Easter Revision Booklet

Maths GCSE Higher Tier Unit 2
Revision Booklet
Name:
This booklet contains past paper questions by topic
1.
Integers and Decimals
2.
Factors and Multiples
3.
Laws of Indices
4.
Standard Form
5.
Fractions
6.
Percentages
7.
Ratio and Scale
8.
Algebra
9.
Angles and Triangles
10.
Formulae
11.
Perimeter and Area
12.
Polygons
13.
Sequences
14.
Volume
15.
Linear Graphs
16.
3D Shapes
17.
Compound Measures
Integers and Decimals
Module U2/1(H)
1.
Work out
(i)
2×3+4
……………………….
(ii)
10 – 2 × 5
……………………….
(iii)
16 ÷ (2 × 4)
……………………….
(Total 3 marks)
2.
(a)
Work out £3.75 × 24
£ .....................................
(3)
(b)
Divide £135 by 20
£ .....................................
(3)
(Total 6 marks)
3.
Use the information that
322 × 48 = 15 456
to find the value of.......
(a)
3.22 × 4.8
..............................
(1)
(b)
0.322 × 0.48
.....................................
(1)
(c)
15 456 ÷ 4.8
.....................................
(1)
(Total 3 marks)
5.
Work out an estimate for the value of
5.79  312
0.523
...........................................
(Total 3 marks)
6.
Work out an estimate for the value of
637
3 .2  9 .8
……………………..
(Total 2 marks)
8.
Work out 25.6 × 1.6 You must show all your working.
..........................................
(Total 3 marks)
9.
Work out 147.6 ÷ 0.24
You must show all your working.
.....................................
(Total 3 marks)
Module U2/2(H)
2.
(a)
Factors and Multiples
Express 108 as the product of powers of its prime factors.
.........................
(3)
4.
(a)
Find the Highest Common Factor of 75 and 90.
……………………………
(2)
(b)
Find the Lowest Common Multiple of 75 and 90.
……………………………
(2)
(Total 4 marks)
7.
The number 40 can be written as 2m × n, where m and n are prime numbers.
Find the value of m and the value of n.
m = …………………
n = ………………….
(Total 2 marks)
Laws of Indices
Module U2/3(H)
1.
Write as a power of 5
(i)
54 × 52
…………………….
(ii)
59 ÷ 56
…………………….
(Total 2 marks)
3.
(a)
Simplify x5 ÷ x2
……………………………
(1)
(b)
Simplify
2w4y × 3w3y2
……………………………
(2)
(Total 3 marks)
4.
75 × 76 = 73 × 7k
Find the value of k.
k = ……………
(Total 2 marks)
5.
Simplify fully
(i)
(p3)3
.................................
(ii)
3q 4  2q 5
q3
.................................
(Total 3 marks)
9.
Work out
(i)
40
.................................
(ii)
4–2
.................................
(iii)
3
16 2
.................................
(Total 3 marks)
Standard Form
Module U2/4(H)
1.
Write in standard form
(a)
………………………
456 000
(1)
(b)
………………………
0.00034
(1)
(c)
16 × 107
………………………
(1)
(Total 3 marks)
(b)
Work out the value of (7 × 104) × (3 × 105)
Give your answer in standard form.
.........................................
(2)
(Total 3 marks)
(b)
Work out
4  10 3
8  10 – 5
Give your answer in standard form.
.....................................
(2)
(Total 4 marks)
10.
Work out the value of
(2 × 104) + (7 × 103)
Give your answer in standard form.
.....................................
(Total 2 marks)
Fractions
Module U2/5(H)
1.
Anil sold his car for £600.
He put £250 of the £600 in a bank account.
Write £250 as a fraction of £600.
Give your answer as a fraction in its simplest form.
……………………………
(Total 2 marks)
2.
Young Person’s RAILCARD
1
off normal price
3
Lisa uses her railcard to buy a ticket. She gets
1
off the normal price of the ticket.
3
The normal price of the ticket is £24.90. Work out how much Lisa pays for the ticket.
£ ..................................
(Total 3 marks)
3.
Work out
2 1

5 7
....................
(Total 2 marks)
4.
Work out the value of 1
2
3
+2
3
4
Give your answer as a fraction in its simplest form.
……………
(Total 3 marks)
6.
(a)
Write these fractions in order of size.
Start with the smallest fraction.
3
5
2
7
4
6
3
12
................................................................
(2)
8.
Convert the recurring decimal 0.2 9 to a fraction.
………………………………
(Total 2 marks)
10.
(a)
Change
3
to a decimal.
11
…………………….
(1)
Module U2/6(H)
1.
Percentages
Work out 70% of £340
£ ..........................................
(Total 2 marks)
2.
Mary scored 14 out of 20 in a test.
Find 14 out of 20 as a percentage.
.......................... %
(Total 2 marks)
3.
There are 800 students at Prestfield School.
45% of these 800 students are girls.
(a)
Work out 45% of 800
..........................
(2)
There are 176 students in Year 10.
(b)
Write 176 out of 800 as a percentage.
......................%
(2)
(Total 4 marks)
6.
Mr Brown buys a garden spade.
The spade costs £20 plus 17½% VAT.
Garden spade
£20 + 17½ % VAT
Calculate the total cost of the spade.
£ .......................................
(3)
7.
Ben bought a car for £12 000.
Each year the value of the car depreciated by 10%.
Work out the value of the car two years after he bought it.
£ ………………….
(Total 3 marks)
Module U2/7(H)
2.
Ratio and scale
Sidra and Gemma share £48 in the ratio 5 : 3
Work out how much more money Sidra gets than Gemma gets.
£ .................................
(Total 3 marks)
4.
Lillian, Max and Nazia share a sum of money in the ratio 2 : 3 : 5
(a)
What fraction of the money does Max receive?
.....................................
(2)
Nazia receives £60
(b)
Work out how much money Lillian receives.
£ .....................................
(3)
(Total 5 marks)
6.
3 metres of ribbon cost £1.26.
Work out the cost of 5 metres of the same ribbon.
£ …………………………
(Total 2 marks)
7.
This is a recipe for making Spaghetti Carbonara for 4 people.
Spaghetti Carbonara
Ingredients for 4 people
400 g of spaghetti
120 g of bacon
2 tablespoons of oil
4 eggs
50 g of cheese
Bill is making Spaghetti Carbonara for 6 people.
Work out the amount he needs.
........................ g of spaghetti
........................ g of bacon
........................ tablespoons of oil
........................ eggs
........................ g of cheese
(Total 3 marks)
8.
Picture NOT accurately drawn
A model of a space shuttle is made to a scale of 2 centimetres to 1 metre.
The length of the space shuttle is 24 metres.
(a)
Work out the length of the model.
Give your answer in centimetres.
………………………cm
(2)
The height of the model is 10 centimetres.
(b)
Work out the height of the space shuttle.
Give your answer in metres.
………………………m
(2)
(Total 4 marks)
Algebra
Module U2/8(H)
1.
(a)
Simplify a + a + a + a
.....................
(1)
(b)
Simplify 3 × b × 4
.....................
(1)
(c)
Simplify completely 4a + 5b – 2a + b
.....................................
(2)
(d)
Factorise x2 – 6x
.....................
(2)
(Total 6 marks)
2.
(a)
Simplify
a×a×a
............................
(1)
(b)
Expand
5(3x – 2)
........................................
(1)
(c)
Expand
3y(y + 4)
........................................
(2)
(d)
Expand and simplify
2(x – 4) + 3(x + 2)
............................
(2)
(e)
Expand and simplify
(x + 4)(x – 3)
........................................
(2)
(Total 8 marks)
3.
(a)
Expand and simplify
(x – 6)(x + 4)
……………………………
(2)
(b)
Factorise completely
12x2 – 18xy
……………………………
(2)
(Total 4 marks)
(b)
Expand and simplify (2x + 5)(3x – 4)
.......................................................
(2)
(c)
Factorise x2 + 7x + 10
.......................................................
(2)
(Total 6 marks)
6.
Factorise x2  5x  14
…………………………
(Total 2 marks)
(b)
Simplify fully
x 2  5x  6
x 2  2x
.....................................
(2)
(Total 6 marks)
Angles and triangles
Module U2/9(H)
1.
R
Diagram NOT
accurately drawn
y°
126° x°
P
Q
PQ is a straight line.
(a)
Work out the size of the angle marked x°.
..............................°
(1)
(b)
(i)
Work out the size of the angle marked y°.
..............................°
(ii)
Give reasons for your answer.
...................................................................................................................
...................................................................................................................
(3)
(Total 4 marks)
(b)
D
62º
E
yº
64º
F
G
Diagram NOT accurately drawn
DE is parallel to FG.
(i)
Find the size of the angle marked y°.
..........................°
(ii)
Give a reason for your answer.
...............................................................................................................................
(Total 2 marks)
Formulae
Module U2/10(H)
1.
P = 4k – 10
P = 50
(a)
Work out the value of k.
.....................................
(2)
y = 4n – 3d
n=2
d=5
(b)
Work out the value of y.
.....................................
(2)
(Total 4 marks)
2.
Work out the value of
p (q – 3)
when p = 2 and q = –7
4
........................
(Total 3 marks)
5.
Find the value of
t2 – 4t
when t = 3
……………………………
(Total 2 marks)
7.
Pat plays a game with red cards and green cards.
Red cards are worth 5 points each.
Green cards are worth 3 points each.
Pat has r red cards and g green cards.
His total number of points is N.
Write down, in terms of r and g, a formula for N.
…………………………..
(Total 3 marks)
Module U2/11(H)
Perimeter and Area
1.
7cm
9cm
5cm
12cm
Diagram NOT accurately drawn
Work out the area of the shape.
.................... cm2
(Total 4 marks)
2.
Diagram NOT accurately drawn
The diagram shows a rectangle inside a triangle. The triangle has a base of 12 cm and a height
of 10 cm. The rectangle is 5 cm by 3 cm.
Work out the area of the region shown shaded in the diagram.
.................................. cm2
(Total 3 marks)
6.
Work out the surface area of the triangular prism. State the units with your answer.
…………………….
(Total 4 marks)
Polygons
Module U2/12(H)
1.
120º
140º
a
58º
Diagram NOT accurately drawn
Work out the size of the angle a.
........................................°
(Total 2 marks)
4.
Diagram NOT
accurately drawn
Calculate the size of the exterior angle of a regular hexagon.
...................................
(Total 2 marks)
5.
The size of each exterior angle of a regular polygon is 40°.
Work out the number of sides of the regular polygon.
.....................................
(Total 2 marks)
Sequences
Module U2/13(H)
1.
Here are the first four terms of a number sequence.
2
(a)
7
12
17
Write down the 6th term of this number sequence.
............................................
(1)
The nth term of a different number sequence is 4n + 5
(b)
Work out the first three terms of this number sequence.
............
............
............
(2)
(Total 3 marks)
5.
Here are the first five terms of a number sequence.
3
(a)
7
11
15
19
Write down an expression, in terms of n, for the nth term of this sequence.
..........................................
(2)
Adeel says that 319 is a term in the number sequence.
(b)
Is Adeel correct?
You must justify your answer.
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 4 marks)
Volume
Module U2/16(H)
1.
A cuboid has
a volume of 40 cm3
a length of 5 cm
a width of 2 cm
(a)
Work out the height of the cuboid.
...................... cm
(2)
(b)
Diagrams NOT
accurately drawn
20
0c
m
100 cm
50
cm
100 cm
20 cm
20 cm
A carton measures 200 cm by 100 cm by 100 cm.
The carton is to be completely filled with boxes.
Each box measures 50 cm by 20cm by 20 cm.
Work out the number of boxes which can completely fill the carton.
.....................................
(3)
(Total 5 marks)
3.
The diagram shows a wedge in the shape of a triangular prism.
Diagram NOT
accurately drawn
cm
10
15 cm2
The cross section of the prism is shown as a shaded triangle.
The area of the triangle is 15 cm2.
The length of the prism is 10 cm.
Work out the volume of the prism.
..........................
(Total 3 marks)
Linear Graphs
Module U2/17(H)
1.
(a)
Complete the table of values for y = 3x + 1
x
–3
y
–8
–2
–1
0
1
2
–2
(2)
(b)
On the grid, draw the graph of y = 3x + 1
y
8
7
6
5
4
3
2
1
–3
–2
–1
O
1
2
x
–1
–2
–3
–4
–5
–6
–7
–8
–9
(2)
(Total 4 marks)
3.
A straight line has equation
(a)
y = 5 – 3x
Write down the gradient of the line.
………………………..
(1)
(b)
Write down the coordinates of the point where the line crosses the y axis.
(…… , ……)
(1)
(Total 2 marks)
3-D Shapes
Module U2/18(H)
1.
The diagram shows a solid triangular prism.
Diagram NOT
accurately drawn
Write down
(i)
the number of faces
..................
(ii)
the number of edges
..................
(iii)
the number of vertices
..................
(Total 3 marks)
Module U2/19(H)
1.
Compound measures
What is 1.5 kilograms in grams?
15 grams
150 grams
1.500 grams
1500 grams
1050 grams
A
B
C
D
E
(Total 1 mark)
2.
Jade measured the length of a line as 54 mm.
What is this length in centimetres?
54 cm
540 cm
5400 cm
5.4 cm
0.54 cm
A
B
C
D
E
(Total 1 mark)
4.
An aeroplane flies from Liverpool to Prague, a distance of 1200 km.
The aeroplane takes 4 hours.
Work out the average speed of the aeroplane.
……………………. km/h
(Total 2 marks)
5.
The distance from Bristol to Leeds is 216 miles.
(a)
Cara drove the 216 miles in 4 hours 30 minutes.
Calculate her average speed.
State the units of your answer.
.................. ..................
(4)

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