OCR GCSE Maths Paper 5: Non-calculator Higher November 2024 question paper J560/05

Work out.

Work out the size of an exterior angle of a regular hexagon.

Use your answer to part (a) to write down the size of an interior angle of a regular hexagon.

The graph shows the time, in minutes, taken by some pupils to travel to school on Tuesday.

Less than 10 10 to 30 More than 30

Time (minutes)

Find the percentage of these pupils that took more than 30 minutes to travel to school.

On Tuesday the number of pupils taking 10 to 30 minutes to travel to school was 25% less than on Monday.

Find the number of pupils taking 10 to 30 minutes to travel to school on Monday.

An electrician charges £30 per visit plus £22 per hour.

Write an expression for the cost, in £, charged by the electrician for one visit lasting n hours.

Anika has a shelf 79.6 cm long. She has many books, each of width 3.4 cm. Anika puts two paperweights, each of width 5 cm, and the maximum possible number of books on the shelf.

Work out the amount of space on the shelf that is left over. You must show your working.

Jack has ten cards numbered 11 to 20. He picks a card at random.

Jack says,

In these ten cards, there are two multiples of 5 and five even numbers. Therefore, the probability that I pick a card that is a multiple of 5 or an even number is

Describe the error in Jack’s method and give the correct answer.

The correct answer is........

Felix makes craft figures at a constant rate. He can make 5 craft figures in 40 minutes.

Find the number of craft figures Felix can make in 4 hours.

Darcie makes craft figures 10% quicker than Felix.

Work out how long Darcie takes to make 15 craft figures.

Here is a question and an incorrect answer.

Explain why the answer is not correct.

Solve.

3 x + 12 = 9 - 7 x

A straight line has equation y = 4 x + 9.

Write down the gradient of the line.

Casey says the graph of y = 4 x + 9 passes through the point (3, 23).

Is Casey correct? Show how you decide.

A bag only contains green, red, blue and yellow discs.

Orla carries out an experiment. She picks one disc at a time from the bag, records its colour and then returns the disc to the bag. When she has finished the experiment, Orla works out the relative frequency of each colour. Some of her results are shown in the table.

The relative frequency of the yellow discs was three times the relative frequency of the blue discs.

In total, there are 2000 discs in the bag.

Use this information to find an estimate for the total number of green and yellow discs that are in the bag. You must show your working.

Explain why your estimate may not be reliable.

A housing estate is built on a triangular piece of land.

There are 3951 people living on the estate.

Work out an estimate of the population density of the estate in people per km².

The expected value of a painting, £ P, is given by the formula

P = 2500 × 1.2ⁿ

where n is the number of years after it was bought and 0 ⩽ n ⩽ 4.

Write down the value of the painting when it was bought.

Write down the annual percentage increase in the expected value of the painting.

The table shows the expected value of the painting n years after it was bought.

On the page opposite, draw a suitable graph to show the expected value of the painting n years after it was bought, where 0 ⩽ n ⩽ 4.

Years after the painting was bought (n)

An art collector correctly works out 2500 × 1.2¹⁰ as 15479.

They say,

The expected value of the painting 10 years after it was bought is £15479.

What assumption has the art collector made.

The diagram shows a rectangle, OPQR, and a circle, centre O, which passes through Q. OR = 6 cm and RQ = 8 cm.

Find the circumference of the circle. Give your answer in terms of π.

AOB is a sector of a circle, centre O and radius 8 cm. Angle AOB = x °. The arc, AB, has length 2 cm. π

Find the area of the sector. Give your answer in terms of π.

In the diagram below, the shaded region is a parallelogram. The parallelogram can be identified by four inequalities. Two of the inequalities are y ⩾ 6 and y ⩾ x.

Write down the other two inequalities that identify the parallelogram.

Work out the area of the parallelogram. You must show your working.

(b)........ square units

A farmer grows pumpkins. The farmer records the masses, m kilograms, of 80 of their pumpkins. The table shows the results.

Complete the cumulative frequency table.

Draw the cumulative frequency graph to represent these results.

Write down the upper quartile of the mass of the 80 pumpkins.

The farmer picks a pumpkin at random.

Find an estimate for the probability that the pumpkin has a mass greater than 18 kg.

Solve.

You must show your working.

A, B, C and D are points on the circumference of a circle, centre O. BD is a diameter of the circle. EBF is a tangent to the circle.

Give a reason why angle BAD = 90°.

Write down one other angle that is 90°. Give a reason for your answer.

Write down the value of angle CAD.

Write down the value of angle EBA.

Simplify.

Work out.

1₃¹ 8

2^x × 4^y = 16

A sequence has nth term 2n² + 1.

Prove algebraically that the sum of any two consecutive terms in this sequence is always a

multiple of 4.