WJEC GCSE Numeracy Unit 1: Non-calculator Higher November 2016 question paper 3310U50-1

The scale diagram opposite shows an Eisteddfod camping field.

The camping field is 100 metres long and 80 metres wide.

The scale used is 1 cm represents 10 metres.

A barbecue area is to be built on the camping field.

The barbecue area must be • nearer to the river than to the opening to the Eisteddfod camping field, • nearer to the river than to the hedge, • more than 30 metres from the corner of the field where the hedge meets the river.

Draw suitable lines on the diagram and shade the region where the barbecue area could be

built.

1 cm represents 10 metres

Lotty and Rafael decide to enter a prize draw. They agree to share any money they win in the ratio 2: 3 respectively. After winning a total of £2000, they think again and decide that Lotty’s share should be increased by 30%.

Rafael thinks that his share will be reduced by 30%.

Without any calculation, explain why Rafael’s thinking is incorrect.

Calculate the amount of money Lotty wins after the decision is made to increase

her share.

Find the ratio that is now used to share the money between Lotty and Rafael.

Express your answer in its simplest form.

Lotty’s winnings: Rafael’s winnings =_........ :_........

In another prize draw, it was planned to give £5000 as the first prize. To make it more popular, the organisers decide to increase this first prize by 26%.

The most efficient method of calculating the amount of the increased first prize is

The second prize was planned to be £3000, but it is now decided to decrease this prize by 6%.

Write down the most efficient method of calculating the amount of the decreased second prize.

You are not expected to work out the answer.

Luc wants this new desk for his bedroom.

The desk is to fit on the straight wall between his wardrobe and his bookcase.

Luc has measured the length of • the wall, which is 600 cm, correct to the nearest 10 cm, • the bookcase, which is 147 cm, correct to the nearest 1 cm, • the wardrobe, which is 250 cm, correct to the nearest 1 cm.

What is the greatest possible length of the wall?

Circle your answer.

600 cm 605 cm 645 cm 610 cm 650 cm

Can Luc be certain that this desk will fit in the space available?

You must • show all your calculations, • give the greatest or least bounds of any measurements used in calculations or comparisons,

• give a reason for your answer.

140 girls were asked how long they spent revising for their GCSE examinations. The cumulative frequency diagram shows the results.

Cumulative frequency

Estimate the median time the girls spent revising.

Circle your answer.

35 hours 40 hours 48 hours 52 hours 70 hours

Calculate the number of girls who spent between 40 and 50 hours revising.

Circle your answer.

0 girls 5 girls 10 girls 15 girls 20 girls

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

140 boys were asked how long they spent revising for their GCSE examinations. The cumulative frequency diagram below shows the results.

Cumulative frequency

Trefor makes two statements.

Are both Trefor’s statements correct?

Show calculations and give reasons to support your answers.

Statement 1:_........

Statement 2:_........

Petra is organising a prom for her year group. The number of people attending the prom is likely to be between 20 and 80.

The cost of holding the prom at Hotel Afonwen would be as follows. • Hire of the room: £100 • Food: £15 per person • Welcome drink on arrival: £3 per person • Decorations: £2 per person

Draw a graph to illustrate the total cost of holding the prom for between 20 and 80 people.

Use the graph paper below.

Petra decides to share all the costs equally between the people attending.

• Let £P be the price paid per person. • Let N be the number of people attending the prom.

Write a formula for P, in terms of N.

Hiring a larger room at Hotel Afonwen costs £200. The cost per person for food, welcome drinks and decorations remains the same.

If the total cost is £2240, how many people attend?

The following box-and-whisker plots illustrate the daily rainfall for April 2016 in Trefwen and in Nawrby.

April rainfall in Trefwen

April rainfall in Nawrby

Iona is going on holiday next April. She is hoping for good weather, with hardly any rain. She decides to go to Nawrby. Give a reason to support Iona’s decision.

Include values for both Trefwen and Nawrby.

During which quarter-hour period was Siân’s acceleration the greatest?

At about what time did Siân stop accelerating?

Siân usually finds cycling at a velocity of 18 km/h very comfortable.

Express 18 km/h in metres per second.

Using her velocities at 14:00, 15:00 and 16:00, calculate an estimate for the total distance

Siân travelled between 14:00 and 16:00.

Distance travelled_{………........ ………} km

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing. Siân estimated the distance she travelled between 16:00 and 17:00 as 5 miles. Is Siân’s estimate reasonable?

You must justify your answer and show your working.

The Big Fish Cymru annual fishing competition is held on the west coast of Wales.

Information about last year’s competition is displayed in the Big Fish Cymru booklet. A section of this booklet is shown below.

Last year, how many of the fish caught had a mass of less than 250 g?

Last year, the final angler to catch their first fish did so after 3 hours.

How many other anglers took more than 3 hours to catch their first fish?

The number of anglers taking part this year was three times as many as took part last year.

How many anglers took part in the competition this year?

Number of anglers this year was_........

The median mass of the fish caught this year was 0.9 kg.

What is the difference, in kg, between the median mass of the fish caught this year and

the median mass of the fish caught last year?

Difference in mass is_........ kg

Approximately 10% of the anglers this year caught their first fish within 1 hour.

How does this percentage compare with last year’s percentage?

You must show all your working.

Do you think it is fair to compare last year’s competition results with this year’s competition results?

You must give a reason for your answer.

The shaded part of the diagram below shows the top surface of an engine part.

The measurements taken by a motor engineer are: • reflex angle BOC = 240°, • AO = OD = 6 cm, • BO = OC = 3 cm.

The top surface of the engine part is to be painted. The paint costs 15p per cm².