WJEC GCSE Numeracy Unit 2: Calculator-allowed Higher June 2018 question paper 3310U60-1

In October 2011, a charge of 5p for a carrier bag was introduced in Wales.

Money raised from this charge is given to charity.

For the period 1st October 2011 to 31st January 2015, it was estimated that a total of between £16.8 million and £21.9 million was donated to charity. This is as a result of people buying 5p carrier bags.

Over time, there has been a reduction in the use of 5p carrier bags. This is because more people are using their own bags.

What impact might this have had on the amount given to charity for the month of

September 2014 when compared with September 2012?

Gary travelled a distance of 231 km in 3 hours and 30 minutes. Calculate Gary’s average speed in km/h.

Circle your answer.

Yared is going to make a door wedge.

The cross-section of the wedge is shown below. The horizontal length is 12 cm and the vertical height is 3 cm.

Calculate the length x.

Give your answer correct to 3 significant figures.

The wedge must fit under Yared’s door. The angle y must be less than 15°. Show that this wedge will fit under Yared’s door.

You must show all your working.

Yared decides to make a larger wedge that is mathematically similar to the one shown in part (a). This wedge is to have a vertical height of 4.5 cm.

Calculate the horizontal length of this door wedge.

The wedge will be_{……........ ………} cm long

A grass racetrack is shown in the diagram below.

This is the region shaded in the diagram. Each end of the grass racetrack is created from semicircles. The inner semicircles have a radius of 15 m. The outer semicircles have a radius of 20 m. Each of the straight sections of the racetrack has a length of 65 metres.

What is the total area of grass in the two straight sections of the racetrack?

You must show all your working.

Calculate the area of the grass racetrack.

You must show all your working.

The grass is to be treated with a fertiliser. It costs 20p to treat each 3 m² of grass. How much will it cost to treat the grass racetrack? Give your answer correct to the nearest pound.

You must show all your working.

A plumbing engineer wants to calculate how long a shower can be used continuously before the water runs cold. He uses the following formulae:

Where: C is the additional volume of water that feeds into the cylinder, in litres. H is the volume of hot water that the cylinder holds, in litres. M is the temperature of the water in the shower, in °C. X is the temperature of the hot water in the cylinder, in °C. Y is the temperature of the cold water that feeds into the cylinder, in °C. T is the time spent using the shower before the water runs cold, in minutes. F is the rate of flow of water in the shower, in litres per minute.

Daisy’s cylinder holds 300 litres of hot water. The temperature of the hot water in her cylinder is 60°C. The temperature of the cold water that feeds into Daisy’s cylinder is 8°C.

The water in Daisy’s shower is set at a temperature of 32°C. Her shower has a rate of flow of 26 litres per minute.

Use the formulae to calculate • the additional volume of water that feeds into Daisy’s cylinder, in litres, • the number of minutes Daisy’s shower will run continuously before the water runs cold.

In her note pad, Dr Khan summarised the temperatures in a grouped frequency table.

Unfortunately, Dr Khan has torn the page containing the table from her note pad and has lost some of the original data.

Calculate an estimate of the mean temperature at 4 p.m. for these 30 days in Dr Khan’s

hallway.

Estimate of the mean temperature at 4 p.m. for April in the hallway is_{…........ ….} °C

What assumption have you made in calculating an estimate of the mean temperature at

4 p.m. for April in Dr Khan’s hallway?

Faryl recorded the same temperatures as her mother at 4 p.m. each day during April. She found that the actual mean temperature in the hallway during April was lower than the correctly calculated estimate of the mean.

Explain how this can be true.

Gwen fills a 10-litre bucket with water from a tap.

She turns the tap until it is fully open. The bucket fills up with water, and when Gwen thinks it is close to being full, she slowly closes the tap. The bucket is full after 20 seconds. The graph below shows the volume of water in the bucket during the 20 seconds.

After how many seconds did Gwen start to close the tap?

Estimate at what rate water is entering the bucket at time t = 10 seconds.

Give your answer in litres per second.

When the tap is fully open, water flows out at 2 litres per second.

Express 2 litres per second in gallons per minute.

You must show all your working.

Can a fully open tap fill a 90-gallon tank in under 3 minutes?

You must show all your working.

Circle either TRUE or FALSE for each statement given below.

Benjamin invests £1000 into an account that pays interest every 6 months. He does not make any further payments into the account, and does not withdraw any money either. After a year, there is £1036 in the account.

Calculate how much was in the account after 6 months. Give your answer correct to the nearest penny.

You must show all your working.

A company makes plastic shelf supports for use in kitchen cupboards. A shelf support is made by attaching a cylinder to a right-angled triangular prism.

The cylinder has a diameter of 6 mm and a length of 9 mm. The prism has dimensions CD = 8 mm, DE = 8 mm, CE = 11.3 mm and BC = 10 mm. The company sells the shelf supports in packs of 500. It needs to know the volume of plastic in 500 shelf supports.

Calculate the volume of 500 shelf supports.

A sensor can detect any movement up to a distance of 6.5 m.

A storeroom is in the shape of a cuboid, as shown below. The sensor is placed at A, so that • it is aimed directly at B, where BD = 2 m, • the front of the sensor is 20 cm from A along the line AB.

Will the sensor be able to detect movement at B?

You must show all your working.