Eduqas GCSE Maths Component 1H Higher November 2018 question paper

The scatter diagram shows the height and mass of 10 dogs.

These dogs are all West Highland Terriers.

Draw a line of best fit on the scatter diagram.

Estimate the mass of a West Highland Terrier that has a height of 26·7 cm.

Another dog has a mass of 8·2 kg and a height of 35 cm.

Is this dog likely to be a West Highland Terrier?

Yes No

Explain your answer.

The graph shows the cost of delivery for goods bought at a furniture shop.

Ceri buys a sofa from this shop and has it delivered. Ceri lives 4 miles from the shop.

How much does Ceri pay for the delivery?

(b) (i) Tick the correct statement about the distance and cost.

Find the gradient of the line and state what it represents in this context.

Light travels at 3 × 10⁵ kilometres per second. The circumference of the Earth at the equator is 40 000 km.

Show that, in theory, a beam of light could circle the Earth at the equator more than 7 times

in 1 second.

A sphere has a radius of metre.

Work out the surface area of the sphere.

Give your answer in its simplest form as a multiple of .

Surface area is_{…………........ ………..} m²

Work out the column vector 4(p + q).

When 2p + xq = r, find the value of x.

It takes

• 2 park keepers 1 hour to weed 2 flowerbeds • 3 park keepers 2 hours to prune 6 trees.

At 9 a.m. one morning, 5 park keepers start work as follows.

When one activity has been completed all the park keepers work on the other activity. You may assume that all the park keepers work at the same rate and are equally skilled.

How long does it take for the park keepers to complete the pruning and weeding?

You must show all your working.

Use the diagram to solve the simultaneous equations

y – x = 3,

x + 2 y = 1.

Give your answers correct to 1 decimal place.

A theme park sells entrance tickets.

2 adult tickets and 3 child tickets would cost a total of £72. 3 adult tickets and 1 child ticket would cost a total of £66.

A family ticket costs £45 and allows entry for 2 adults and 2 children.

How much cheaper is it to buy a family ticket than it would be to buy 2 adult and 2 child

tickets?

It is £_{………........ ……………} cheaper to buy a family ticket.

8. (a) Factorise x² + 2x – 15.

Write down the solutions of the equation x² + 2x – 15 = 0.

Thirty shoppers were asked which of apples, oranges and bananas, they regularly liked to eat.

Of these 30 shoppers • 2 liked all three fruits, • 5 liked oranges but did not like apples or bananas, • 6 liked both oranges and bananas, • 17 liked apples, • 10 liked bananas.

Extra information from the 30 shoppers has been shown in the Venn diagram below.

Complete the Venn diagram using the information given above.

One shopper is chosen at random.

Find the probability that this shopper does not like any of the three fruits.

One shopper is chosen at random from those who like apples.

Find the probability that this shopper does not like oranges.

Alec bought a house.

By the end of the first year, the value of Alec’s house had increased by 1%. By the end of the second year, its value had decreased by 10% of its value at the end of the first year.

Use multipliers to work out the overall percentage decrease in the value of Alec’s house for this

two-year period.

12. (a) Write 80 as a product of prime factors using index notation.

8112 = 2⁴ × 3 × 13²

Find the value of the smallest square number that is a multiple of 8112.

13. (a) Jo estimates the value of 2·75⁴ to be less than 81.

Show that Jo is correct.

Find the value of each of the following.

5¹¹ ÷ 5⁸

On the graph paper below, draw the region which satisfies all of these inequalities.

Indicate clearly the region that is your answer.

Sita is investigating the popularity of two social media websites, A and B.

She asked 60 technology students how much time they each spent using social media website A yesterday. The table summarises the data she collected.

Time spent, t (minutes)	t 20	t 30	t 40	t 50	t 60	t 70	t 80
Cumulative frequency	0	5	25	45	52	58	60

How many students spent more than 60 minutes using social media website A?

Draw a cumulative frequency diagram to represent Sita’s information.

Cumulative frequency

Time spent,

Use your diagram to find an estimate of the median time and the interquartile range of the

times the students spent using social media website A.

Median_{…………........ ………..} minutes Interquartile range_{…………........ ………..} minutes

Sita asked the same 60 technology students how much time they each spent using social media website B yesterday. She used her data to draw the histogram shown below.

Calculate an estimate for the difference between the number of students who use social media website B for more than 60 minutes and those who use social media

website A for more than 60 minutes.

Sita uses her results to state which social media website is more popular. Is her conclusion likely to be reliable?

Explain how you decide.

A, B, C and D are points on a circle. The line PQ is a tangent to the circle at B. PBA = 51°, BCD = 118° and ABD = w°.

Find the value of w.

You must show all your working.

E, F and G are points on a circle with centre H. EFH = x and GFH = y. Complete the proof of the following statement:

The angle at the centre is twice the angle at the circumference.

Proof: EFG = x + y FEH = x (triangle FEH is isosceles)

Diagram not drawn to scale

At a factory, clay travels through a pipe with rectangular uniform cross-section measuring 25 cm by 12 cm.

The pipe is always full of clay which travels along the pipe at a constant speed of 5 cm per second.

How long does it take a 3-litre block of clay to travel completely through the 40 cm section of

pipe from A to exit the pipe at B ?

The intensity of a light source, I candela, is inversely proportional to the square of the distance, d metres, from the light source.

From a distance of 2 metres, a torch has a light intensity of 7 candela.

Find the light intensity of the torch from a distance of 4 metres.

Complete the following identity.

.. (ii) Hence calculate (1·27)², giving your answer as a mixed number in its simplest

form.

21. (a) Janesh wants to draw the graph of y = f(x) and the graph of y = –f(x).

Janesh says,

‘To draw y = –f(x) I must reflect the graph of y = f(x) in the y-axis because the y-coordinates all change sign.’

Is Janesh correct?

Yes No

Explain how you decide.

Yasmin wants to draw the graph of y = f(x) and the graph of y = –f(x)

Yasmin draws both of her graphs on this diagram.

Make one criticism of Yasmin’s diagram.

The functions g (x) and h (x) are defined for all real x by

g (x) = 4 – 3 x,

Solve g^–1(x) = x + 2.

Find and simplify an expression for gg(x).

Explain why gh(–1) = gh(1).

23. (a) On the axes below, sketch the graph of y = sinx for 0° x 540°.

Write down the number of solutions of the equation sinx = 0·25 for 0° x 540°.

Anna has 7 photographs.

Find the number of different ways that Anna can arrange her 7 photographs in a line on a

table.

Find the number of different ways that Anna can randomly select 3 of her 7 photographs

and arrange them in a line on a shelf.

A solution of the equation x² – 0·5 = 0 lies between 0 and 1.

Jane uses the method of decimal search to find the solution correct to one decimal place.

Complete Jane’s table.

Explain why Jane’s solution lies between 0·7 and 0·8.

You are given that 74² = 5476.

Show that Jane’s solution is 0·7 correct to one decimal place.

In this question all dimensions are in centimetres.

The diagram shows a sketch of two circles, both with centre O.

The equation of the inner circle is x² + y² = 4. The equation of the outer circle is x² + y² = 144. The points A and B lie on the inner circle and outer circle respectively. OAB is a straight line.

Find the length of the line AB.

You must show all your working.

Write down the equation of the tangent to the outer circle at the point B.