Eduqas GCSE Maths Component 2H Higher June 2017 question paper

Work out the sizes of angle x and angle y.

Steve invests £3400 in an account paying 2·6% compound interest per annum. Steve leaves his investment in the account for 10 years.

How much less than £5000 will this investment be worth at the end of the 10-year period? Give your answer correct to the nearest penny.

You must show all your working.

Write an equation in terms of x and solve it.

You must show all your working.

An amount of money is shared in the ratio 2: 3: 4.

What fraction of this money is the largest share?

The area of a circle is 24 cm².

Calculate the radius of the circle.

Work out each of the following.

Give your answers in standard form.

4·5 × 10^–6 × 3·4 × 10²⁰

What is the bearing of Jamestown from Abbeyford?

What is the bearing of Jamestown from Hillsridge?

The actual distance between Abbeyford and Jamestown is 20 km. On the map the distance between Abbeyford and Jamestown is 8 cm. Work out the scale of the map.

Give your answer in the form 1:_........

Scale of map 1:_........

It takes 3 people 6 days to mow a grass verge.

How many days would it take 9 people to mow a grass verge that is twice as long?

State one assumption you have made in answering this question.

9. (a) Expand and simplify (2 x + 3)(x – 5).

Factorise x² + 5x + 6.

A festival was held over 10 days.

An ice cream van was parked on the festival site each day.

The scatter diagram shows the number of people attending the festival on each of the days and the amount of money taken by the ice cream van.

Amount of money taken (£)

It was really cold and wet on one of the days. Although lots of people attended on this day, the amount of money taken by the ice cream van was very low.

On this cold and wet day: • how many people attended the festival?

• what was the amount of money taken by the ice cream van?

Amount of money taken £_........

Ignoring the outlier, draw a line of best fit on the scatter diagram.

(c) (i) Estimate the amount of money that the ice cream van may have taken at the festival

had only 50 people attended on a particular day.

Why is this estimate unlikely to be accurate?

Estimate how much each person attending the festival spends at the ice cream van.

You must give the unit of your answer.

Estimate is_........ per person

Rosa starts a 27 km cycle race at 14:20.

She finishes the cycle race at 16:00. Rosa set herself a target of achieving an average speed of 20 km per hour for the race.

Did Rosa achieve her target?

You must show all your working.

During the cycle race Rosa stopped for 25 minutes to mend a puncture. Had she not needed to stop to mend her puncture, how would this have impacted on her • average speed and • achieving her target?

You must show all your working.

The table shows rainfall for each day during a month.

Rainfall, r (mm)	Number of days
0 r 4	2
4 r 8	7
8 r 12	10
12 r 16	8
16 r 20	3

Calculate an estimate for the mean daily rainfall.

13. (a) Roberto buys 3 kg of carrots and 8 kg of turnips. He plans to make soup.

The recipe he plans to use says,

‘The ratio of carrots: turnips: onions is 5: 3: 2.’

Roberto plans to use all of the carrots.

• How many kilograms of turnips will he have left?

• How many kilograms of onions will he need?

A farm shop sells carrots and turnips.

Hadley buys 4 kg of carrots and 5 kg of turnips. Daisy buys 3 kg of carrots and 8 kg of turnips. Hadley spends £4.25 and Daisy spends £5.61.

Use an algebraic method to calculate the total cost of 1 kg of carrots and 10 kg of turnips.

You must show your working.

Total cost of 1 kg of carrots and 10 kg of turnips is_........

A store manager measured the length of the electrical cords on 60 different hairdryers.

The cumulative frequency diagram illustrates the store manager’s findings.

Cumulative frequency

How many electrical cords are between 1·6 m and 2 m in length?

The store had a target: • at least 75% of hairdryers checked should have an electrical cord longer than 100 cm. Does the store meet the target?

Give a reason for your answer. State any assumption you made when calculating your answer.

You must show all your working.

Working:

Assumption:

(c) (i) Use the cumulative frequency diagram to estimate the median length of the electrical

cords.

The store manager realised that she had measured the shortest electrical cord incorrectly. The cord actually measures 79 cm. What impact does this have on the median?

You must give a reason for your answer.

The cost of a coat is reduced by 10% in a sale.

In the final clearance this coat is reduced by a further 25% of the sale price. The final clearance price of the coat is £175.50.

Calculate the original price of the coat before any reduction in price.

Pattern 1
Pattern 2
Pattern 3
Pattern 4

The diagram shows four patterns made using square grey tiles. There are 4 tiles in Pattern 1.

How many tiles are there in Pattern 5?

(b) (i) Find an expression for the number of tiles in Pattern n.

Describe how the arrangement of the tiles can be used to explain your expression

in (b) (i).

17. (a) Robin has a rectangular blanket made from 100% wool. Robin knows that the wool in his blanket has a mass of 136 g per m². The mass of his blanket is 952 g. The width of his blanket is 2·5 m.

Calculate the length of Robin’s blanket.

Length of Robin’s blanket is_........

Rugs are made from a material that is a mix of polyester and recycled plastic. The polyester in the material has a mass of 120 g per m². The recycled plastic in the material has a mass of 140 g per m².

Dafina buys one of these rugs. The rug is rectangular. Its width is 1·5 m and length is 2 m. The label on the rug says it is made from 65% polyester and 35% recycled plastic.

Show that Dafina’s rug has a mass of less than 400 g.

You must show all your working.

The diagram shows a cuboid. A, B and C are all vertices of the cuboid. Calculate the size of CAB.

Give your answer correct to 3 significant figures.

Fifty raffle tickets are sold.

The tickets sold are numbered from 1 to 50. The raffle tickets are placed in a box for a draw. One raffle ticket is selected at random and not replaced in the box. A second ticket is then randomly selected.

Find the probability that one of the tickets drawn is odd and the other is even.

Find the probability that at least one of the tickets drawn is even.

The vectors OK, OL and OM are shown in the diagram.

Find each of the following vectors in terms of a and b. Give each answer in its simplest form.

LM

KL

What do your answers to (i) and (ii) tell you about the following?

The lengths of the lines LM and KL.

The points K, L and M.

The point Q is the midpoint of the line OL. Find MQ in terms of a and b.

Give your answer in the form xa + yb.

Show that 7x² + 4x – 93·4 = 0.

Use the quadratic formula to solve 7x² + 4x – 93·4 = 0.

Give both of your answers correct to 2 decimal places.

Find each of the lengths of the parallel sides of the trapezium.

You must justify any decisions that you make.

The lengths of the parallel sides are_{………........ ………} cm and_{………........ ………} cm.

Decision and justification:

Calculate the area of triangle BCD.

An experiment was carried out to record the velocity of a particle during the first 6 seconds of its journey.

• v is the velocity of the particle measured in m/s. • t is the time in seconds. • The relationship found was v = 6t – t².

Draw a graph of v = 6t – t² for values of t from t = 0 to t = 6.

(b) (i) Calculate an estimate for the distance the particle travelled from t = 0 to t = 6.

You must use six regions, each of equal width, in your calculation.

Sharmin says,

Is Sharmin correct?

You must give a reason for your answer.

A thin piece of card, which is a sector of a circle with centre O, is shown below.

Find an expression for the length of the arc DE.

Give your answer, in terms of x and , in its simplest form.

The thin card is made into a cone by sticking edges OD and OE together without overlapping.

Show that the expression for the perpendicular height, h, of the cone in terms of x is