WJEC GCSE Numeracy Unit 2: Calculator-allowed Intermediate June 2018 question paper 3310U40-1

In a survey, 720 students were asked if they preferred to take part in gym activities, team sports or individual sports.

They were asked to choose just one of these options. The results are displayed in the pie chart below.

How many students selected individual sports?

Circle your answer.

90 180 270 405 540

Carwyn plans to split team sports on the pie chart into football and other team sports. Of the students who selected team sports, said their preferred team sport was football

What angle should Carwyn draw to represent football?

720 students took part in the survey. Only 45% were female.

How many males took part in the survey?

Number of males is_........

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

By how much has Miss Price been overcharged or undercharged?

You must show all your working.

Use this conversion to calculate how much fresh water Miss Price used in gallons.

Explain why your answer in part (b)(i) is not the exact number of gallons Miss Price

used.

Emrys, Layla and Rhys go shopping together for fruit.

They buy pears and apples from a market stall.

How much change will Rhys receive from £5 when paying for 5 pears and 2 apples?

Change from £5 is £_........

Carys has to write a report on the water levels of the River Tad.

She has recorded the depth of the water in the River Tad between 1 p.m. and 7 p.m. This is shown in her graph below.

What was the greatest recorded depth of water in the river?

Circle your answer.

26 cm 27 cm 46 cm 48 cm 50 cm

For what period of time was the depth of water in the river greater than 45 cm?

Circle your answer.

48 minutes 1 hour 1 hour 12 minutes

1 hour 24 minutes 1 hour 30 minutes

Complete the key for the pictogram.

What is the following ratio in its simplest form?

number of people who went to Spain: number of people who went to the USA

Circle your answer.

6: 4 4: 6 400: 600 3: 2 2: 3

Look at the pictogram. The ratio of the number of people who went to Wales to the number of people who went to another country is 2: 3.

Which country is this?

2: 3 Wales:_........

Mena goes on holiday to France. She takes 590 euros with her on holiday.

Mena only spends 40% of her euros.

When she returns from holiday, she exchanges her remaining euros for pounds. The exchange rate is £1 = 1.18 euros.

How many pounds does Mena receive?

Grace sees a newspaper advertisement for Blake’s Mopeds.

Blake’s Mopeds

Best deal! Valid if you show this advertisement.

Grace is planning to save for this offer. She also wants to save enough money for the first month’s fuel.

The moped travels 20 miles on each litre of fuel. A litre of fuel costs £1.26. Grace estimates she will travel approximately 350 miles each month on her moped.

Starting this month, Grace will be able to save £60 per month.

After how many complete months will Grace have saved enough money for this offer, including the first month’s fuel?

You must show all your working.

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.

Calculate an estimate of how much per month was given to charity between 1st October 2011 and 31st January 2015.

You must show all your working.

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.