OCR GCSE Maths Paper 3: Calculator Foundation November 2017 question paper J560/03

Use one of these words to complete the sentence.

The diagram shows a triangle ABC.

Mark angle CAB.

Write down all the possible values of n.

Calculate the volume of this cuboid.

In this cuboid all lengths are in centimetres.

The cuboid has a volume of 320 cm³.

Find the value of k.

Fill in each missing number.

24 –........ = 36

The length of a line is 10.4 cm, correct to 1 decimal place.

Write down the shortest possible length of the line.

To find the number in a square, multiply the numbers in the two circles connected to it.

Fill in the missing numbers.

Lucy and Ben share £42. Lucy’s share is £30.

Write the ratio Lucy’s share: Ben’s share in its simplest form.

The ratio 2.5 metres to 70 centimetres can be written in the form 1: n.

Find the value of n.

Water flows at a steady rate from a tap. It takes 50 seconds to fill a 5 litre watering can from this tap.

The rate at which water flows from the tap is halved.

Complete.

Find the rate at which the water is now flowing from the tap. Give your answer in cubic centimetres per second (cm³/s).

A hotel manager asked some people to choose their favourite breakfast fruit juice. They each chose one from Orange, Apple or Grapefruit.

• 20 men chose Orange

• Equal numbers of men chose Apple and Grapefruit.

• 10 women chose Orange

• Twice as many women chose Apple as Grapefruit.

Use this information to complete the frequency tree.

In one week 200 men have breakfast at the hotel.

How many men may be expected to drink Orange?

Give one reason why the number of men who drink Orange in this week may be different to your answer to part (b)(i).

The average mass of a man is 84 kg and of a woman is 70 kg.

A lift can safely carry 630 kg.

To find how many people the lift can safely carry, Dan divides the safe total mass by the average mass of a person.

630 ÷ 77 = 8.18...

How has the average mass of a person, 77 kg, been worked out?

Dan decides that his answer shows the lift can safely carry 8 people.

Explain why he is wrong and give an example, with working, to support your answer.

Elsie changes to a decimal.

This is her working.

Where a line of working is wrong, write the correct working beside it.

Ali has 1 litre of squash. He always mixes 0.05 litres of squash with 200 ml of water to make a glass of drink.

Find the total volume of the drink that Ali can make. Give your answer in litres.

Write 7 × 7 × 7 × 7 as a power of 7.

Complete this working to write 4³ as a power of 2.

4³ = 4 × 4........

so 4³ = 2 × 2 × 2 ×........

Write these numbers in order, starting with the largest.

8.1 × 10¹ 1.02 × 10³ 9.83 × 10^–2 3 × 10²

largest

A company tests a new battery for an electric car. The distance the car travels, d km, and the charge left in the battery, C %, are measured.

Some measurements are shown in the table.

Plot these values on the grid and use them to draw a straight line.

Use your line to estimate the greatest distance the car will travel.

What assumption is made when estimating the greatest distance?

For your line in part (a), find

the gradient,

the C-axis intercept.

Use your answers to part (c) to write down the equation of your graph.

Give your equation in the form C = ad + b.

Use your equation to find the value of C when d = 210.

Comment on your answer.

Find the coordinates of the point where y – 2 x = 1 crosses the y-axis.

The diagram shows the graph of y = 3 x + c, where c is a constant.

Find the value of k.

A company makes sweets. The sweets are put into packets.

Here are some facts.

Calculate the mean number of sweets in one packet.

Sweets are made on 288 days each year.

Calculate the number of sweets made each year. Give your answer in standard form.

The company has 152 machines making the sweets. Each machine operates for 15 hours each day.

Calculate the number of sweets made by one machine each hour. Give your answer as an ordinary number correct to the nearest 10.

State one assumption you have made in part (c)(i).

A shop records the time taken by its customers to complete a purchase on its website. The results from one day are summarised in this table.

Calculate an estimate of the mean time taken.

Explain why it is not possible to use the information from this table to calculate the exact value of the mean time taken.

Luka invests £1500. At the end of the first year, 2% interest is added. At the end of the second year, after interest has been added, the investment is worth £1606.50.

Show that 5% interest has been added at the end of the second year.

Two bags each contain only red counters and yellow counters.

In Bag A, the ratio of red counters to yellow counters is 1: 4.

Sharon says

The proportion of the counters that are red is the same in both bags.

Explain why Sharon is not correct.

The number of counters in the two bags is the same.

Complete the table below to show how many counters of each colour could be in the bags.

In another bag, Bag C, the ratio of red counters to yellow counters is 3: 4. If 3 of the red counters are removed from Bag C, the ratio of red counters to yellow counters is 3: 5.

How many yellow counters are in Bag C?

PQRS is a square. G is the midpoint of PQ and H is the midpoint of QR. Triangle GHS is shaded.

Find the ratio shaded area: area of square in its simplest form. Show all your working.

The diagram shows a scale drawing of a park, ABCD.

Scale: 1 cm represents 10 m

A straight water pipe runs across the park. The pipe runs equidistant from DA and DC.

Construct, using compasses and ruler only, the position of the water pipe.

You must show all your construction lines.

A straight path connects the entrance to the exit. This path is perpendicular to CB.

Construct, using compasses and ruler only, the position of the path.

Leave in all your construction lines.

Find the actual length of the path, in metres.

Two congruent, isosceles triangles are joined, as shown, to form a parallelogram. The largest angle of the parallelogram is 110°.

Write two equations. Solve them to find the value of a and the value of b.

The middle number of three consecutive whole numbers is 2 a.

Prove that the sum of these three numbers cannot be 250.