WJEC GCSE Mathematics Unit 2: Calculator-allowed Higher June 2023 question paper 3300U60-1

Solve the equation 7 5x 2 3x 8.

Make f the subject of the formula h 13 2 f.

Factorise 15x 35y.

A large number of prize tokens are placed in a box.

The tokens are identical in shape and size.

Gold, Silver, Bronze or No Prize is written on each token.

One token is chosen at random from the box. The table below shows the probability of choosing a Gold prize token and the probability of choosing a Silver prize token.

There are three times as many No Prize tokens in the box as there are Bronze prize tokens.

Complete the table.

There are 15 Gold prize tokens in the box.

How many Silver prize tokens are there in the box?

A solution of the equation

lies between 2 and 3.

Use the method of trial and improvement to find this solution correct to 1 decimal place.

You must show all your working.

Give your answer correct to 2 significant figures.

Calculate the reciprocal of 23.

Give your answer correct to 3 decimal places.

Circle the correct answer for each of the following.

The Lowest Common Multiple (LCM) of 4 and 6 is:

2 4 6 12 24

The Highest Common Factor (HCF) of 10 and 15 is:

5 10 15 30 150

In the diagram below, AD is a straight line.

BAC = 90°, BDE = 90° and CBE = 90°.

AC = 7·7 cm, BC = 11·3 cm and BD = 13·1 cm.

Calculate the value of x.

Hence find the length DE.

A number is decreased by 5% of its value. This is done 4 times in total. Each time, the value decreases by 5%.

Circle the multiplier that you would use to find the value after the 4 decreases.

A number has been decreased by 17% to give an answer of 3569.

What was the original number?

The diagram below shows a semicircle, with radius r, drawn inside a trapezium.

The area of the semicircle is 77 cm².

The semicircle touches the line AB. AB = 22 cm.

Calculate the area of the trapezium ABCD.

Enlarge the given triangle by a scale factor of –2, using point A as the centre of enlargement.

ABCDE is a regular pentagon with sides of length 11 cm. CDE is a sector of a circle with centre D and radius 11 cm. The two shapes are joined together, as shown below.

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Calculate the length of the arc CE shown in the diagram.

You must show all your working.

In a shape similar to the one shown on the previous page, the regular pentagon has sides of length 671 cm.

Complete the following statement.

Total area of new shape = ………………………… × total area of original shape

You must show all your working.

Make x the subject of the formula ax² x² b.

Factorise 8x² 18.

Hence solve 8x² 18 0.

Hence, sketch the graph of y 8x² 18 on the axes below.

Mark clearly the coordinates of any point where this graph crosses an axis.

Space for working:

Catherine has three spinners, as shown below.

She spins each spinner once.

Calculate the probability that all three spinners land on prime numbers.

The numbers that the three spinners land on are added together.

Calculate the probability that the total is greater than 4.

The cube shown below has a volume of 10 648 cm³.

Calculate the length of the internal diagonal AB.

Use the quadratic formula to solve the equation 1.

Give your answers correct to 2 decimal places.

You must show all your working.

In triangle ABC shown below, AB = 13 cm and BC = 11 cm.

D is a point on AC where BD = 7 cm and DC = 5 cm.

Calculate the size of BAD.

You must show all your working.