WJEC GCSE Numeracy Unit 1: Non-calculator Higher November 2020 question paper 3310U50-1

Rosie recorded the rainfall and the number of hours of sunshine each day last week.

Rosie says,

Is Rosie correct?

Yes No

You must give a reason for your answer.

At 3 p.m. each day last week, Rosie recorded the wind speed and the number of birds feeding in her garden.

On Wednesday last week, the wind speed at 3 p.m. was a quarter of that on Friday.

Complete the following table.

Albert, Terri and Gareth are going camping.

Albert, Terri and Gareth paid for a tent between them. The amount they each paid for the tent was in the ratio 1: 4: 6 respectively. Gareth paid £66.36 towards the tent.

Calculate the cost of the tent.

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

The charge to stay at a campsite has increased by 5% each year for the last two years. Two years ago, the charge was £24 per night for a large tent and three people.

Calculate the current charge per night for a large tent and three people.

You must show all your working.

The diagram shows the groundsheet of a tent.

The area of the groundsheet is 6.8 m₂. The width of the groundsheet is 2.2 m.

Calculate the overall length of the groundsheet.

The scale diagram below shows Haydn’s garden.

His garden is 27 metres long and 18 metres wide. The scale used is 1 cm represents 3 metres.

Haydn is planting a tree in his garden.

He decides that the tree must be planted: • 15 metres from the fence, • equidistant from the house and the fence.

Draw suitable lines on the diagram and show where Haydn should plant the tree.

There are 600 pupils in a school.

8 of these pupils are to be selected to discuss changes to the school uniform.

The headteacher has a spreadsheet of the names of all 600 pupils. There are 600 rows of pupil names in the spreadsheet, starting at row 1. There is one pupil name on each row.

The headteacher uses a systematic sampling method.

The first pupil selected on the headteacher’s list is a boy whose name is in the 25th row.

Give the row numbers in the spreadsheet of the other 7 pupils who would be selected.

Complete the table below.

Explain how the headteacher selected the first pupil.

Meinir is planning a charity event to be held at a hotel.

A section of a straight line graph showing the hotel charges for this event is shown below. These charges include a single payment for the room hire and the cost of one drink for each person attending.

Overall cost (£)

Meinir decides to pay the room hire cost herself. She decides to price the tickets so that she will be able to make £500 to give to charity.

Calculate the selling price of each ticket if Meinir plans the event for 50 people.

Calculate the selling price of each ticket if Meinir plans the event for 400 people.

A square piece of card measures 1 m by 1 m.

Calculate the area of this piece of card.

Give your answer in standard form in mm².

Some fabric shrinks when it is washed.

A piece of fabric is washed twice.

After the first wash, the area of the fabric is 75% of the area of the original piece of fabric. After the second wash, the area of the fabric is 90% of the area of the fabric after the first wash.

After these two washes, the area of the fabric is 2700 cm².

Calculate the area of the original piece of fabric.

A box for mints is to be made in the shape of a hexagonal prism.

The cross-section of the box is a regular hexagon. The volume of the box must be greater than 230 000 mm³.

Using the measurements above, show that this would make a suitable box for the mints.

You must show all your working.

Calculate how many bricklayers would be needed to lay 9000 bricks in 10 hours.

You must show all your working.

Give one assumption that you made in answering part (a).

Carwyn owns a car and a motorcycle.

Write down a formula for the value V, in pounds, of Carwyn’s motorcycle after he

has owned the motorcycle for t years.

Which one of the following best represents the graph of V against t?

Circle your answer.

15 patients had to wait up to 20 minutes.

Complete the scale on the frequency density axis.

Show that there were 80 patients in total who waited to see a doctor on this Tuesday.

Calculate an estimate of the inter-quartile range of the waiting times recorded.

You must show all your working.

Estimate of the inter-quartile range =_{……........ …………………} minutes

One Saturday, the waiting time for each patient was recorded. The inter-quartile range of the waiting times for this Saturday was smaller than the inter- quartile range for the Tuesday.

The management used this fact to conclude that waiting times were shorter on Saturdays than on Tuesdays. Was the management correct to come to this conclusion?

Yes No

Explain your answer.

Môr-Dda is a company that makes buoys for use at sea.

Môr-Dda makes 4 types of buoy. Each week, they make the following numbers of each type of buoy.

This week, Môr-Dda plans to take a sample of the buoys it makes to check on the quality of their production. It plans to take a stratified sample of 12 buoys, based on the type of buoy.

Calculate the number of each type of buoy that should be included in the sample.

You must show all your working.

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The design for a new buoy is shown below. It is made up of a cone attached to a hemisphere.

The base radius of the cone and the radius of the hemisphere are both 2 m.

The total volume of this new buoy is 10 m³.

Calculate the total height of the buoy.

Eleri’s cycle computer shows a speed-time graph for the first 60 seconds of her cycle ride.

Speed (ms⁻¹)

The cycle computer has also generated the following table, showing Eleri’s speed after every 10 seconds, for the first 40 seconds of her ride.

Calculate an estimate of the distance travelled in the first 40 seconds of Eleri’s cycle ride.

You must use 4 strips of equal width.

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After 40 seconds, Eleri’s speed remained constant.

Calculate an estimate of Eleri’s average speed over the first 60 seconds of her ride. Give your answer in ms⁻¹, correct to 2 significant figures.

You must show all your working.