WJEC GCSE Numeracy Unit 2: Calculator-allowed Higher November 2016 question paper 3310U60-1

The Headteacher of Ysgol Bro Gwyn investigates building a new bike shed.

Bike sheds are built on a rectangular base of width x metres and length y metres.

The Headteacher is given a formula for working out the number of bikes, b, that can be stored in a bike shed that has a base of width x metres and length y metres.

The formula is as follows:

According to the details the Headteacher has been given, what is the formula for calculating the length, y metres, of a bike shed x metres wide that can hold b bikes?

Circle your answer.

The Headteacher decides to place signs around the school site to stop pupils using their bikes on grassed areas.

He introduces a new sign to pupils in the school newsletter. The size of the sign in the newsletter is shown below.

A mathematically similar new sign is placed near the side of the playing field.

It is 33.6 cm high.

How wide is this sign?

The wire window guard shown below is to be made.

The length of the sides of each small wire square shown is 3.3 cm.

Llinos considers the length of the diagonal of each small square.

She says,

Calculate the length of the diagonal of a small square.

Give your answer correct to 1 decimal place.

Calculate the area of the window guard.

You must show all your working.

Gwenda enjoys road running.

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

She keeps a record of her run each day this week.

Last week, her average speed for the week was 9.6 kilometres per hour. Calculate Gwenda’s percentage improvement in her average speed from last week to this week.

You must show all your working.

Percentage improvement is_{…………........ …………} %

The diagram shows the cross-section of one part of her run.

Calculate the angle of elevation of the road.

Gwenda runs on another section of uneven road from A to B. The rise in this section of the road is 300 metres. The angle of elevation of B from A is 10°.

Calculate an estimate of how far Gwenda has run.

State any assumption you have made.

What is the impact of your assumption on your answer?

Rhodri has carried out an experiment to measure the diameters of 20 spherical dust particles, in microns.

Here are his results.

Diameter, d (microns)	Frequency
1 d 2	2
2 d 4	6
4 d 5	8
5 d 9	4

Calculate an estimate of the mean diameter of a dust particle.

Rhodri measures the diameters of another 25 dust particles.

Rhodri is told,

‘The ratio of dust particles with diameters less than 4 microns to those with diameters greater than or equal to 4 microns is 7: 8.’

He finds this fact is true when he considers all 45 dust particles.

How many of the extra 25 dust particles have a diameter of less than 4 microns?

You must show your working.

Rhodri studies a cylindrical cell under his microscope. The height of the cell is 2 microns. The circumference of the cell is 5 microns.

Calculate the volume of the cell he sees under the microscope.

Give your answer in microns³, correct to 1 significant figure.

Volume is_{…………........ …………} microns³

Porth Ifan Hospital has made some changes to improve patient care.

A survey is to be used to find out the views of the hospital staff.

The table shows the total number of staff in each job type.

The survey is to be given to a sample of 75 staff.

Use a stratified sampling method to calculate the number of staff from each job type that should be asked to complete the survey.

You must show your working.

The hospital decides to take a random sample of its 120 doctors to select those needed for the survey. Use the following list of random numbers to select the first 5 doctors. You must start with the first number in the list, explaining clearly how you are using the

numbers to select the sample.

Here is some information from a 2014 geographical journal:

• Population of the UK: 6∙5 × 10⁷, correct to the nearest 1 000 000

• Area of the UK: 244 000 km², correct to the nearest 1000 km²

Using these figures, calculate the greatest possible value for the population density of the UK,

in population per km².

Calculate the angle that one of the triangular faces makes with the base of the pyramid.

The company knows that it costs 0∙08p per cm² to apply a chocolate covering.

Calculate the cost of applying a chocolate covering to all 5 faces of a biscuit.

A metal round-headed nail can be thought of as a cone sitting on top of a cylinder, which sits on top of a hemisphere.

A company produces round-headed nails of different sizes, but made of the same metal. Each nail has the following dimensions: • height of cone = 9r, • height of cylinder = 15r, • radius of the hemisphere = 12r, where r is the radius of the cylinder and the base radius of the cone.

A metal cuboid of volume 18 000 mm³ is melted down, and re-cast to form round-headed nails of size A, where r = 0∙4 mm.

Circle either TRUE or FALSE for each statement given below.

Huw wants to open a savings account.

Here are the details of savings accounts advertised by two local Welsh banks.

What is 1∙98% as a decimal?

Circle your answer.

0∙0198 0∙198 1∙098 1∙98 98∙0

Which of these two banks should Huw choose in order to gain the most interest per annum?

You must show your working.

Interest earned from savings is taxable, according to the table below.

Matthew is a higher rate taxpayer. Therefore, any savings interest he earns over £500 within a year is taxed at 40%.

On 1st May 2016, he invested £150 000 in a savings account that pays interest at a rate of 1∙98% per annum.

What is this interest rate per month, written as a decimal?

Circle your answer.

0∙0033 0∙00495 0∙00165 0∙0099 0∙0066

Savings interest is added at the end of every month.

Calculate the date when the interest that Matthew earned went above his annual tax-free limit, and the amount of tax he would have to pay on this interest if he had

closed the account on this date.

Date_........ Tax Matthew would have to pay_........