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Higher tier Paper 1

Date of Exam Morning Time allowed: 1 hour 45 minutes

Materials

For this paper you must have:

• a calculator

• mathematical instruments.

Instructions

• Use black ink or black ball-point pen. Draw diagrams in pencil.

• Fill in the boxes at the top of the page.

• Answer all questions.

• You must answer the questions in the spaces provided. Do not write outside the box around each page or

on blank pages.

• Do all rough work in this book. Cross out any work you do not want to be marked.

Information

• The marks for questions are shown in brackets.

• You may ask for more answer paper and graph paper. These must be tagged securely to this answer

In a running club there are 50 females and 80 males.

If a female is chosen at random, the probability she has blue eyes is 0.38

If a male is chosen at random, the probability he has blue eyes is 0.6

One person is chosen at random.

Show that the probability the person has blue eyes is more than 0.5

Paul gives a survey to every 5th student on the school registers.

Circle the name for this type of sampling.

[1 mark]

17 w =

5 x

3

Circle the expression for w

2

[1 mark]

2 10

6

x

2 25

9

x 10x

6

25x

9

----------

The length of a roll of ribbon is 30 metres, correct to the nearest half-metre.

A piece of length 5.8 metres, correct to the nearest 10 centimetres, is cut from the roll.

Work out the maximum possible length of ribbon left on the roll.

[3 marks]

Answer metres

----------

Doug owes an amount of £600

He wants to pay off this amount in five months.

He says,

“Each month, I will pay back 20% of the amount I still owe.”

Show working to check if his method is correct.

----------

An approximation for the value of π is given by

22 22 22 22 22 4 1

57 85 105 117 242

  −+− + −    

Use your calculator to show that this approximation is within 0.1 of 3.14

----------

Work out

10

4

9.12 10

3.2 10

×

×

Give your answer in standard form.

----------

The volume of a medal is 45 cm3

The medal is made from copper and tin.

volume of copper : volume of tin = 22 : 3

The density of copper is 8.96 g/cm3

The density of tin is 7.31 g/cm3

Work out the mass of the medal.

[4 marks]

Answer grams

----------

f(x) =

x + 2

x g(x) = x

2 – 2

Work out fg(x)

Give your answer in the form a + bx n

where a, b and n are integers.

[3 marks]

Answer

----------

y is 1

2

1 times x.

Circle the ratio that is equivalent to y : x

[1 mark]

2 : 5 5 : 2 3 : 2 2 : 3

----------

Theo starts with savings of £18

James starts with no savings.

Each week from now,

Theo will save £4.50 and James will save £4

In how many weeks will Theo and James have savings in the ratio 15 : 8 ?

----------

Show that, for x ≠ –1

4 4

8 8 2

+

−

x

x simplifies to the form ax + b where a and b are integers.

----------

Solids X and Y are similar.

X has volume 64 cm3

Y has volume 343 cm3

The surface area of X is 176 cm2

Work out the surface area of Y.

----------

Write these numbers in descending order.

9563 9.56 × 103 9.56 × 310

[2 marks]

Answer

----------

Rana sells 192 cakes in the ratio small : medium : large = 7 : 6 : 11

The profit for one medium cake is twice the profit for one small cake.

The profit for one large cake is three times the profit for one small cake.

Her total profit is £532.48

Work out the profit for one small cake.

[5 marks]

Answer £

----------

Solve 5x

2 = 10x + 4

Give your answers to 2 decimal places.

[4 marks]

Answer

----------

Use your calculator to work out 19.422 – 3 1006 ÷ 4.95

Write down your full calculator display.

[1 mark]

Answer

----------

The pressure at sea level is 101 325 Pascals.

Any rise of 1 km above sea level decreases the pressure by 14%

For example,

at 3 km above sea level the pressure is 14% less than at 2 km

Work out the pressure at 4 km above sea level.

Give your answer to 2 significant figures.

[4 marks]

Answer Pascals

----------

Bag X contains 9 blue balls and 18 red balls.

Bag Y contains 7 blue balls and 14 red balls.

Liz picks a ball at random from bag X.

She puts the ball into bag Y.

Mike now picks a ball at random from bag Y.

Show that

P (Liz picks a blue ball) = P (Mike picks a blue ball)

[4 marks]

Adam recorded the temperature outside his house at 1pm every day for 6 months. He used the data to find the average temperature for each of those months. The average values he calculated are shown in the table below.

Draw a line graph to represent Adam's data.

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