Eduqas GCSE Maths Component 2H Higher November 2017 question paper

An amount of money is shared in the ratio 2: 3: 15.

The largest share is £330.

Calculate the smallest share.

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Seb wants to travel around the world in 7 years’ time.

In total, he will need £4000.

Seb has just been given £3000. He invests this in an account that pays 2·5% interest per annum.

How much extra money will Seb need in 7 years’ time?

Give your answer correct to the nearest pound.

Extra money needed_........

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The table shows the daily rainfall in Hightown during September 2017.

Rainfall, r mm	Number of days
0 r 4	4
4 r 6	14
6 r 10	10
10 r 14	2

(a)

Calculate an estimate of the mean daily rainfall in Hightown for September 2017.

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(b)

The actual mean daily rainfall in Seabank during September 2017 was 5·9 mm. Explain how it is possible that the actual mean daily rainfall in Hightown and

Seabank were both the same for September 2017.

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The score from the two spinners shown is 2 + 5 = 7.

The score is the sum of the two outcomes.

(a)

What is the lowest possible score?

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(b)

Is it possible to get a score maths symbol 9?

Give a reason for your answer.

Yes No

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(c)

Ryan says,

• Comment on Ryan’s method.

• Find the probability of scoring 5.

Comment on Ryan’s method:

Probability of scoring 5:

Probability of scoring 5 is_........

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(a)

5. (a) Solve 11 x – 3 = 9 x + 25.

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(b)

Factorise 5x² + 10x.

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(a)

(a)(i)

Claire is trying to find a value for w to calculate the lengths of the parallel sides. She has started her work by using the formula for the area of the trapezium.

Claire then plans to • collect like terms within the brackets, and • multiply by 2 throughout.

Complete the next step in Claire’s work in the box below.

$Question 6, shown as an image$

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(a)(ii)

From your answer in (a)(i) show that w² + 7w – 30 = 0.

You must show all your working.

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(a)(iii)

Factorise w² + 7w – 30 and hence solve w² + 7w – 30 = 0.

You must give both possible solutions to the equation.

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(a)(iv)

Hence find the length of each of the parallel sides.

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(b)

The diagram below shows a different trapezium.

Calculate the size of the angle y.

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The table below gives the densities, in g/cm³, of aluminium, copper, iron and zinc.

Metal	Density g/cm³
Aluminium	2·70
Copper	8·96
Iron	7·87
Zinc	7·13

A metal sphere of radius 3·6 cm is placed on weighing scales. The reading, in kg, shows:

The sphere is made from a single metal. Which metal is the sphere made from?

You must show all your working.

The sphere is made from_........

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Each wheel on a truck has a diameter of 1·22 metres.

During April each wheel made 2·4 × 10⁶ revolutions.

How far did the truck travel in April?

Give your answer in kilometres.

Distance travelled in April_{………………....…………..……..} km

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The diagram below shows triangle ABC.

(a)

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(b)

Use the angles on the straight line at C to obtain a further equation.

Use the two equations to show that ABC is an isosceles triangle.

You must use an algebraic method.

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(a)

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(b)

A straight line has a gradient of 2 and passes through the point (0, 4). Find the equation of this straight line.

Give your answer in the form y = mx + c.

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A yacht set sail, at the start of its journey, on a bearing of 048°.

It sailed on this bearing for 3·8 km to Kew Rocks. At Kew Rocks the yacht changed course and sailed to Dolphin Reach.

A triangle representing the yacht’s journey is shown below. Some angles are given.

(a)

Find the bearing on which the yacht sailed from Kew Rocks to Dolphin Reach.

Bearing of Dolphin Reach from Kew Rocks is_{……........ …………..} °

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(b)

Calculate the distance the yacht would need to travel to go directly from Dolphin Reach back to the start.

Give your answer correct to 2 significant figures.

Distance is_{……........ …………..} km, correct to 2 significant figures

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The diagram shows the aerial view of a hotel swimming pool.

A poster at the swimming pool gives the following information.

The swimming pool is filled to the top with water.

Calculate the possible volume of the water in the swimming pool. Give your answer in m³.

• You must state any assumption you make in calculating the volume.

• Show how this assumption impacts on your solution.

Volume:

Volume is_{……........ …………..} m³

Assumption:

Impact of this assumption on your solution:

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Imran records details of his car journeys for 3 days.

Day Average speed	Time
Monday 52 m.p.h.	3 hours 30 minutes
Tuesday 45 m.p.h	2 hours 20 minutes
Wednesday 44 m.p.h.	1 hour 45 minutes
	Total time: 7 hours 35 minutes

You are given the following information. • His car’s fuel consumption was 40 miles per gallon. • 1 litre is approximately equal to 0·22 gallons. • The cost of fuel is £1.25 per litre.

(a)

Calculate the total cost of the fuel Imran used for the 3 days.

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(b)

Imran usually spends a further 7 hours 35 minutes travelling in his car during the week.

(b)(i)

Give an estimate for Imran’s weekly fuel bill.

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(b)(ii)

Why might this estimate be unrealistic?

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Beth is making some designs using small square tiles.

She labels the patterns, as shown below.

Pattern 1
Pattern 2
Pattern 3
Pattern 4

(a)

Beth has a further 75 small square tiles.

How many tiles will Beth have left after making Pattern 5?

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(b)

Write an expression for the number of small square tiles in Pattern n.

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(c)

Show that Beth cannot make a complete design using exactly 796 tiles.

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At breakfast, the probability that Stefan has a bowl of cereal is 0·7.

The probability of Stefan having a slice of toast for breakfast is independent of him having a bowl of cereal. The probability that Stefan has a bowl of cereal and a slice of toast is 0·28.

(a)