WJEC GCSE Numeracy Unit 2: Calculator-allowed Higher June 2024 question paper 3310U60-1

A survey was carried out to find the total time people took to read the book ‘Wales is a Celtic Country’. The results are shown in the frequency polygon below.

Which is the modal group?

Circle your answer.

18 to 24 hours 21 hours 12 to 18 hours 34 hours 30 to 36 hours

How many people took part in the survey?

Circle your answer.

34 30 33 97 108

How many of the people in the survey took 24 hours or more to read this book?

Circle your answer.

13 34 47 24 84

The thickness of each book is measured correct to the nearest mm.

Show that the total height of the stack of these four books cannot be more than 109 mm.

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

How much would be saved per week if the 8 street lights were only on from 7 p.m. to 5 a.m.? Give your answer in pounds, correct to the nearest penny.

You must show all your working.

A lamp post is vertical and stands on horizontal ground. The angle of elevation of the top of the lamp post is 68° when measured from a point 3. 3 m from the centre of the base of the lamp post.

Calculate the height of the lamp post.

Calculate an estimate of the mean number of walks per person each week.

High tide in the morning is, on average, 35 minutes later each day. The morning high tide on 3rd March was at 08:03.

At what time was the morning high tide on 1st March?

A new concrete sea-defence wall is to be built. The sea-defence wall will have a uniform cross-section. A sketch of the new wall is shown below.

Calculate the volume of concrete needed to make this new sea-defence wall.

You must show all your working.

An estimated 500 000 000 people live near active volcanoes.

What is 500 000 000 written in standard form?

The teragram is a unit of mass. 1 teragram = 10⁹kg

Last year, a volcano released a total of 140 teragrams of carbon dioxide in 300 days.

Calculate the average number of kilograms of carbon dioxide that were released by this volcano per hour. Give your answer correct to 3 significant figures.

You must show all your working.

The surface area of Venus is 460 234 320 km². The surface of Venus is wrinkled-volcanic, smooth-volcanic or non-volcanic. The areas of these three different types of surface are in the ratio 7: 1: 2.

Wrinkled-volcanic: Smooth-volcanic: Non-volcanic = 7: 1: 2

Calculate the total surface area of Venus that is volcanic.

You must show all your working.

Caryl needs to calculate the cost of the petrol she used for a recent car journey.

She knows the following information about her journey:

• For part of her journey, she travelled a distance of 36 miles at a steady speed of 25 mph. • For the rest of her journey, she travelled at a steady speed of 65 mph for 1 hour 24 minutes.

Some fuel economy information for her car is given in the following table:

Calculate how many gallons of petrol Caryl used during her journey.

Caryl paid £1.49 for each litre of petrol.

Calculate the cost of the petrol used for the journey.

C-clips are used in motors and turbines as a type of fastener. Clip Zone makes metal C-clips. They have a uniform cross-section, as shown below.

O is the centre of the circular arcs AC and BD. OAB and OCD are straight lines. OA = OC = 50 mm. AB = CD = 4 mm. The C-clips have a uniform thickness of 2 mm.

C-clips are made by melting down metal bars and re-casting them. Calculate the number of C-clips that can be made from a metal bar with a volume of 1 500 000 mm³.

You must show all your working.

Clip Zone makes four types of fastener. The table below shows the number of each type produced each week.

Clip Zone takes a sample of these 149 000 fasteners to check the quality of its products. A stratified sample of 1500 fasteners is taken, based on the type of fastener. Calculate the number of each type of fastener that should be included in the sample.

You must show all your working.

Sara and Tanvi are taking part in an orienteering race.

The start and finish points of the race are the same. They will take different routes from the start point to get to the same last marker point. They then head directly back to the start/finish point.

Here is a diagram showing some information about Sara’s route.

Show that the distance Sara travels from the last marker back to the finish point is

7∙7 km, correct to 1 decimal place.

17 17

The diagram below shows some information about Tanvi’s route.

Tanvi started her race by running 6∙3 km on a bearing of 120º to point A. She then ran 2∙1 km to reach the last marker.

Calculate the bearing of the last marker from point A.

The map that Sara and Tanvi were each given before the start of the race was 33 cm long. Tanvi decided to reduce the size of her map to a mathematically similar size.

The area of Tanvi’s map is now 19% less than the area of Sara’s map.

Calculate the length of Tanvi’s map.

Sara’s distance from the start, for the first part of her race, is shown in the graph below.

Estimate Sara’s speed 20 minutes after the start of the race.

Give your answer in miles per hour.

The Cardiff Saver account pays interest at a rate of 0.6% every 3 months. Evan invests £5000 in this account.

Evan does not make any further deposits or withdrawals after opening the account. Calculate how much money is in the account after 4 years.

The Pontypridd Saver account has an AER of 4%. The account pays interest every 6 months. Myles invests money in this account.

Calculate the interest rate that is applied to the account every 6 months. Give your answer as a percentage correct to 2 decimal places.

You must show all your working.