WJEC GCSE Numeracy Unit 1: Non-calculator Higher November 2023 question paper 3310U50-1

Rhodri is organising a 21st birthday party.

Confetti for the party is packed in small boxes. Each box is in the shape of a triangular prism. The cross-section of each box is an isosceles triangle. The measurements are shown on the diagram below.

Show that the perpendicular height of the cross-section of a confetti box is 40 mm.

You must show all your working.

This is the label on a confetti box..

Calculate the volume of a confetti box to show that the statement on the label is

correct.

Rhodri finds 2 venues that arrange party nights.

Rhodri calculates the total cost of organising the party at each venue. He finds that the total costs are the same. For how many people is Rhodri planning the 21st birthday party?

You must show all your working.

A supermarket sells 2 varieties of washing powder: Dazzle and Sparkle.

Both washing powders are sold in 3·3 kg packets. The ratio of the prices of the washing powders is as follows.

Dazzle: Sparkle = 9: 10

The price of a 3·3 kg packet of Sparkle is £4.40.

Calculate the cost per kilogram of Dazzle.

You must show all your working.

Anwen has an outdoor mobile coffee stall.

Give the coordinates of the point through which a line of best fit should be drawn.

Hence, draw a line of best fit on the scatter diagram.

Coordinates of the point are (_........ ,_........ )

Estimate the number of cups of coffee that Anwen expects to sell on a day when the rainfall is 2·0 mm.

Use your line of best fit to find your estimate.

Number of cups of coffee is_........

The height of the storage space under Anwen’s serving counter is 97·5 cm, correct to the nearest 0·5 cm.

Anwen is going to buy a recycling bin of height exactly 97·3 cm. Can Anwen be certain that she can fit this bin under her serving counter?

Yes
No
Can’t decide

You must show working to support your answer.

Giovanni has a takeaway pizza van. He sells whole pizzas and slices of pizza from his van.

For the last 3 days, he has timed how long it takes to complete the food order for each of his customers. Giovanni recorded his results in the table below.

Complete the cumulative frequency table and the cumulative frequency diagram.

Time, t (minutes)	Frequency	Cumulative frequency
3 t 5	8	8
5 t 7	24	32
7 t 9	74	106
9 t 11	40	..............................
11 t 13	14	..............................

Cumulative frequency

Use your cumulative frequency diagram to give the best estimates for the answers to each of the following questions.

Find the median time taken to complete a food order.

The median time is_........ minutes.

Giovanni is concerned that food orders are taking too long to complete. He says,

“Only 25% of the food orders are completed in under_........ minutes.”

Use one of the five values below to complete Giovanni’s statement.

6·4 6·6 7·2 8 9·6

For the last 3 days: • Giovanni spent £180 on ingredients • he spent £220 on the running costs for the pizza van • he received a total of £700 from the food orders.

Calculate Giovanni’s percentage profit.

Eva grows three varieties of organic potato on her farm: Maris Piper, King Edward and Desiree.

She weighs and records the masses of 400 potatoes of each of the 3 varieties.

Eva constructs box-and-whisker diagrams for the masses of the potatoes weighed.

Complete each of the following statements.

The_........ potatoes have the highest median mass.

The median mass of these potatoes is_........ g.

The range of the masses recorded for the Maris Piper potatoes

In the future, Eva wants to grow potatoes that are quite similar in size.

Use the box-and-whisker diagrams to advise Eva which of these three varieties of

potato she should grow.

Select which variety of potato she should grow.

Maris Piper
King Edward
Desiree

Select the measure you used to help you decide.

Median
Interquartile range
Lower quartile

Select a reason for your choice of measure.

The measure is greater than for the other 2 varieties

The measure is less than for the other 2 varieties

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

An old postage stamp has a width of 2 cm and a height of 2·4 cm. Frank makes a poster that is mathematically similar to the postage stamp, as shown below.

Postage Stamp
Poster

He places a thin tape along the four edges of the poster. Calculate the total length of this tape, correct to 1 significant figure.

You must show all your working.

Answer the following questions using information from the table.

Calculate the percentage of track in the USA that was electrified in 2020.

Calculate the fraction of the whole world’s railway track that was electrified in 2020.

Give your answer in its simplest form.

On average, Hywel’s car travels a distance of 11 miles per litre of petrol used.

The petrol tank in his car can hold 70 pints of petrol. At Hywel’s local garage, it would cost him £56 to fill the tank from empty. Hywel’s petrol tank is full. At his local garage, he spends £28 on petrol. Calculate the distance Hywel can travel in the car before the tank is empty.

You must show all your working.

Akago is a food delivery company.

5 Akago delivery vans can deliver food to 100 houses in 4 hours.

Akago wants to: • increase the number of deliveries to 240 houses • shorten the total delivery time to 3 hours.

Calculate the number of delivery vans that would be needed to deliver food to 240 houses in 3 hours.

You can assume that all vans deliver food to all the houses at the same rate.

Anisa is comparing the ages of the populations of Cardiff and Wrexham in July 2019.

She has used published data to draw these two histograms.

In July 2019, the biggest difference between the populations of Cardiff and Wrexham was in the number of 20-to 30-year-olds. Calculate how many more 20- to 30-year-olds there were in Cardiff than there were in

Wrexham.

Anisa has used her histograms to carry out data analysis. Some of her results are shown in the table below.

Use Anisa’s histogram to calculate an estimate of the median age of the population of

Cardiff in July 2019.

The graph below shows the depth of water in a reservoir during a 200-day period.

For approximately how many of the 200 days was the depth of water in the reservoir decreasing?

Circle your answer.

120 days 200 days 80 days 100 days 40 days

Use 5 strips of width 40 days to estimate the area under the curve. Hence, calculate an estimate of the average depth of the water during this 200-day

period.

Estimate the rate of increase in the depth of the water on the 60th day of this period.

Give your answer in its simplest form.