WJEC GCSE Numeracy Unit 1: Non-calculator Intermediate June 2019 question paper 3310U30-1

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

Sioned works in a grocery shop. She has made a poster for the window of the shop.

Sioned has forgotten to write the price of raspberries on the poster. Mr Thomas buys kg of strawberries and 1 kg of raspberries. He pays with a £20 note. He gets £2.55 change. Calculate the price of 1 kg of raspberries.

You must show all your working.

Dieter planted 8 sunflower seeds in May. He labelled the sunflowers A, B, C, D, E, F, G and H.

On 21st August, he measured the heights of all the sunflower plants in cm.

Dieter then drew a graph, as shown below.

Use the graph to answer each of the following questions.

What fraction of the height of the tallest sunflower is the height of the shortest sunflower?

Circle your answer.

What is the ratio of the number of sunflowers with heights less than 55 cm to the number of sunflowers with heights greater than 55 cm?

Circle your answer.

5: 3 3: 5 1: 3 3: 1 1: 1

Dieter’s friend, Glyn, also planted sunflower seeds. Glyn’s tallest sunflower grew to a height of 24 inches. Is this taller or shorter than Dieter’s tallest sunflower?

You must show all your working to support your answer.

Taller than Dieter’s tallest sunflower

Shorter than Dieter’s tallest sunflower

Aled and Gareth went on holiday to France.

The total cost of the holiday was £660. • Aled’s mother paid of the total cost. • Aled and Gareth shared the remaining cost in the ratio 1: 9.

Calculate how much each person paid towards the cost of the holiday.

Aled’s mother paid £_........

Explain how you could use your answers to check that they are correct.

Gareth’s luggage weighed 21.13 kg. This was over the maximum of 20 kg allowed.

Gareth removed items from his luggage so that its mass was: • as close to 20 kg as possible, • not greater than 20 kg.

From the following list of items, which two items did Gareth remove?

You must show all your working.

Before going on holiday, Aled made a conversion graph to help him understand prices in

Use Aled’s conversion graph to answer the following questions.

A camera costs £90.

How much is this in euros?

Camera costs_........ euros

A meal costs £25.

How much is this in euros?

Meal costs_........ euros

Gareth looked at exchange rates for buying euros. He recorded the exchange rates for the previous 60 days, as shown below.

£1 = b euros	Frequency
1.00 b 1.04	2
1.04 b 1.08	8
1.08 b 1.12	16
1.12 b 1.16	33
1.16 b 1.20	1

Gareth started to draw a frequency diagram to show this information.

Complete the frequency diagram.

Which is the modal group?

Circle your answer.

The distance a car will travel using 1 gallon of fuel is called its fuel economy.

The fuel economy of a number of cars with different engine sizes is shown below.

Fuel economy (miles per gallon)

Use the scatter diagram to answer the following questions.

State the fuel economy of the car with the largest engine size.

Fuel economy_........ miles per gallon

State the engine size of the car with a fuel economy of 42 miles per gallon.

Engine size_........ litres

Calculate the mean fuel economy of the 5 cars with the smallest engine sizes. [3]

Mean fuel economy is_........ miles per gallon

Draw, by eye, a line of best fit on the scatter diagram.

Rupert Shoes sells shoes online.

The designer has drawn a sketch of a new label to stick on the shoeboxes.

She takes the sketch to the printers. The table shows the costs for printing 100 labels.

How much will it cost to have 500 of the designer’s label printed?

You must show all your working.

Pairs of shoes are packed in shoeboxes. The dimensions of the shoebox used are given on the diagram below.

What is the area of the smallest face of the shoebox?

Circle your answer.

S = value of the sum of the 3 dimensions of the package F = value of the area of one of the largest faces of the package

How much does it cost Rupert Shoes to send the package? Give your answer in pounds.

You must show all your working.

A builder has drawn a plan for building 3 office blocks on a plot of land.

They are numbered 1, 2 and 3, as shown below.

The scale of the plan is 1 cm represents 20 m.

The builder is planning to plant a tree so that it is: • the same distance from Block 1 as it is from Block 2, • 80 metres from the top left hand corner of Block 3.

Mark the position for the planting of the tree.

What is the shortest possible distance between Block 2 and Block 3?

Sam’s Garden Centre buys trees to sell.

Sam bought 200 trees. Each tree cost Sam £25.

22% of the trees were not sold. Sam sold all the other trees for £40 each.

How much profit did Sam make?

You must show all your working.

The trees are planted in identical pots. They each have a uniform cross-section in the shape of a regular hexagon.

Show that these pots will tessellate.

A helicopter pilot is planning a route from Milford Haven to Ruabon and then on to Swansea.

To plan the flights, the pilot needs to find the bearings from a map.

Find the bearing of Ruabon from Milford Haven.

Find the bearing of Swansea from Ruabon.

The plan for the flight is shown below.

Calculate the total distance of the flight. Give your answer in miles.

You must show all your working.

Total distance is_........ miles

On average, the helicopter uses 0. 4 gallons of fuel per minute.

Use this information to calculate how many litres of fuel the helicopter would be expected to use for the flight planned in (b) (i).

You must show all your working.

You are given that:

1 gigalitre = 1 000 000 m³ 1 megalitre = 1 million litres

Lake Vyrnwy is a reservoir in mid Wales.

Lake Vyrnwy can release between 25 and 45 megalitres of water per day from the dam.

The lake also supplies water through underground pipes to another reservoir at a rate of 230 000 m³ per day.

How many litres are there in 25 megalitres?

Circle your answer.

Which is the best estimate for the volume of water passing through the underground pipes per hour ?

Circle your answer.

Estimate of average depth is_{………………........ ……………………} m

Maesystrad, Rhewlteg and Glanmawr are three colleges. Each college recorded the times Year 12 students took to travel to college. The results are displayed in the box-and-whisker plots below.

Which of the three colleges has the greatest range of times?

What is the range of times for this college?

College_{………………………........ ……………} Range_{………………………........} minutes

On average, in which college did Year 12 students have the longest travel times?

You must give a reason for your answer.

Which college has the greatest difference between the median and the lower quartile?

What is this difference?

College_{………………………........ ……………} Difference_{…………………........} minutes

Which of the three colleges has the greatest number of Year 12 students?

Give a reason for your answer.

Maesystrad Rhewlteg Glanmawr Don’t know

At another college, Wynne College, there are 240 students in Year 12.

The interquartile range of the times taken for these students to travel to college is 32 minutes.

How many of these students have travel times within this interquartile range?

75% of the Year 12 students at Wynne College take less than 55 minutes to travel to college. Complete the following statement.

‘25% of the Year 12 students at Wynne College take less than

........ minutes to travel to college.’

The table below shows the approximate land area and population for 5 countries in 2014.

Which of the 5 countries had a population density of approximately 100 people per km²

Circle your answer.

Argentina Austria Canada Pakistan United Kingdom

Which of these countries had the greatest population density?

Circle your answer.

Argentina Austria Canada Pakistan United Kingdom

Which of these countries had a population density that is approximately 4 times the population density of Canada?

You must show all your working.