WJEC GCSE Numeracy Unit 2: Calculator-allowed Higher November 2019 question paper 3310U60-1

Rowan lives in New Zealand.

He is coming to Wales on holiday. The currency used in New Zealand is the New Zealand dollar ($). 1 New Zealand dollar = 100 cents.

The conversion rate at the exchange shop is $1 = £0.53. The exchange shop only has £10 and £20 notes.

Rowan only has $550 saved. He wants to exchange as close to $550 as possible. He asks for as few notes as possible.

Calculate: • how many of each British note Rowan gets, • how much he pays for his currency, correct to the nearest cent.

You must show all your working.

The picture shows a solid concrete step.

The step: • stands on horizontal ground, • has all of its edges vertical or horizontal, • has a uniform cross-section.

Draw a sketch of the plan view of the concrete step.

The volume of concrete in the step is 66 000 cm³.

The concrete to make the step costs 39p per litre. A builder charges a rate of £27 per hour. Any fraction of an hour is charged as that fraction of his hourly rate. (For example, half an hour is charged at half of £27.) It takes him 1 hour 20 minutes to make the step. There were no other costs.

Calculate the total cost of making the step.

Calculate the length of the step. Give your answer in cm.

You must show all your working.

Calculate an estimate of the mean number of mugs these people have in their

cupboards.

Calculate the volume of the tea in the mug.

The diameter of each wheel on Finbar’s skateboard is 6.4 cm. He uses his skateboard to go to visit his friend Sab. Sab lives 2340 metres from Finbar.

What assumption did you make in answering (a)(i)?

Calculate an estimate of the length of the plank that is to be placed diagonally.

Give your answer in metres.

What assumption did you make in calculating the length of the plank that is to be

placed diagonally?

cost of 1 horizontal plank: cost of 1 diagonal plank: cost of 1 end plank

= 3: 4: 5

An end plank costs £8.55.

Calculate the total cost of the planks needed to make the gate.

Dafydd carries bags of gravel on the back of his lorry.

Each bag of gravel has a mass of 90 kg, correct to the nearest 5 kg.

The maximum mass the lorry can carry without overloading is 7500 kg. However, this measurement is only correct to the nearest 100 kg.

Calculate the maximum number of bags that the lorry is guaranteed to be able to carry without overloading.

You must show all your working.

Maximum number of bags that the lorry is guaranteed to be able to carry is_........

Llinos walks to the summit of Snowdon, passing the lake called Llyn Glaslyn.

Her height above sea level increases by 485 m from Llyn Glaslyn to the summit.

From the summit, she sees two small boats on Llyn Glaslyn. Both boats are in the same direction from the summit. The angles of depression of the two boats are 41º and 27º, as shown in the diagram.

Calculate the distance between the boats.

Show that 9 engines would be able to pump 143 000 gallons of water in under

9 minutes 15 seconds.

Give one possible reason why the 9 engines may not be able to pump 143 000 gallons of

water in under 9 minutes 15 seconds.

A company makes Welsh flags in mathematically similar sizes.

Two of their similar flags are shown.

The area of the larger flag is 96% greater than the area of the smaller flag. The height of the smaller flag is 40 cm.

Calculate the height of the larger flag.

On 1st January 2017, Samantha and Dyfan invested money into different savings accounts.

They did not make any further payments into their accounts or withdraw any money from their accounts.

Samantha invested £2000 in a savings account that paid interest at a rate of 0∙95% every 3 months.

Show that Samantha would have £2038.18 in the account after 6 months.

Dyfan invested £3000 in a savings account that paid interest at a rate of 1∙02% every 3 months. Interest is paid on the last day of each 3-month period.

Calculate the date when Dyfan will first have over £3600 in his account.

Date when Dyfan will first have over £3600 in his account is_{…………........ ……………}

Two farmers have bought some farmland between them.

The farmland is in the shape of a quadrilateral ABCD, as shown below.

The farmers want to divide the farmland equally by building a straight fence.

One of the farmers has suggested building the fence from A to C.

Show that this does not divide the farmland equally.

To divide the land equally, the fence is built from A to F where CF = 17∙9 m. To construct the fence, posts are placed at A and F. Other posts are then located along AF, so that the posts are no more than 3 m apart.

Calculate the smallest number of posts needed, including the posts at A and F.

Laura and Matthew are buying a house priced at £150 000.

In order to buy the house, they will need to have a mortgage.

A mortgage is a loan that is paid back over a number of years.

They have saved a deposit of £15 000. They need a mortgage of £135 000.

A bank has offered them a mortgage of £135 000 at an interest rate of 2∙4% per annum, with interest added monthly.

To calculate the monthly payments needed in order to pay back the mortgage, they use the following formula:

where:

M is the amount of each monthly payment, P is the mortgage needed, r is the monthly interest rate as a decimal, n is the number of years taken to pay back the mortgage.

The annual interest rate is 2∙4%. What is the monthly rate, as a decimal?

Circle your answer.

0∙24 0∙024 0∙00002 0∙002 0∙2

Laura and Matthew are considering whether to take out a mortgage over 25 years or 30 years. They have correctly calculated their monthly payments to be £598.86 when paying back the mortgage over 25 years. How much more will it cost in total to pay back the mortgage over 30 years than over

25 years?