represented by the
histogram.
..............................................................
(2)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q12
16.4 The table gives some information about the weights, in kg, of 50 suitcases at an airportcheckin desk.
Weight(wkg)
Frequency
0<w10
16
10<w15
18
15<w20
10
20<w35
(a) Work out an estimate for the mean weight.
6
Passengers have to pay extra money for any suitcase that weighs more than 20 kg.
Two of the 50 suitcases are chosen at random.
(b) Work out the probability that both suitcases weigh more than 20 kg.
(c) On the grid, draw a histogram for the information in the table.
(4)
(2)
(3)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q10
17.1
There are 10 socks in a drawer.
7 of the socks are brown.
3 of the socks are grey.
Bevan takes at random two socks from the drawer at the same time.
(a) Complete the probability tree diagram.
(2)
(b) Work out the probability that Bevan takes two socks of the same colour.
(3)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q12
17.2 The probability that it will rain on Monday is 0.6.
When it rains on Monday, the probability that it will rain on Tuesday is 0.8.
When it does not rain on Monday, the probability that it will rain on Tuesday is 0.5.
(a) Complete the probability tree diagram.
(2)
(b) Work out the probability that it will rain on both Monday and Tuesday.
(2)
(c) Work out the probability that it will rain on at least one of the two days.
(3)
June 2011 – Unit 1 (Modular) – Higher – Calculator – Q10
17.3 The probability that Rebecca will win any game of snooker is p.
She plays two games of snooker.
(a) Complete, in terms of p, the probability tree diagram.
(2)
(b) Write down an expression, in terms of p, for the probability that Rebeccawill win both
games.
(1)
(c) Write down an expression, in terms of p, for the probability that Rebeccawill win exactly
one of the games.
(2)
June 2012 – Unit 1 (Modular)– Higher – Calculator – Q12