WJEC GCSE Numeracy Unit 1: Non-calculator Higher June 2018 question paper 3310U50-1

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

The concrete base of Miss Morgan’s new bungalow is shown below.

The concrete base of Miss Morgan’s bungalow is 0.2 m thick.

Calculate the volume of the concrete base.

You must show all your working.

Mr Graham orders of the maximum load of concrete for the base of his garage floor.

What is the total cost of Mr Graham’s order?

Total cost is £_{………........ ………….}

Olga took out a high-interest loan for £400. She paid back £49 per month for 20 months to clear the loan.

Calculate the total interest that Olga paid as a percentage of the original loan.

Sara is carrying out a survey of the three villages, Cwm, Allthir and Gwyndir.

The diagram below shows the positions of the three villages.

What is the bearing of Allthir from Gwyndir?

Circle your answer.

010° 170° 180° 190° 200°

What is the bearing of Cwm from Allthir?

Circle your answer.

028° 152° 242° 332° 352°

The area of the land covered by the three villages is 200 km². The total population of the three villages is 8400 people.

What is the population density of the three villages?

Give your answer in population/km².

The populations of Cwm, Allthir and Gwyndir are in the ratio 3: 4: 5.

Calculate the population of Gwyndir.

Kingsley invests £3000 in an account that pays 2% compound interest per annum. He does not make any further payments into his account. He does not withdraw any money from his account.

How much will Kingsley have in his account after two years?

Amount in Kingsley’s account after two years is £_........

Kingsley buys a portable Bluetooth speaker. The speaker has been reduced by 20% in a sale. He pays £72 for the speaker in the sale.

What was the original price of the speaker?

Original price of the speaker is £_........

Michelle owns a café.

She stacks coffee mugs as shown in the diagram below.

Michelle measures the height of each coffee mug as 12 cm, correct to the nearest centimetre Each stacked coffee mug creates 4 cm extra height, correct to the nearest centimetre.

Michelle knows that the vertical height between two shelves is exactly 39 cm, as shown below.

Can Michelle be certain that she will be able to place one stack of 7 coffee mugs between the two shelves? Give a reason for your answer.

You must show all your working.

Which is the modal group?

Circle your answer.

20 to 25 minutes 25 to 30 minutes 30 to 35 minutes

35 to 40 minutes 40 to 45 minutes

Is it certain that the last runner’s finish time was 45 minutes?

You must give a reason for your answer.

Yes No

The organisers hoped that 80% of the runners would finish the race within 30 minutes.

Complete the following two statements.

‘_........ % of runners finished the race within 30 minutes.’

‘80% of runners finished the race within_........ minutes.’

Last year, the median finish time was 26 minutes. By how many minutes was the median time better this year?

You must show all your working.

There are two entrances to a stadium, North Entrance and South Entrance.

At each entrance, 3000 people queued to pass through security. The length of time each of these people spent in the queue was recorded. The box-and-whisker diagrams show the results.

At the North Entrance, how many people had to queue for more than 44 minutes?

You must show all your working.

Number of people is_........

For the South Entrance, calculate an estimate of the number of people who had to queue there for between 40 and 60 minutes.

You must show all your working.

Number of people is_........

Use your answer from part (a) to find the number of months’ pay Eirlys has received.

Matas knows the following information about the amount of fuel his car uses.

During one journey, Matas drove at 50 mph for part of the time and at 70 mph for the rest of the time. He drove for 3 hours at a speed of 50 mph. For the whole journey, Matas used 4∙6 gallons of fuel. For how long did Matas travel at 70 mph?

You must show all your working.

Astronomers use astronomical units (AU) to describe distances in our solar system.

The distance between the Sun and the Earth is 1 AU. 1 AU is 1∙496 × 10⁸km, correct to 4 significant figures.

The distance of Pluto from the Sun is 5∙913 × 10⁹km, correct to 4 significant figures.

Siôn says that the distance of Pluto from the Sun is less than 50 AU.

Using suitable approximations, estimate the distance of Pluto from the Sun, in AU, to show that Siôn is correct.

You must show all your working.

A light year is the distance light travels in one year.

1 light year is approximately 63 000 AU.

Estimate the length of a light year in km.

Give your answer in standard form.

The initial mass of the particle was 160 mg.

Write down a formula for the mass m, in milligrams, of the particle after t seconds.

Ffiol-Aur is a company that makes vases.

They make one of their vases in two mathematically similar sizes.

A decorative glaze covers the surfaces of each vase. The glaze covers an area of: • 400 cm² on the smaller vase, • 3600 cm² on the larger vase.

The height of the larger vase is 48 cm.

Calculate the height of the smaller vase.

The heights of all the Year 11 girls at a school were measured.

Nia has started to draw a histogram of the results.

Frequency density

There were 24 girls in Year 11 whose heights were in the group 155 h 160 cm.

Use this information to complete Nia’s histogram.

Nia has started to do some data analysis on the heights of the Year 11 girls. She has estimated the median and the upper quartile, as shown in the table below.

Use the histogram to calculate an estimate of the lower quartile of the heights of the

Year 11 girls.

The diagram shows the simplified model of part of an engine. It shows a belt which runs around three circular cogs. The engine rotates Cog 1. Cog 1 rotates the belt, which then makes Cogs 2 and 3 rotate.

AB, CD and EF are straight sections of the belt. AB = 12 cm, CD = 34 cm and EF = 29 cm. The belt bends around the outer edges of the circular cogs, represented by the arcs BC, DE and AF. The dimensions of the cogs are: • radius of Cog 1 = 6 cm • radius of Cog 2 = 4.5 cm • radius of Cog 3 = 3 cm

What is the length of arc AF in terms of ?

Circle your answer.

Calculate the total length of the belt.

Give your answer in terms of in its simplest form.

Elen notices that when Cog 3 makes two revolutions, Cog 1 makes only one revolution, because the radius of Cog 3 is half the radius of Cog 1.

In one minute, Cog 3 makes 2400 revolutions.

Calculate the number of revolutions Cog 2 will make in one minute.