OCR GCSE Maths Paper 4: Calculator Higher June 2024 question paper J560/04

Work out.

₃ 19.5⁴ - 18²

Write your answer correct to 4 significant figures.

The diagram shows a triangle and a trapezium.

Show that they have the same area.

Four numbers are written, in ascending order, as algebraic expressions.

a a + b a + 2 b 3 a - b

The mean of these four numbers is 27. The range of these four numbers is 24.

Find the value of a and the value of b. You must show your working.

A school is deciding on a charity to support. Each student at the school votes for one of four charities, A, B, C or D. The results are to be shown in a pie chart.

This pie chart shows the sector for charity A. Twice as many students voted for charity C than charity B. Twice as many students voted for charity D than charity C.

Show that the sector for charity B will have an angle of 44°.

Complete the pie chart.

39 students voted for charity A.

Calculate the total number of students at the school.

The school asks 80 of the students to choose a new logo from three designs G, H and J. The same results are shown in a pie chart and in a bar chart.

Give one advantage of using the pie chart rather than the bar chart.

Give one disadvantage of using the pie chart rather than the bar chart.

The same dog food is sold in three different sized packs. The diagram shows the price of each pack.

Which pack is the best value for money? Show how you decide.

The........ pack because........

A regular polygon has n sides. The interior angle of the polygon is 15 times its exterior angle.

Find the value of n.

Write the following in order of size, smallest first. 0.2 2^-2 2 × 10^-2

Show how you decide.

smallest

The price of a television is increased by 35%. In a sale, the new price of the television is decreased by r %.

The overall percentage increase in the price of the television is 16.1%.

Find the value of r. You must show your working.

Sasha and Taylor each have a stamp collection.

They organise their stamp collections according to where the stamps come from: United Kingdom (UK), European Union (EU), Other.

The table shows the number of stamps in each collection and the ratio UK: EU: Other.

When they put the two stamp collections together, Sasha and Taylor claim that at least of all the stamps come from the UK.

Are they correct? Show how you decide.

They are........ because........

Here is a question and an incorrect solution.

Describe the error made and write out a correct solution.

A correct solution is........

A student attempts two tasks. The result of each task is either “Pass” or “No pass”.

The probability of the student passing the first task is 0.6. The probability of the student passing the second task is x.

Complete the tree diagram.

First task
Second task

Write down the mathematical assumption that has been made about the two tasks.

The probability of the student passing just one of these two tasks is 0.528.

Work out the value of x.

P, Q, R and S are points on the circumference of a circle, centre O. Angle SQR = 14 ° and angle SPQ = 62 °.

Find the size of angle ROQ.

(a) Angle ROQ =........ °

D, E and F are points on the circumference of a circle.

Line GH is a tangent to the circle at F. Line DE is parallel to line GH.

Complete these statements to prove that triangle DEF is isosceles. Give reasons for your statements. You may not need all of the lines.

Angle........ = Angle........ because........

Angle........ = Angle........ because........

Angle........ = Angle........ because........

Angle........ = Angle........ because........

Angle........ = Angle........ because........

Triangle DEF is isosceles because........

Function A and function B are shown below.

The output of function B is x.

Write an algebraic expression, in terms of x, for the inverse of function B.

Function C is shown below as a composite function.

Complete the diagram below using two arithmetic operations to show function C as a single function.

The diagram shows a circle, centre O and radius 52 cm.

AB is a chord of the circle. The line through T is a tangent to the circle.

The chord is parallel to the tangent. The perpendicular distance between the chord and the tangent is 72 cm.

Calculate the area of the shaded segment. You must show your working.

Solve by factorisation.

Write x² + 8x + 11 in the form (x + a)² - b.

Write down the coordinates of the turning point of the graph y = (x - 3)² + 8.

Describe the single transformation which maps the graph of y = x² onto the graph of y = (x - 3)² + 8.

A lift can travel at a maximum speed of 9.83 m / s, correct to 3 significant figures. The lift travels a distance of 174 m, correct to the nearest metre, between the ground floor and the top floor of a building.

Use the above information to work out the shortest possible time for the lift to travel between the ground floor and the top floor. You must show your working.

Explain why your answer to part (a) may not be possible to achieve.

The box plot shows the distribution of the waiting time of cars at a road junction.

Write down the median waiting time.

What percentage of the waiting times were less than 30 seconds?

Given that a randomly chosen car waited for more than 30 seconds, write down the probability that the car waited for more than 90 seconds.

The graph shows the speed of an object during the first 20 seconds of its motion.

Calculate the distance travelled by the object during the 20 seconds.

The graph shows the distance travelled by an object during the first 4 seconds of its motion.

Work out the average speed of this object between 2 and 4 seconds.

Use the graph to estimate the speed of this object at 3 seconds. You must show working to support your estimate.

What happens to the speed of this object during these 4 seconds of motion. Explain how you know.

I know this because........

You must show each step in your working.