# University of Cumbria

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```					                         University of Cumbria

Mathematics Practice Paper 08

Time Allowed: 2 hours

Do not begin each question on a new sheet of paper.

You will require a calculator.

Answers should, where appropriate, be given correct to 3 significant figures.

Please do not remove this examination paper from the examination room.

This paper has 22 questions.

The mark allocation for each part of a question is shown in brackets and the total
marks for the question at the end of the question.

Show all of your working and hand in any rough working, indicating the relative
question number.
1.   The height of a pile of 24 magazines is 160 mm.
All the magazines are the same thickness.
Work out the height of a pile of 30 magazines.
(2 marks)

2    (a)       Simplify 7p + 2q + p – 3q                                (1)

(b)    (i) Use the formula y = 5x + 4 to work out the value of y when x = 3

(1)

(ii) Use the formula y = 5x + 4 to work out the value of x when y = 14

(1)

(3 marks)

3     (a)      Calculate       52  23                                  (2)

(b)      From this list

6    8    9   10   12   13      16

(i)        Write down a cube number                      (1)
(ii)       Write down a prime number                     (1)

(4 marks)

4.     A box of sweets contains 8 toffees, 4 chocolates and 5 mints.

Mark selects a sweet at random.
What is the probability that he chooses a toffee?

(1 mark)
5.   The diagram shows a rectangular lawn with a path around it.
The path is the same width all the way round.
The lawn is 22 m long and 8 m wide.
The total width of the lawn and path is 13 m.

22 m

Lawn
8m        13 m

Path

x
Not drawn accurately

(a)    Work out the length x shown on the diagram.
(1)

(b)     Work out the area of the path.
(4 marks)

6     The table shows the exchange rates between different countries.

£1 is worth 1.85 dollars
£1 is worth 193 yen

Petra buys a camera in America and pays 300 dollars.
James buys a similar camera in Japan and pays 28 400 yen.

How much is saved in pounds by buying the camera in the cheaper country ?

(4 marks)
7. A cricket coach records the number of runs the players in his team scored in
a match.
He shows the data in a stem and leaf diagram.

Key    |1|5    represents 15 runs scored

0     1      1
1     2      5       8
2     3      7
3     6
4     0      3
5     9

(a)   What is the range of the data?                            (1)

(b)   What is the median score?                                 (1)

(c)   Would the mode be a good representative average for

(3 marks)

8   Sabine earns £22 100 a year.
She is awarded a pay rise of 3.8%
How much does she earn after the pay rise?

(3 marks)

9   A second-hand dealer pays £200 for 120 CDs.
4
He sells of them for £3 each.
5
He sells the remainder for £2 each.

(a)   How much money does he receive from selling the CDs?
(3)

(b)   Work out the percentage profit he makes on these sales.
(2)
(5 marks)
10   (a)    The diagram shows triangle PQR.
S is a point on PR such that PS = RS = QS.
Angle QRS = 35o

Q

35       R

S                         not drawn accurately

P

Work out the size of angle PQR.
You must show your working.                                       (3)

(b)    Work out the size of angles x and y.

x
30

not drawn accurately
y

50

(2)
(5 marks)

11   The weight of a 2p coin is 7 g.
Find the weight of £20 worth of 2p coins.
(3 marks)
12                A hockey club is choosing a new top.
(a)      The club asks 80 supporters to help choose the colour.
The pie chart shows the results of their choices.
Not drawn accurately

Green
Other

72

Blue

Red

How many of the 80 supporters chose green?                   (2)

(b)    Players at the Hockey Club want a striped top.
Each player chooses a colour for the top and a colour for the stripe.
The two-way table shows the numbers of players choosing different
combinations of colours.

Colour of top
Red       Blue           Green

White            8          7             2
Colour of stripe
Black           4          2             5

A player is chosen at random.
What is the probability he chooses a green top or a black stripe?
(2)
(4 Marks)
13   Solve the equations.

w
(a)       8                                                           (1)
5

(b)     3x - 7 = 11                                                    (1)

(c)    7y + 11 = 3(y + 9)                                              (3)

(5 marks)

14   Mr Gates buys a car for £16 400.
The car decreases in value at the rate of 30% each year.
Find the value of the car after two years.
(3 marks)

15   The diagram shows two triangles A and B.
y

5

4
B
3
A
2

1

0
0   1       2    3    4       5   6     7       8       9    x

Describe fully the single transformation that maps triangle A onto triangle B.

(2 marks)

16   A cuboid is made from centimetre cubes.
The area of the base is 7 cm2.
The volume of the cuboid is 14 cm3.
Work out the surface area of the cuboid.
(3 marks)
17   (a)    t is an even number.
t2
Amy says             is always even.
2
Give an example to show that Amy is wrong.                  (1)

(b)    r and s are both odd numbers.
Is 2r + s always an odd number, an even number or could it
be either?

(3 marks)

18   (a)    The number of people who work in a factory is 595.
The ratio of women to men is 3:4.
How many women work at the factory?
(2)

(b)    A bottle of water weighs 595 g correct to the nearest gramme.

(i)     What is the minimum weight of the bottle?           (1)

(ii)    The bottles are sold in packs of six.
What is the minimum weight of a pack?               (2)

(5 marks)

19   Calculate the value of
26.36  7.95
5.93  2.67

(2 marks)
20    (a)
(i)        Write 32 000 in standard form.                 (1)

(ii)       Write 0.000 042 in standard form.              (1)

(b)          The table shows the populations of three European countries in 2002.

Country      Population

Denmark       5.4  106

Germany       8.3  107

Sweden        8.9  106

Work out the difference between the smallest and largest population.
(2)

(4 marks)

21   (a)    Simplify

(i)          x6  x2                                             (1)

(ii)         x6  x2                                             (1)

(iii) (x6)2                                                      (1)

(b)          Expand and simplify (x – 2)(x + 5)                        (2)

(a)          Factorise x2 – 16                                         (1)

(b)          Make x the subject of the formula z  y  x               (2)

(8 marks)
22   A lawn fertiliser can be bought in either bottles or packets.
Two bottles and three packets cost £32, whereas
Four bottles and one packet cost £29.

Use algebra to find the cost of a bottle and the cost of a packet.

(4 marks)

END OF QUESTIONS

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