Questions
Q1.
(a) Work out the reciprocal of 1.25
...........................................................
(1)
(b) Work out the value of
Give your answer correct to 2 decimal places.
...........................................................
(2)
(Total for question = 3 marks)
Q2.
On an activity day students play one sport.
They play football or hockey or tennis.
120 students are on the activity day.
30 of the students are boys.
12 of the boys and 26 of the girls play hockey.
45 of the students play football.
35 of the 45 students who play football are girls.
Work out the number of girls who play tennis.
..............................................................................................................................................
(Total for Question is 4 marks)
Q3.
The diagram shows a tile.
The tile is in the shape of a semicircle of radius 8 cm.
Work out the perimeter of the tile.
Give your answer correct to one decimal place.
........................................................... cm
(Total for Question is 3 marks)
Q4.
Use ruler and compasses to construct the perpendicular from point C to the line AB.
You must show all your construction lines.
(Total for Question is 2 marks)
Q5.
Here are some patterns made from white centimetre squares and grey centimetre squares.
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)
(Total for Question is 4 marks)
Q6.
Describe fully the single transformation that maps shape P onto shape Q.
.............................................................................................................................................
.............................................................................................................................................
(Total for Question is 3 marks)
Q7.
Work out
⁄5 + 3⁄8
2
Give your answer in its simplest form.
..............................................................................................................................................
Total for Question is 2 marks)
Q8.
Solve 3(x – 2) = x + 7
x=......................
(3)
(b) Solve
y=......................
(2)
(Total for Question is 5 marks)
Q9.
There are yellow discs, red discs, blue discs and green discs in a bag.
Dinesh is going to take at random a disc from the bag.
The table shows each of the probabilities that Dinesh will take a red disc, or a blue disc, or a green disc.
(a)
Work out the probability that he will take a yellow disc.
...........................................................
(2)
Dinesh takes at random a disc from the bag.
He writes down the colour of the disc.
He puts the disc back into the bag.
He will do this 60 times.
(b)
Work out an estimate for the number of times he takes a red disc from the bag.
..........................................................
(2)
(Total for Question is 4 marks)
Q10.
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 is 3 marks)
Q11.
(a) Factorise
x2 + 5x + 4
..............................................................................................................................................
(2)
(b) Expand and simplify
(3x −1)(2x + 5)
..............................................................................................................................................
(2)
(c) Write as a single fraction
⁄2x + 1⁄5x − 1⁄3x
1
..............................................................................................................................................
(2)
(Total for Question is 6 marks)
Q12.
In a sale normal prices are reduced by 20%.
A washing machine has a sale price of £464
By how much money is the normal price of the washing machine reduced?
£ ...........................................................
(Total for Question is 3 marks)
Q13.
The table gives some information about the weights, in kg, of 50 suitcases at an airport check-in desk.
Weight (w kg)
Frequency
0 < w ≤ 10
10 < w ≤ 15
15 < w ≤ 20
20 w ≤ 35
16
18
10
6
(a) Work out an estimate for the mean weight.
. . . . . . . . . . . . . . . . . . . . . . kg
(4)
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.
......................
(2)
(c) On the grid, draw a histogram for the information in the table.
(3)
(Total for Question is 9 marks)
Q14.
Ali has two solid cones made from the same type of metal.
Diagram NOT accurately drawn
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 ml of paint to paint cone A.
Ali is going to paint cone B.
(a) Work out how much paint, in ml, he will need.
. . . . . . . . . . . . . . . . . . . . . . ml
(2)
The volume of cone A is 171 700 cm3.
(b) Work out the volume of cone B.
. . . . . . . . . . . . . . . . . . . . . . cm3
(3)
(Total for Question is 5 marks)
Q15.
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 is 3 marks)
Q16.
*
A, B, C and D are points on the circumference of a circle with centre O.
Angle ABC = 116°
Find the size of the angle marked x.
Give reasons for your answer.
(Total for Question is 4 marks)
Q17.
Here are the times, in seconds, that 15 people waited to be served at Rose's garden centre.
5
9
11
14
15
20
22
25
27
27
28
30
32
35
44
(a) On the grid, draw a box plot for this information.
(3)
The box plot below shows the distribution of the times that people waited to be served at Green's garden
centre.
(b) Compare the distribution of the times that people waited at Rose's garden centre and the distribution
of the times that people waited at Green's garden centre.
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
(2)
(Total for Question is 5 marks)
Q18.
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 is 4 marks)
Q19.
Calculate the length of PR.
Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . cm
(Total for Question is 3 marks)
Q20.
Solve the simultaneous equations
4x − 5y = 33
3x + y = 1
x = ...........................................................
y = ...........................................................
(Total for Question is 3 marks)
Q21.
D is directly proportional to x.
D = 36 when x = 5
Work out the value of D when x = 8
D =...........................................................
(Total for Question is 2 marks)
Q22.
182 students go to an outdoor activity centre for a day.
Each student chooses one activity, climbing or sailing.
The table shows information about the activities the students chose.
The manager of the centre gives a questionnaire to some of the students.
He takes a sample of 50 students stratified by gender and the activity chosen.
Work out the number of male students who chose climbing he should have in his sample.
..............................................................................................................................................
(Total for Question is 2 marks)
Q23.
Jerry wants to cover a triangular field, ABC, with fertiliser.
Here are the measurements Jerry makes
angle ABC = 50° correct to the nearest degree,
BA = 225 m correct to the nearest 5 m,
BC = 175 m correct to the nearest 5 m.
Work out the upper bound for the area of the field.
You must show your working.
...........................................................m2
(Total for Question is 3 marks)
Q24.
(a) Write down an equation of a straight line that is parallel to the straight line y = 3x – 5
..............................................................................................................................................
(1)
A straight line, L, is perpendicular to the straight line y = 3x – 5 and passes through the point (6, 5)
(b) Find an equation of L.
..............................................................................................................................................
(3)
(Total for Question is 4 marks)
Q25.
Event A and event B are independent events.
The probability that event A will happen is 0.3
The probability that event B will happen is 0.6
(a) Complete the probability tree diagram.
(2)
(b) Work out the probability that either event A will happen or event B will happen but not both.
...........................................................
(2)
(Total for Question is 4 marks)
Q26.
OAB is a triangle.
N is the point on AB such that AN : NB = 3 : 1
(a) Find
in terms of a and b.
..............................................................................................................................................
(1)
(b) Find
in terms of a and b.
Give your vector in its simplest form.
..............................................................................................................................................
(3)
(Total for Question is 4 marks)
Q27.
(a) On the grid, draw the graph of x2 + y2 = 4
(2)
(b) On the grid, sketch the graph of y = cos x for 0° ≤ x ≤ 360°
(2)
(Total for Question is 4 marks)
Mark Scheme
Q1.
Q2.
Q3.
Q4.
Q5.
Q6.
Q7.
Q8.
Q9.
Q10.
Q11.
Q12.
Q13.
Question
Working
Answer
Mark
Notes
(a)
5×16 = 80
12.5×18 = 225
17.5×10 =175
27.5×6 =165
645÷50 =12.9
or
5.5×16 = 88
13×18 = 234
18×10 =180
28×6 =168
670 ÷ 50 = 13.4
12.9
4
M1 for fx
consistently
within interval
including ends
(allow 1 error)
M1 consistently
using
appropriate
midpoints
M1 (dep on first
M1) for Σ fx ÷Σ f
A1 for 12.9 or
13.4
⁄245
2
(b)
⁄50 × 5⁄49 = 30⁄2450
6
3
(c)
0 ≤ d < 10 fd 1.6
10 ≤ d < 15 fd
3.6
15 ≤ d < 20 fd 2
20 ≤ d < 35 fd
0.4
Correct
histogram
3
M1 for 6⁄50 × 5⁄49
A1 for 3⁄245 oe
If M0A0, SC B1
for 9⁄625 oe
B2 for 4 correct
histogram bars (
± ½`square)
(B1 for 2 or 3
histogram bars
of different
widths correct)
B1 for frequency
density label or
key and
consistent
scaling SC if B0
then M1 for
clear attempt to
use frequency
density or area
Q14.
Q15.
Q16.
Q17.
Q18.
Q19.
Q20.
Q21.
Q22.
Q23.
Q24.
Q25.
Q26.
Q27.