Answer ALL TWENTY FIVE questions.

Write your answers in the spaces provided.

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You must write down all the stages in your working.

5 3 3
1 Show that 1  2  3
7 16 4

(Total for Question 1 is 3 marks)

2 The length of a table is measured as 1.4 metres correct to one decimal place.
(a) Write down the upper bound of the length of the table.

............................................ . . . . . . . . . . . . . . . . . . metres
(1)
(b) Write down the lower bound of the length of the table.

............................................ . . . . . . . . . . . . . . . . . . metres
(1)
(Total for Question 2 is 2 marks)

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3 The diagram shows triangle PQR
P

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Diagram NOT
8.6 cm
accurately drawn

43°
Q x cm R

Work out the value of x

Give your answer correct to one decimal place.

x= ......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 3 is 3 marks)

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 4 N is a number.
17% of N is 357
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(a) Work out the value of N

N = ......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)
In 2019, the population of a village was 650
In 2020, the population of the village was 806
(b) Work out the percentage increase in the population.

................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %
(3)
(Total for Question 4 is 5 marks)

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5 Cody has a biased 5-sided spinner, numbered 1, 2, 3, 4, 5
The table gives the probabilities that when the spinner is spun it will land on 2 or on

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3 or on 5

Number 1 2 3 4 5

Probability 0.14 0.17 0.21

The probability that the spinner will land on 1 is the same as the probability that the
spinner will land on 4
Cody is going to spin the spinner 400 times.
Work out an estimate for the number of times the spinner will land on 4

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(Total for Question 5 is 4 marks)

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 6 The diagram shows a solid triangular prism.

Diagram NOT
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accurately drawn
10 cm

6 cm

15 cm

8 cm

Work out the total surface area of the triangular prism.

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(Total for Question 6 is 3 marks)

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7 (a) On the grid, draw the straight line with equation
(i) x = 3   (ii) y = 1   (iii) x  y  7

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Label each line with its equation.

y
8

O 1 2 3 4 5 6 7 8 x

(3)
(b) Show, by shading on the grid, the region that satisfies all three of the inequalities
x  3    y  1    x + y  7

Label the region R

(1)
(Total for Question 7 is 4 marks)

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 8 Kim puts 4 bananas in a bag.
The mean weight of the 4 bananas in the bag is 145 grams.
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Andy puts one more banana into the bag.

The mean weight of the 5 bananas in the bag is 142 grams.
Work out the weight of the banana that Andy puts into the bag.

........................................... . . . . . . . . . . . . . . . . . . . grams
(Total for Question 8 is 3 marks)

9 Nisha invests 20 000 euros for 3 years in a savings account.

She gets 3.5% per year compound interest.
Work out how much money Nisha will have in her savings account
at the end of the 3 years.
Give your answer correct to the nearest euro.

......................................... . . . . . . . . . . . . . . . . . . . . . euros
(Total for Question 9 is 3 marks)

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10 All the students in year 10 and all the students in year 11 named their favourite science
subject from Biology, Chemistry and Physics.

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The pie chart shows information about the results for the year 10 students.
The table shows information about the results for the year 11 students.

science number of
subject students
Biology Chemistry
102° Biology 3x + 6
126°
Chemistry 5x + 8
132°
Physics Physics 7x − 9

Pie chart for year 10 Table for year 11

There are 300 students in year 10

There are 320 students in year 11
More students in year 10 than in year 11 said Biology was their favourite
science subject.
How many more?

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(Total for Question 10 is 5 marks)

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11
C

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Diagram NOT

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I accurately drawn
D
B

H
E
A

G
F

ABCDE is a regular pentagon.

DEFGHI is a regular hexagon.
AF is a straight line.
Work out the size of angle EAF

°
............................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 11 is 5 marks)

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 3x  2 2 x  1
12 (a) Solve  x
5 3
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Show clear algebraic working.

x= ......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)
a  bc
(b) Make c the subject of the formula f 
cd

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(4)
(Total for Question 12 is 7 marks)

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13 The frequency table gives information about the weights, in kilograms, of 60 parcels in
a delivery van.

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Weight
(w kilograms) Frequency

0<w1 4

1<w2 15

2<w3 20

3<w4 11

4<w5 6

5<w6 4

(a) Complete the cumulative frequency table.

Weight
Cumulative frequency
(w kilograms)

0<w1

0<w2

0<w3

0<w4

0<w5

0<w6

(1)
(b) On the grid opposite, draw a cumulative frequency graph for your table.
(2)

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 60
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50

40

Cumulative
frequency 30

20

10

0
0 1 2 3 4 5 6
Weight (kg)

(c) Use your graph to find an estimate for the median weight of the 60 parcels.

..................................................... . . . . . . . . . kilograms
(1)
(d) Use your graph to find an estimate for the number of these parcels that weigh more
than 3.7 kilograms.

......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)
(Total for Question 13 is 6 marks)

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 32 n  3
14 Given that  33  31  2 n
4
3

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find the value of n
Show your working clearly.

n= ......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 14 is 3 marks)

  42
15 Use algebra to show that 0.7 63 
55

(Total for Question 15 is 2 marks)

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 16 A, B, C and D are points on a circle, centre O
C
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Diagram NOT
54° accurately drawn

B
O
28°
D

(a) (i) Work out the size of angle AOD

º
........................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)
(ii) Give a reason for your answer to part (a)(i)

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............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)
(b) Work out the size of angle CAO

º
........................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)
(c) Work out the size of angle ABC

º
........................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)
(Total for Question 16 is 5 marks)

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17 Here are two vectors.

 5   4

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 2 14 

Calculate the magnitude of the vector

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(Total for Question 17 is 3 marks)

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 18 The straight line L is perpendicular to the straight line with equation 2 x  y  9
and passes through the point with coordinates (8, 11)
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Find an equation for L

Give your answer in the form y  mx  c

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(Total for Question 18 is 4 marks)

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19 A curve has equation y  f x 
There is only one minimum point on the curve.

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The coordinates of this minimum point are (5, 4)
Write down the coordinates of the minimum point on the curve with equation
(i) y  f  x  5 

(............................... , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(1)
(ii) y  3f  x 

(............................... , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(1)
(iii) y  f  x   7

(............................... , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(1)
(Total for Question 19 is 3 marks)

20 Solve the inequality 10 x 2  11x  21  0

Show clear algebraic working.

......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 20 is 3 marks)

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 21 The Venn diagram shows information about the numbers of items in
set A, set B and set C, where x is an integer.
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E
A B

x+2
3x 4x
x
x+7 2x

5x 3x + 2

Given that n( A  B)  26

find n( A  C )

n( A  C )  ......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 21 is 4 marks)

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22 Solve the simultaneous equations
x2  y 2  y  3

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x2 y

Show clear algebraic working.

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(Total for Question 22 is 5 marks)

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23 Show that  2  (7  8 x )  n
x7 x  5 x  14
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where n is an integer to be found.

Show clear algebraic working.

(Total for Question 23 is 4 marks)

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24 A, B and C are three points on horizontal ground.
AB = 8.4 metres BC = 9.2 metres

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B is on a bearing of 067° from A
C is on a bearing of 129° from B
Calculate the bearing of A from C
Give your answer correct to the nearest degree.

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º
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(Total for Question 24 is 6 marks)

Turn over for Question 25

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25 The diagram shows an equilateral triangle ABC and a circle with centre O

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C
Diagram NOT
accurately drawn

x cm

A B

AB, BC and CA are tangents to the circle.

The radius of the circle is x cm
The total area, in cm2, of the regions shown shaded in the diagram is nx²
Find the value of n
Give your answer correct to 3 significant figures.

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n= ......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 25 is 5 marks)

TOTAL FOR PAPER IS 100 MARKS

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