WJEC GCSE Numeracy Unit 1: Non-calculator Higher November 2017 question paper 3310U50-1

Which school and year group has an approximately equal split between the 3 categories: • pupils who cycle to school, • pupils who would like to cycle to school, and

• other pupils?

School:_........ Year Group:_........

Circle either TRUE or FALSE for each of the following statements.

In January 2011, there were 1200 miles of National Cycle Network (NCN) routes in Wales. In January 2016, there were 1400 miles of NCN routes in Wales.

If the number of miles of NCN routes in Wales were to continue to increase by the same number of miles per year, how many miles of cycle routes would there be in

January 2018?

Why is your answer in (i) unlikely to be an accurate estimate of the number of miles

of NCN routes in Wales in January 2018?

Why does the graph not pass through (0, 0)?

What is the increase in the daily running costs for each additional dog that is kept in the

kennels?

Freda also runs a dog kennels. The cost of keeping 20 dogs in her kennels for one day is £130. She knows that as the number of dogs increases, the overall cost increases at the same rate as in William’s kennels.

Display this information on the graph paper opposite.

Find the cost of keeping 30 dogs for one day in Freda’s kennels.

Meirion is a window cleaner. From Monday to Friday, he records how long he spends cleaning windows for each of his customers.

He draws a cumulative frequency diagram to display the findings.

Use Meirion’s cumulative frequency diagram to find the median and interquartile

range of the times he spends cleaning windows for each of his customers.

Interquartile range_........ minutes

Meirion looks back at his raw data. He finds that the median is actually 17 minutes 30 seconds. Why is there a difference between the median from his cumulative frequency

diagram and the actual median from his raw data?

Meirion is looking at the time it took to clean individual customers’ windows. Find the number of customers whose windows took between 10 and 15 minutes to clean.

Meirion thinks that for approximately 80% of his customers, he cleaned their windows in less than 20 minutes. Is Meirion correct?

You must show all your working.

Megan Pugh’s electricity bill is shown below.

It covers the period May, June and July 2017.

Megan Pugh 203 Stryd Bryntor

Amount to pay: £112.80 + £5.64 = £118.44

On 1 August 2017, the charge per unit for electricity was increased by 5%. What is the increased cost per unit of electricity?

Circle your answer.

20.5p 21p 21.5p 22p 22.5p

In this part of the question you will be assessed on the quality of your organisation, communication and accuracy in writing. Megan wants to calculate her next 3-monthly electricity bill. She knows the following: • Her meter reading on 31 October 2017 was 14400. • The charge per unit for electricity has increased by 5% since her last bill. • The standing charge has increased by 20p per month since her last bill. • VAT remains at 5%. On 31 October 2017, Megan had £470 in her bank account. After paying her next 3-monthly electricity bill, will Megan be able to buy a new washing machine costing £330?

You must show all your working.

Complete each of the following statements.

‘Apples from the_........ apple tree have the least median width.

The median width of apples recorded for this tree is_........ mm.’

‘The range of the widths of apples recorded for the Gala apple tree

is_........ mm.’

‘The_........ apple tree has apples with the greatest interquartile range of widths.

The interquartile range of the widths of apples recorded for this tree

is_........ mm.’

Which tree has a higher proportion of larger apples?

You must give a reason for your answer.

The times taken by a group of pupils to answer a numeracy question were recorded. The histogram below shows some of the results.

The remaining 16 pupils took between 25 and 35 seconds to answer the question.

Complete the histogram.

What is the greatest possible range of times taken by the pupils to answer the question?

Circle your answer.

50 seconds 4 seconds 40 seconds 45 seconds 35 seconds

Calculate the total number of pupils that were in the group.

Gareth was one of the pupils in the group. He says,

“The time I took to answer the question was 18 seconds. This means I was in the fastest 50% of the pupils.”

Explain how Gareth’s statement could be true.

You must use calculations to justify your answer.

Explain how Gareth’s statement could be false.

The cost of the paint needed for the smaller road sign is £1.60.

Calculate the cost of the paint needed for the larger sign.

The selling price of the smaller road sign is £12.00. This selling price was calculated from the cost price by: • adding a profit of 25%, • then adding VAT at 20%.

Calculate the cost price of the smaller road sign.

You must show all your working.

Two runners, Catrin and Delyth, start a race at the same time.

The velocity-time graph shows their velocities over the first 5 seconds of the race.

After the start of the race, what was the earliest time that Catrin’s acceleration was

0 m/s²?

Use the trapezium rule to calculate an estimate of the distance Catrin travelled in the first 5 seconds of the race. Use Catrin’s velocities at times t = 0, t = 1, t = 2, t = 3, t = 4 and t = 5.

You must show all your working.

Calculate an estimate of how far Catrin was ahead of Delyth after 5 seconds.

Explain why your answer to (c) (i) is an underestimate.

The diagram below shows two similar flasks for measuring liquid.

The flasks are in the shape of cones. The smaller flask has a base radius of 8 cm and a vertical height of 20 cm. The larger flask has a base radius of 14 cm.

Calculate the vertical height of the larger flask.

The larger flask is now partly filled with liquid up to a vertical height of 15 cm.

Calculate the volume of liquid in the flask.

Give your answer in terms of .

A company is building a new headquarters.

The diagram below shows the ground plan of the new headquarters.

The plan consists of a square and a sector of a circle.

Using the information given in the diagram, calculate the radius of the sector of the circle.

The square is to be covered in concrete.

Calculate the area of the square.

Expand any brackets, and simplify your answer.