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

Rhodri makes a statement about their kite being able to fly in strong wind,

“The length of the long diagonal must be at least 120% of the length of the short diagonal.”

Assuming Rhodri is correct, should their kite be able to fly in strong wind?

You must show all your working.

Sioned says,

“The best length for the tail on a kite depends on the area of the kite.”

Sioned refers to the table below that she has seen on the internet.

Area of the kite, A	Best length for the tail
A 500 cm2	2 m
500 cm2 A 900 cm2	2.4 m
900 cm2 A 1200 cm2	3.1 m
1200 cm2 A	3.5 m

Work out the best length of tail for Sioned and Rhodri’s kite.

You must show all your working.

A pasta factory in Italy produces 5 km of spaghetti per day. How many centimetres of spaghetti will this factory produce in 7 days?

Give your answer in standard form.

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

Agata is paid in pesos. The tax rates are as follows:

Agata’s total earnings before tax are 600 000 pesos. Calculate how much tax Agata is due to pay.

You must show all your working.

Gwilym is stacking 6 boxes in his garage. The height of his garage is 2.5 m, correct to the nearest 10 cm. 5 of Gwilym’s boxes each have a height of 40 cm, correct to the nearest 10 cm. The other box has a height of 55 cm, correct to the nearest 5 cm.

Calculate the maximum possible gap between the stack of 6 boxes and the garage

ceiling.

On 1st July every year, Trefor estate agents record the time from when a phone rings to when it is answered.

The time taken to answer the phone is recorded in seconds.

Trefor displays the data for their agents to see. The displays for 1st July 2018 and 1st July 2019 are shown below.

1st July 2018

Cumulative frequency

Use the diagrams on the previous page to answer the following questions.

What is the range of times taken to answer the phone for 1st July 2018?

Circle your answer.

101 seconds 80 seconds 78 seconds 106 seconds 104 seconds

What is the maximum possible range of times taken to answer the phone for 1st July 2019?

Circle your answer.

86 seconds 106 seconds 80 seconds 56 seconds 83 seconds

The manager of Trefor estate agents claims that there has been an improvement in the median time taken to answer the phone from 1st July 2018 to 1st July 2019. Is this true?

Yes No

You must show all your working.

Complete the following statements.

‘On 1st July 2018, 75% of the phone calls were answered within........

seconds.’

‘On 1st July 2019, 75% of the phone calls were answered within........

seconds.’

Mr Aston lives at 137 Ffordd Uchel.

He is ordering some new signs for his house and for his gatepost from a website.

All the signs available on the website are mathematically similar.

He selects a rectangular sign for the front of his house. It has a length of 42 cm and a height of 24 cm. The digits 1, 3 and 7 on the sign are all 18 cm high.

The rectangular sign Mr Aston is considering for his gatepost has a height of 20 cm.

Calculate the height of the digits 1, 3 and 7 on the sign Mr Aston is considering for his

gatepost.

Height of the digits 1, 3 and 7 is_........ cm

Mr Aston’s gatepost is 30 cm wide. Will the sign he is considering fit his gatepost?

Yes No

You must show all your working and give a reason for your answer.

Calculate an estimate of the percentage of passengers who were aged 60 or more.

On the graph paper opposite, draw a histogram to show the distribution of the ages of the

passengers.

The velocity-time graph below shows the velocity of an aircraft for the first 20 seconds of take-

Calculate an estimate of the acceleration of the aircraft at time 16 seconds.

Calculate an estimate of the distance travelled by the aircraft during the first 20 seconds of take-off. Use 5 strips of equal width.

You must convert your answer into miles. Give your answer as a decimal.

Distance is_{……………........ …………..} miles

The aircraft carries cargo. One customer wants to use the aircraft to transport a new product that is to be packaged in cuboid boxes, as shown below.

The boxes will meet the following conditions: • The boxes will be of width 8 cm and length 10 cm. • The length of the diagonal AB will be 14 cm.

Calculate the height of a box.

Nicola makes the hats by folding pieces of card that are in the shape of sectors of a circle. The hats are formed when the straight edges meet.

Calculate the sector angle Nicola uses in her design.

Nicola also makes party hats for adults. They are made from pieces of card that are sectors of a circle, with radius 24 cm and sector angle 150º.

Nicola cuts each sector of a circle from a sheet of rectangular card that measures 24 cm by 50 cm. Calculate the area of card that is wasted from each rectangular sheet.

Give your answer in terms of in its simplest form.

A company makes steel solids that each have a mass of 1 kg.

One of their solids is a square-based pyramid joined to a cuboid as shown below.

The base edges of the pyramid are of length 5 cm, and the height of the cuboid is 4 cm. The density of the steel used by the company is 8 g/cm³.

The complete solid has a mass of 1 kg.

Calculate the vertical height of the pyramid.