WJEC GCSE Numeracy Unit 1: Non-calculator Higher June 2019 question paper 3310U50-1

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.

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

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

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.

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

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.

Bronwen is investigating the increase in the growth of algae on the surface of a pond.

The surface area covered by the algae is measured in cm². She finds the surface area covered by the algae t days after the start of her investigation is given by the following expression.

What surface area was covered by algae at the start of her investigation?

Circle your answer.

404 cm² 401 cm² 4 cm² 402 cm² 400 cm²

Bronwen calculated the surface area covered by the algae 5 days after the start of the investigation. She also calculated the surface area 7 days after the start of the investigation. By how much did the surface area covered by the algae increase between these two

times?

The voltage, V volts, of an electric circuit is given by the formula

V = IR,

where I is the current measured in amps, and R is the resistance measured in ohms.

During an experiment, • V was measured at 280 volts, correct to the nearest 10 volts, • I was measured at 0∙2 amps, correct to the nearest 0∙1 amps.

Calculate the least possible value and greatest possible value of the resistance R.

A tent company is designing a new 2-person tent.

The base of the tent is in the shape of a kite, as shown below. The width of the kite is 160 cm, and the two shorter sides are of length 100 cm. The point where the diagonals of the kite intersect has been marked O on the diagram below.

E is the highest point of the tent, and is 110 cm vertically above O. Part of the frame that supports the tent cover is a straight pole that goes from A to E.

Calculate the length of pole AE. Give your answer as a surd.

You do not need to simplify your answer.

Alun is a jeweller. He is designing a symmetrical pendant, as shown below.

The pendant will be made from solid silver, with a uniform thickness of 3 mm. In order to calculate the cost of making the pendant, Alun wants to calculate an estimate of the volume of the pendant. He has accurately drawn one of the symmetrical halves of the shape on graph paper.

Calculate an estimate of the volume of the whole pendant.

Use the graph opposite, with 6 strips of equal width.

Alun makes pendants that are mathematical shapes.

At the end of last month, Alun took a stratified sample of 30 of these 240 pendants to check their quality.

Calculate how many pendants of each shape were in Alun’s sample.

You must show all your working.

A new athletics stadium is to be built in Alltycapel.

Use your answer to (i) to calculate the area to be painted.

Give your answer in terms of in its simplest form.

A new running track is to be built at the stadium.

Athletes in a 200-metre race run in lanes. The inside line of one of the lanes is shown below. The inside line consists of: • a straight section of length 90 m, • an arc of a circle with radius 36 m. The length of this inside line is 200 m.

Show that the value of x is .