Eduqas GCSE Maths Component 1H Higher June 2025 question paper

A quarter of a circle has been cut from a rectangular card.

Calculate the perimeter of the remaining piece of card.

Give your answer in the form aπ + b.

Perimeter of the remaining piece of card is_{…………........ …………} cm

“The trainers have been reduced in price by a total of 35%.”

Explain why Jamie is incorrect.

Given that 3^m+4 = 1, find the value of m.

Betty bought c cakes costing £2 each and d doughnuts costing £1.50 each. She paid with a twenty pound note and was given some change.

Write an inequality to show this information.

Given that:

• distance x = 15 miles • distance y = 36 kilometres • 5 miles is approximately equal to 8 kilometres.

Circle the ratio that best represents

distance x: distance y.

3:5 5:12 3:4 2:3 2:5

The shape below is a triangular prism with CD = 7 cm.

The cross-section of the prism is a right-angled triangle where AB = 6 cm and AC = 10 cm.

Calculate the total surface area of the triangular prism.

The total surface area of the triangular prism is_{…………........ …………} cm²

Last week, 142 pupils in Year 7 were given English homework and French homework.

10 pupils did not complete either homework. Each expression in the following Venn diagram represents the number of pupils that completed at least one homework.

Calculate the value of x.

One pupil is chosen at random from the group.

What is the probability that this pupil completed only the French homework?

The probability that a pupil completed only the French homework is_{…………........ …………}

6.

Give your answer in its simplest form.

Calculate the value of the reciprocal of 0∙4. Give your answer as a decimal.

A cuboid rests on a horizontal floor.

The cuboid exerts a force of 6∙2 newtons on the floor. The pressure of this cuboid on the floor is 0∙05 N/cm².

The base of the cuboid in contact with the floor has a width of 8 cm.

Calculate the length of the base of the cuboid.

Work out the value of 5^–32 ÷ 5^–35.

In a vacuum, a particle of light travels at approximately 3 × 10⁸ metres per second.

What is this speed in kilometres per minute?

Give your answer in standard form.

A square KLMN and a rectangle PQRS are shown below.

Use an algebraic method (not trial and improvement) to find the value of x and the value of y Hence, calculate the perimeter of PQRS.

You must show all your working.

The perimeter of PQRS is_{……........ ……} cm

It takes 5 workers a total of 24 hours to build a wall 180 m long.

The workers have enough materials left over to build a further 300 m of the same wall.

How long will it take 8 workers to build this 300 m of wall?

It will take 8 workers_{…………........ …………} hours to build 300 m of wall.

What assumption have you made in answering part (a)?

If your assumption is not correct, what effect would this have on your answer to

part (a)?

The nth term of a sequence is given by 2n² + 9.

Show that 90 is not a term in the sequence.

The first four terms of a sequence are:

2a¹⁷b³, 4a¹⁵b⁶, 8a¹³b¹², 16a¹¹b²⁴,…

Write down the sixth term of this sequence.

Grey and white tiles are used to make the four patterns in the diagram below.

Pattern 1 Pattern 2
Pattern 3
Pattern 4

Write an expression for the total number of tiles needed to make Pattern n.

On the graph paper below, draw the region that satisfies the following inequalities.

Indicate clearly the region that is your answer. x 3 y 2 y x + 1 y 5 – 2x

Rearrange the following formula to make g the subject.

Cally, Deena and Juan are working on a GCSE project.

They are each in a different class. Cally, Deena and Juan each record the journey times to school of pupils in their own class.

The times for pupils in Cally’s class are shown in the table below.

Journey time, t (minutes)	Number of pupils
0 t 5	5
5 t 15	5
15 t 30	6
30 t 50	5
50 t 60	4

She decides to draw a histogram of her results.

Frequency density

Most of the frequency densities used in the histogram are incorrect.

What error did Cally make when she calculated the frequency densities?

Deena has correctly drawn the histogram for her results. 4 pupils take between 0 and 5 minutes to travel to school.

Frequency density

Complete the scale on the frequency density axis.

Calculate an estimate of the median journey time for the pupils in Deena’s class.

You must show all your working.

Juan decides to display the journey times of the 24 pupils for his class on a cumulative frequency diagram.

Cumulative frequency

Use the cumulative frequency diagram to give the best estimates for the answers to each of the following questions.

Calculate the percentage of pupils in Juan’s class that take 45 minutes or longer

to travel to school.

Complete the table for the journey time to school of the pupils in Juan’s class.

Two pupils were absent when Juan collected his data. The journey times of these two pupils are 6 minutes and 40 minutes.

What effect would including these two results have on the median journey time for

the class?

Factorise and hence solve 3x² – 13x – 10 = 0.

Use the iterative formula x_n+1 = 2x_n – 5.

Calculate the value of x₄ when x₁ = 6.

Use the iterative formula x = .

Calculate the value of x₃ when x₅ = 8.

Calculate the value of 144^0∙5 × 6^–2.

Give your answer as a fraction in its simplest form.

The diagram shows triangle FGH. X is a point on FH where FX:XH = 3:2. Y is the midpoint of FG.

FX = 9j and GH = 8k.

Write the vector FY in the form aj + bk.

The vectors OA, OB and OC are shown in the diagram.

Show that the points A, B and C lie on a straight line.

A bag contains 3 pink cubes and 5 green cubes.

The following steps are taken.

• Step 1: A cube is chosen at random from the bag and replaced by 2 more cubes of the other colour. • Step 2: Repeat step 1. • Step 3: A third cube is chosen at random.

Show that the probability that all three cubes are pink is

Calculate the probability that the first two cubes are the same colour and the third cube

is a different colour.

The sketch below shows a circle with diameter PQ.

The line y – 2x + 5 = 0 is a tangent to the circle at the point Q.

Find the equation of the line PQ.

Write your answer in the form ax + by + c = 0.

The function f () x is defined by f () x = 5 x − 2.

Find f⁻¹()x.

Find and simplify an expression for ff ()x.

Given that fg (−2) = 73, calculate the value of k.