WJEC GCSE Numeracy Unit 1: Non-calculator Higher June 2024 question paper 3310U50-1

Some houses in a village have new driveways laid by DriveDown.

The scatter diagram shows the area and cost of each driveway.

The measurements of Gwenda’s driveway are shown below.

Consider the exact area of Gwenda’s driveway. Calculate an estimate of how much it would cost Gwenda to have a new driveway laid by DriveDown.

You must show all your working.

Tanya’s driveway covers an area of 23 m². She decides to have her driveway repaired instead of having a new driveway.

Tanya thinks the repair will cost her 40% of the estimated cost of having a new driveway laid by DriveDown. She has budgeted £575 for the repair of her driveway. Will Tanya’s budget cover the cost of repairing her driveway?

Yes No

You must show all your working and give a reason for your answer.

Josif produces a scale drawing to show where he wants a tree planted in his garden.

Scale: 1 cm represents 0. 5 m

He writes out instructions to show where the tree is to be planted.

Which two of the following instructions describe where the tree is to be planted?

A. The tree must be 2 m from the hedge. B. The tree must be 1 m from the hedge. C. The tree must be 6 m from the hedge. D. The tree must be 3 m from the hedge. E. The tree must be 1 m from the wall.

F. The tree must be equidistant from the hedge and the fence. G. The tree must be equidistant from the hedge and the wall. H. The tree must be equidistant from the wall and the house. I. The tree must be equidistant from the hedge and the house.

J. The tree must be equidistant from the wall and the fence.

The two instructions are_........ and_........

Calculate the percentage profit the garden centre makes from buying and selling

one tree.

The garden centre buys 10 of these trees to sell. One of the trees gets damaged and cannot be sold. The other 9 trees are sold. Calculate the overall percentage profit or loss the garden centre makes from selling these trees. You must state whether your answer is a profit or a loss.

You must show all your working.

Of the 10 trees bought by the garden centre, what is the minimum number that need to be sold to ensure that the garden centre makes a profit?

Circle your answer.

5 6 7 8 9

On 1st June last year, 200 customers used cash to pay at Shop Lil. The cumulative frequency diagram represents the time each of these 200 customers waited to be given change at the checkout.

How many of these customers waited between 30 and 50 seconds for their

change?

Use the graph to estimate the median time these 200 customers waited for their change.

Circle your answer.

24 seconds 32 seconds 38 seconds 80 seconds 100 seconds

Calculate the fraction of these 200 customers who waited 40 seconds or longer for their change.

Give your answer in its simplest form.

On 1st June this year, the manager at Shop Lil drew a box-and-whisker plot of the times 200 customers waited for their change at the checkout.

Based on the results of these 200 customers, the manager made the following statements. Complete the statements.

“On 1st June this year, 50% of our customers were given their change in

........ seconds or less.”

“On 1st June this year, the interquartile range of the times taken to give

customers their change was........ seconds.”

Consider the 50 customers waiting the longest times to get their change on 1st June last year and this year. Has the speed of giving change at the checkout improved since last year?

Yes No

You must give a reason for your answer.

What was the increase in the population of Wales between 1977 and 1998?

Circle your answer.

Estimate the population density of Wales in 2015.

Population density of Wales in 2015 was_........ people / km²

Cardiff is the largest city in Wales. In 2018, the population of Cardiff was approximately 360 000. The population of Cardiff increased by 20% from 1991 to 2018.

Calculate the population of Cardiff in 1991.

Most aircraft are held together with metal rivets.

The rivet used on one type of aircraft is shown below. It can be thought of as a cylinder connected to a hemisphere.

The cylinder has a diameter of 6 mm and a length of 9 mm. The hemisphere has a diameter of 12 mm.

Calculate the volume of the rivet.

Give your answer in terms of in its simplest form.

The manufacturer plans to reduce the length of the cylindrical part of the rivet from 9 mm to 8 mm.

Calculate the fractional reduction in the volume of a rivet this would produce.

The headteacher of Ynysgorwen School wants to know how long it takes pupils to travel to school.

The results for a sample of 120 pupils are shown in the table below.

Time taken, t (minutes)	Frequency	Frequency density
0 t 10	34	3∙4
10 t 20	40	........................................................
20 t 35	24	........................................................
35 t 50	18	........................................................
50 t 70	4	........................................................

Complete the frequency density column.

Draw a histogram to display this data.

Frequency density

Calculate an estimate of the median travel time for the sample of pupils.

What is the greatest possible median travel time for the sample of pupils?

Sian ran a 100-metre race.

The graph below shows Sian’s speed over the first 8 seconds of the race. Sian then ran the rest of the race at a constant speed of 8 m/s.

Speed (m/s)

By first using the trapezium rule with 4 strips of equal width for the first 8 seconds, estimate the total time it took Sian to run the 100-metre race.

You must show all your working.

Sian’s total time to run the 100-metre race =_{……………........ …………} seconds

Geraint has bought a new front cog for his bike.

The cog has a mass of 150 g, correct to the nearest 10 g. The cog has been made from a metal that has a density of 3 g/cm³, correct to the

This picture shows part of Geraint’s bike.

A simplified diagram of the cogs and the chain is shown below.

X and Y are the centres of the cogs and XY is a line of symmetry. BC and AD are straight sections of the chain. The larger cog has a radius of 12 cm. The smaller cog has a radius of 2 cm.

Calculate the total length of the chain.

7 water pumps can fill a swimming pool in 12 hours. These 7 water pumps work together at the same rate.

When the pool is empty, the 7 pumps are turned on. After working for 3 hours, 2 of the pumps are turned off. The other pumps carry on working until the swimming pool is full.

Calculate how long in total it takes for the swimming pool to be filled.

Give your answer in hours and minutes.

Total time taken for the pool to be filled =_{……........ ……….} hours_{……........ ……….} minutes