1. This is a list of ingredients for making a pear & almond crumble for 4 people.

Ingredients for 4 people.

80 g plain flour

60 g ground almonds

90 g soft brown sugar

60 g butter

4 ripe pears

Work out the amount of each ingredient needed to make a pear & almond crumble for 10

people.

..................... g plain flour

..................... g ground almonds

..................... g soft brown sugar

..................... g butter

..................... ripe pears (Total 3 marks)

2. Use your calculator to work out the value of 49.103.2

84.795.8

(a) Write down all the figures on your calculator display.

..................................... (2)

(b) Write down your answer to part (a) correct to 3 significant figures.

..................................... (1)

(Total 3 marks)

* 3. A museum has these charges.

Adult Ticket

Child Ticket

2.50

1.25

Family Ticket

(2 adults and 3 children)

6.50

Mr and Mrs Iqbal and their three children visit the museum.

Work out how much they will save by buying one family ticket rather than

5 separate tickets

(Total 4 marks)

4. Here are the first five terms of an arithmetic sequence.

7 11 15 19 23

(a) Write down, in terms of n, an expression for the nth term of this sequence.

............................................ (2)

Pat says that 453 is a term in this sequence.

Pat is wrong.

(b) Explain why.

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

..................................................................................................................................... (1)

(Total 3 marks)

3.80

200 gLarge

3.50

175 gRegular

5. The top of a table is a circle.

The radius of the top of the table is 50 cm.

(a) Work out the area of the top of the table.

cm2 (2)

The base of the table is a circle.

The diameter of the base of the table is 40 cm.

(b) Work out the circumference of the base of the table.

cm (2)

(Total 4 marks)

* 6.

A Large tub of popcorn costs 3.80 and holds 200 g.

A Regular tub of popcorn costs 3.50 and holds 175 g.

Rob says that the 200 g Large tub is the better value for money.

Linda says that the 175 g Regular tub is the better value for money.

Who is correct?

Explain the reasons for your answer. You must show all your working.

(Total 2 marks)

7. (a) Work out the value of 3p + 4q when p = 5 and q = 0.7

(2)

(b) Expand and simplify (t + 4) (t 2)

................................... (2)

(c) Write down the integer values of x that satisfy the inequality

2 x < 4

................................... (2)

(Total 6 marks)

8.

Menu

Hot dog

Chicken salad

Hamburger

Pizza

$5.10

$5.50

$4.80

$6.50

A British family are on holiday in San Francisco.

At a caf they order 3 hot dogs and 1 chicken salad.

The exchange rate is 1 = $1.54

Work out their total bill in pounds ().

(Total 4 marks)

9. Verity and Jean share 126 in the ratio 5 : 3

Work out how much money Verity receives.

(Total 2 marks)

10. Marcus collected some pebbles.

He weighed each pebble.

The grouped frequency table gives some information about weights.

Weight (w grams) Frequency

50 w < 60 5

60 w < 70 9

70 w < 80 22

80 w < 90 27

90 w < 100 17

Work out an estimate for the mean weight of the pebbles.

grams (Total 4 marks)

11. The equation x3 15x = 31

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.

x = . (Total 4 marks)

12.

A

B

C

Use ruler and compasses to construct the bisector of angle ABC.

You must show all construction lines. (Total 2 marks)

13.

y

8

7

6

5

4

3

2

1

O 1 2 3 4 5 6 7 8 9 10 x

On the grid, enlarge the shaded shape by scale factor of 2, centre (1,1). (Total 3 marks)

14. (a) Complete the table of values for y = x2 3x 1.

x 2 1 0 1 2 3 4

y 3 1 3 3

(2)

(b) On the grid below, draw the graph of y = x2 3x 1.

(2)

(c) Use your graph to find an estimate for the minimum value of y.

(1)

x

y

2 1 1 2 3 4O

10

9

8

7

6

5

4

3

2

1

1

2

3

4

5 (Total 5 marks)

15. (a) (i) Write 48 000 000 in standard form.

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

(ii) Write 3.2 105 as an ordinary number.

................................... (2)

(b) Work out the value of

3.2 105 48 000 000

Give your answer in standard form.

................................... (2)

(Total 4 marks)

16. Some students took a test.

The table shows information about their marks.

Minimum mark 10

Lower quartile 33

Interquartile range 35

Median mark 43

Range 65

Use this information to draw a box plot.

0 10 20 30 40 50 60 70 80Mark

(Total 3 marks)

17. Loren has two bags.

The first bag contains 3 red counters and 2 blue counters.

The second bag contains 2 red counters and 5 blue counters.

Loren takes one counter at random from each bag.

(a) Complete the probability tree diagram.

35

Red

Blue......

Red

Blue......

27

Red

Blue......

......

Counter fromfirst bag

Counter fromsecond bag

(2)

(b) Work out the probability that Loren takes one counter of each colour.

............................................... (3)

(Total 5 marks)

18. Adam invests 2000 for 3 years at 1.4% per annum compound interest.

Calculate the value of the investment at the end of 3 years.

. (Total 3 marks)

19. Solve the simultaneous equations

6x 2y = 33

4x + 3y = 9

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

y = .................... (Total 4 marks)

AB C

6.2 cm

24

70

A

B

C

DO

* 20. Diagram NOT accurately drawn

A, B, C and D are points on the circumference of a circle, centre O.

BOD is a straight line.

Angle COD = 70

(a) Find the size of angle BAD.

Give a reason for your answer.

..................................... (2)

(b) Find the size of angle CBD.

Give a reason for your answer.

..................................... (2)

(Total 4 marks)

21.

Diagram NOT accurately drawn

Angle ABC = 90.

Angle ACB = 24.

AC = 6.2 cm.

Calculate the length of BC.

Give your answer correct to 3 significant figures.

. cm (Total 3 marks)

22. The table shows the number of students in each year group at a school.

Year group 7 8 9 10 11

Number of students 190 145 145 140 130

Jenny is carrying out a survey for her GCSE Statistics project.

She uses a stratified sample of 60 students according to year group.

Calculate the number of Year 11 students that should be in her sample.

............................................... (Total 3 marks)

23. In a factory, chemical reactions are carried out in spherical containers.

The time, T minutes, the chemical reaction takes is directly proportional to the square of the

radius, R cm, of the spherical container.

When R = 120, T = 32

Find the value of T when R = 150

T = ............................... (Total 4 marks)

24. The table gives information about the number of hours worked by some factory workers.

Number of hours (n) worked Frequency

0 < n 5 15

5 < n 15 42

15 < n 35 40

35 < n 50 6

Use the table to draw a histogram.

5

4

3

2

1

10 20 30 40 50

0

Frequencydensity

Number of hours ( ) workedn

(Total 3 marks)

25.

B

A

C

8 cm

15 cm

70

Diagram NOT accurately drawn

In triangle ABC,

AC = 8 cm,

BC =15 cm,

Angle ACB = 70.

(a) Calculate the length of AB.

Give your answer correct to 3 significant figures.

................................ cm (3)

(b) Calculate the size of angle BAC.

Give your answer correct to 1 decimal place.

................................... (2)

(Total 5 marks)

26. The time period, T seconds, of a pendulum is calculated using the formula

T = 6.283 g

L

where L metres is the length of the pendulum and g m/s2 is the acceleration due to gravity.

L = 1.36 correct to 2 decimal places.

g = 9.8 correct to 1 decimal place.

Find the difference between the lower bound of T and the upper bound of T.

..................................... (Total 5 marks)

27.

p

q

P

Q

R S

O

Diagram accurately drawn

NOT

OPQ is a triangle.

R is the midpoint of OP.

S is the midpoint of PQ.

OP = p and OQ = q

(i) Find OS in terms of p and q.

OS = ..........................

(ii) Show that RS is parallel to OQ.

(Total 5 marks)