Eduqas GCSE Maths Component 1H Higher June 2023 question paper

The lengths of the three sides of a triangle are in the ratio 3: 5: 7.

What fraction of the perimeter is the longest side of this triangle?

The perimeter of this triangle is 60 cm.

Find the length of each of the three sides of this triangle.

The bearing of Q from P is 140°.

Find the bearing of P from Q.

The n th term of a sequence is given by 2 n + 9.

Work out the difference between consecutive terms.

Solve 2n 9 99.

Write down the number of terms of this sequence that are less than 99.

The diagram shows a quadrilateral.

Use algebra to find the size of the exterior angle y.

Sam cycled south for 16 km. He then turned and cycled east. When he stopped for a rest, the shortest distance back to his starting point was 20 km.

Calculate how many kilometres Sam cycled while travelling east.

Sam cycled the 20 km back to his starting point at a constant speed of 25 km/h.

How many minutes did this take?

Use the diagram to solve the following simultaneous equations.

Give your answers correct to 1 decimal place.

The diagram shows the curve y x² 2x 8.

Write down the y-intercept of the curve.

Find the coordinates of the turning point of the curve.

Use the diagram to solve x² 2x 8 0.

The diagram shows a fair spinner. Eve spins it twice.

What is the probability that the spinner lands on red both times?

In an athletics club: • 20 of the female athletes have a mean height of 170 cm • 30 of the male athletes have a mean height of 180 cm.

What is the mean height of these 50 athletes?

A boat crew has 8 rowers and a cox who steers.

The heights, in cm, of the 9 people in the crew are as follows.

150 183 193 201 203 198 201 188 193

The mean of these heights is 190 cm.

Explain why the mean is not the best average to use for this data set.

The table shows some information about the cost per person to take a boat across a river.

The Jones family of 4 adults and 1 child pay £9.50 to take the boat. The Patel family of 5 adults and 2 children pay £13 to take the boat.

The Lee family has 3 adults and 2 children.

How much does the Lee family pay to take the boat?

You must use an algebraic method and show all your working.

The Lee family pays_........

Circle the equation of a line parallel to the line y = 4x + 5.

The gradient of the line which passes through the points (a, 3) and (2a, 9) is

Find the value of a.

Find the next term of the following Fibonacci-type sequence.

Here are the first 4 terms of a sequence.

Find the 6th term of this sequence.

Simplify your answer.

Find the nth term of the following sequence.

–3 0 5 12 21

Draw the enlargement of rectangle A with scale factor and centre (0, 0).

Triangle P is reflected in the line y = x. The image is triangle Q.

Triangle Q is reflected in the line y = –x. The image is triangle R.

Describe a single transformation that maps triangle P to triangle R.

A small tank is a cuboid. It has a square base of side 20 cm.

The tank contains some liquid but is not full.

More of the same type of liquid is added to the tank: • The total mass of the liquid in the tank is now 5400 grams. • The depth of the liquid has increased by 50%. • The density of the liquid is 0·9 g/cm³.

Calculate the original depth of the liquid.

You must show all your working.

Write 13² 13⁷ as a single power of 13.

Find the value of a and the value of b.

Gracie has collected data about the heights of 30 giant sunflowers. The table shows her results.

Height, h (m)	3 < h 3·5	3·5 < h 4	4 < h 4·5	4·5 < h 5
Frequency	5	8	12	5

Gracie attempts to draw a cumulative frequency diagram.

Make two different criticisms of Gracie’s diagram.

Gracie also collects data about the amount of money each of a group of 40 gardeners spent on their gardens during the months of April and May. The table shows the data for April.

Amount for April, (£x)	0 < x 30	30 < x 40	40 < x 50	50 < x 60	60 < x 80
Frequency	6	9	12	5	8

Draw a histogram to represent the data for April.

The histogram below represents the data for May.

Calculate an estimate of how many more of the 40 gardeners spent £45 or less in May than spent £45 or less in April?

You must show all your working.

ABE is an isosceles triangle. AB is parallel to DC so that ABCD is an isosceles trapezium.

Prove that ABCD is always a cyclic quadrilateral.

State any reasons that you use in your proof.

You are given that y is inversely proportional to x².

When x 4, y 3.

Find a formula for y in terms of x.

Use your formula to find the value of y when x = 8.

Use your formula to find the positive value of x when y = 1200.

In this question all lengths are in centimetres.

Calculate the exact area of this rectangle.

OA = a and OB = b. C is the point on AB such that AC: AB = 1: 4. D is the mid-point of OB.

Find DC in terms of a and b.

Give your answer in its simplest form.

Use factorisation to solve the following equation.

The following probabilities are given for events A and B.