Eduqas GCSE Maths Component 2H Higher November 2019 question paper

25 years ago, Raveena’s grandparents invested £500 for her in an account paying 3·4% compound interest per annum. No extra money was paid in and no money was withdrawn during these 25 years.

Raveena has decided to withdraw all the money in the account after 25 years.

How much should Raveena receive? 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.

The table below gives information from the Highway Code on stopping distances for cars.

The stopping distances given in the Highway Code assume good driving conditions and alert drivers.

When a driver is tired and the road is wet, the thinking distance increases by 30% and the braking distance increases by 20%.

A tired driver travels at 64 km/h in wet driving conditions.

Calculate their stopping distance in metres.

4. (a) Expand and simplify (2 x – 7)(3 x – 8).

Solve w² + 8w – 33 = 0.

Factorise b² – 144.

Rearrange the following to make e the subject. Simplify your answer.

9e² = t⁴

5. (a) In Queenbridge, the mean daily snowfall for a week was 1∙6 cm. If there had been 1 cm more snowfall on each day, what would the mean daily snowfall

have been?

In Sansburg, the snowfall for each of the first 10 days in January was measured. The results are summarised in the table below.

Daily snowfall, s in cm	Number of days
1·5 s 2·5	4
2·5 s 3·5	2
3·5 s 4·5	1
4·5 s 5·5	0
5·5 s 6·5	3

Calculate an estimate for the mean daily snowfall for these 10 days.

During the first 5 days of February, the mean snowfall in Awezell was 4·7 cm. On 6th February the snowfall was 23·9 cm.

Calculate the mean snowfall for the first 6 days of February.

Calculate the size of the angle between the roof of the shed and the horizontal.

Petra has a mathematically similar shed.

Calculate the two missing measurements on the diagram above.

You must show all your working.

Nadeen has 102 g of butter and plenty of flour and sugar. Nadeen uses all this butter to make scones.

Calculate the quantity of flour and sugar Nadeen needs.

Nadeen has been recommended to eat 2200 kcal per day. She eats two scones for lunch. Her breakfast was 390 kcals.

What percentage of the recommended daily kcals does Nadeen have left for meals later in the day?

Give your answer correct to the nearest 0.01%.

Calculate the area of the top face of a scone.

Calculate the total surface area of a scone. State any assumption you make.

Assumption:

Total surface area_........ cm²

8. (a) In 2015, the average price of coal sold by a mine in the USA was $31.83 per ton. This coal was then delivered to power stations. The power stations paid $42.58 per ton for this coal. The difference in price was the delivery cost.

What percentage of the original price of the coal was this delivery cost?

Give your answer correct to 3 significant figures.

In the USA and the UK the word ‘ton’ means different amounts: • a UK ton = 1016 kg, • a USA ton = 907 kg, • a tonne (called a metric ton in the USA) = 1000 kg.

What is the difference between a UK ton and a USA ton?

Give your answer in tonnes.

A preformed piece of coal weighs 100 g correct to the nearest 5 g. A bag contains 30 pieces of preformed coal.

Complete the sticker to attach to this bag of coal.

A square lawn has a side of length 8 m.

A builder is asked to make a path around the outside edge of the square lawn.

The plan was for a path of width y metres with all the edges of the path being straight.

Find an expression for the area of this path in terms of y.

Give your answer in its simplest form.

Before the builder started, the plan was updated and the following agreed: • at each corner of the lawn the path should be a quarter circle, • the width of the path is to be 1·5 m, • the path is to be made of 8 cm thick concrete.

Calculate the volume of the concrete needed for the path.

Candice has been given a bracelet.

The dimensions of the bracelet are given below.

Candice knows it is made entirely from one metal. She is not sure if it is copper, silver or gold. Her bracelet has a mass of approximately 18 g.

Convince Candice that her bracelet is made from silver.

You must show all your working.

P is the midpoint of OB. Express each of the following in terms of x and y. Give each of your answers in the simplest form.

Does P lie on CA?

Yes No

You must give a reason for your answer.

12. (a) Factorise and hence solve the following equation.

Find the nth term of the following sequence.

7, 10, 15, 22, 31, 42,........

Ali walks slowly from home through a forest and back home again. He walks a total distance of (3x + 1) km in a time of + 6) hours. Ali’s average speed is 2 km/h. He left home at 9 a.m.

At what time did Ali return home?

Ali returned home at_........

The expression x² + 18x + 2 has a minimum value. By completing the square, complete the statements below.

You must show all your working.

‘The minimum value of x² + 18x + 2 occurs when x = ………………….’

Calculate the area of ABCD.

The velocity-time graph below shows the first 60 seconds of a car’s journey.

After how many seconds was the velocity of the car 9 km/h?

Harriet argues that the acceleration at t = 22 represents the typical acceleration of the car during the first 32 seconds of this period.

Explain why Harriet’s argument is correct.

Over the same 60 seconds, the velocity, v m/s, at time, t seconds, of another car is given by the following equation.

Find two times for which the difference in the two cars’ velocities was 2·5 m/s. Give these times correct to the nearest second.

You must show all your working.

The radii of two spheres are in the ratio 2: 7. The volume of the smaller sphere is 10∙4 cm³.

Calculate the volume of the larger sphere.