WJEC GCSE Numeracy Unit 2: Calculator-allowed Higher June 2017 question paper 3310U60-1

Mali’s scooter depreciated (decreased) in value by 24% in the first year.

In all further years, her scooter depreciated by 13% of its previous year’s value. She originally paid £850 for her scooter.

Calculate the value of Mali’s scooter after 7 years.

After 7 years, the value of Mali’s scooter was £_........

Sanjay stacks three boxes in a pile.

The heights of the boxes are 25 cm, 36 cm and 47 cm. They are all measured correct to the nearest centimetre.

What is the greatest possible height of the stack of the three boxes?

Greatest possible height of the stack of three boxes is_........ cm

Ursula is lying on her surfboard 180 metres away from the foot of a vertical cliff. The height of the cliff is 146 metres.

Ursula was told that if the angle of elevation of the top of the cliff from her lying position is between 42° and 45°, it is safe for her to attempt to stand on her surfboard. Calculate the angle of elevation of the top of the cliff from Ursula’s position lying on her surfboard. State whether it is • safe for Ursula to attempt to stand, or • not safe as she is too near the cliff, or

• not safe as she is too far out at sea.

Marta buys a new television.

Marta wants to fit the television in a bookcase on the wall. In the shop she forgot to write down the length of the television. She did write down the height and the diagonal of the screen.

Marta needs to know the length of the screen before she opens the box, in case she wants to return the television. Calculate the length of the screen.

Give your answer correct to 2 significant figures.

Length is_{………........ ………………} inches, correct to 2 significant figures.

The television was reduced in the sale by 26% of its original price. It cost Marta £710.40 in the sale.

What was the original price of the television?

A television uses 1 unit of electricity every 10 hours. A unit of electricity costs 9.8 p.

Calculate the cost of having a television turned on for 24 hours.

Circle your answer.

£23.52 £2.35 40.83 p 23.52 p 2.45 p

On average, Marta watches 4 hours of television each day. On average, how much a week does it cost her to watch television?

Circle your answer.

27.44 p £27.44 £39.20 39.2 p 10.78 p

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Elin’s old fish tank is leaking.

This old fish tank is in the shape of a cuboid. The base of this tank measures 60 cm by 40 cm. Before the leak, the height of the water level in Elin’s old fish tank was 45 cm.

Elin decides to replace her fish tank with a cylindrical one.

She selects a new cylindrical fish tank that has a radius of 25 cm and a height of 70 cm.

Will all the original contents, including the water and the fish, fit into this cylindrical tank?

You must show all your working.

Simon plans to make gloves.

One morning, Simon decided to carry out a survey to find the mean hand span of people in Wales.

He decided to sample systematically. He decided to sample from the first 240 people who pass him in the street during the morning.

He wanted to take 20 people’s hand span measurements.

Explain how Simon could use systematic sampling to obtain 20 measurements.

Yesterday morning, Simon only managed to sample 10 people. He calculated the mean hand span of these 10 people to be 22.8 cm. Yesterday afternoon, Simon recorded the hand spans of a further 20 people. The results for these 20 people are shown in the frequency table below.

Calculate an estimate of the mean of all 30 hand spans that Simon measured

yesterday.

What could Simon do to improve his estimate of the mean hand span of people in

Wales?

The table shows the number of Year 11 pupils attending schools in Cwmifan.

In total there are 690 Year 11 pupils attending these three schools.

A new youth theatre has been set up in Cwmifan. On the opening night, a total of 80 Year 11 pupils from these three schools are going to be invited to attend.

Use a stratified sampling method to calculate the number of Year 11 pupils from each school who should be invited.

You must show all your working.

A company produces metal badges to be worn by its employees. The badge is made up of two parts. One part is in the shape of a sector of a circle as shown in the diagram.

The perimeter of the sector is decorated with a coloured edging strip.

Calculate the length of edging strip needed to decorate the sector.

The other part is in the shape of a quarter-circle of radius 3 cm.

To make the badge, the two pieces are joined together with the sector in front of the quarter-circle, as shown in the diagram. The badge has a vertical line of symmetry.

The visible surface of the front of the badge is painted.

Calculate the area that is painted.

A plan view of Lowri’s garden is shown below.

All the measurements are correct to the nearest 10 cm.

Calculate the greatest possible area of Lowri’s garden.

Lowri plans to spread grass seed over her garden using a spreading tool. Over each square metre, the spreading tool spreads 30 g of grass seed, correct to the nearest 5 g.

Lowri has exactly 1∙5 kg of grass seed. Can she be certain that she has enough grass seed?

You must show all your calculations.

The front views of two mathematically similar milk cartons are shown below.

Circle either TRUE or FALSE for each statement given below.

It is claimed that the larger carton contains double the amount of milk contained in the smaller carton. Show that this claim is not true.

Explain your answer.

Another similar milk carton has a label with an area that is one quarter of the area of the label on the carton of height 24 cm.

Calculate the height of this new carton.

How far does Ioan cycle in going from A to B?

Show that Ioan’s route up this section of road is less steep than Delyth’s route.

You must show all your working.