WJEC GCSE Mathematics Unit 1: Non-calculator Higher June 2024 question paper 3300U50-1

Write the reciprocal of 4 as a decimal.

You must show all your approximations in your working.

Evaluate

Give your answer in its simplest form.

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

The right-angled triangle A B C is a cross-section of a prism, as shown below. A B = 9 cm, B C = 10 cm and A B C = 90°. The length of the prism is 20 cm.

Calculate the volume of the prism.

You must show all your working.

Point P lies on:

• the bisector of angle A B C • the perpendicular bisector of line B C.

Using only a ruler and a pair of compasses, construct suitable lines and arcs to show the position of point P.

Construction arcs must be clearly shown.

The diagram below shows a shape made by joining two rectangles together.

The area of the whole shape is 89 cm².

Form and solve an equation to find the value of x.

Calculate the value of n.

You must show all your working.

A group of people hired two buses, Bus A and Bus B, to take them home from a party.

Bus A left the party at 11:00 p.m. Bus B left the party at midnight.

A person from the group is chosen at random. The probability that this person left the party on Bus A is . The probability that this person sat on the left-hand side of the bus is equal to the probability that this person sat on the right-hand side.

Complete the following tree diagram.

What is the probability that this person sat on the right-hand side of the bus that left at

midnight?

Express 0·0057 in standard form.

Give your answer in standard form.

A car travels a distance of x miles in 2 hours.

In the next hour, it travels a further distance of 36 miles.

Its average speed for the whole journey is 42 mph.

Calculate the value of x.

You must show all your working.

A kite and an isosceles triangle are shown below.

They are not drawn to the same scale.

Using the information shown on the kite, calculate the perimeter of the isosceles triangle. Do not use a trial and improvement method.

You must show all your working.

Describe fully the single transformation that transforms triangle A onto triangle B.

Also, y is inversely proportional to x, and y = 8 when x = 15.

Find the value of y when w = 25.

Points A, B, C, D lie on a circle.

The line F A E is a tangent to the circle at A. B C D = 114°. D B A = x°. B A E = 2x°.

Calculate the value of x.

You must state any circle theorems that you use.

Factorise 2x² − 17x + 30.

Circle the correct answer in each of the following questions:

Make f the subject of the following formula.

Eleven cards are placed in a box.

Seven of the cards are red and the rest are blue.

Gareth selects two cards at random and does not replace them.

He claims that the probability of selecting two cards of the same colour is equal to the probability of selecting two cards of different colours.

Is Gareth correct?

You must show your working and justify your answer.

The highest point of a curve is called a maximum point. The diagram below shows a sketch of the curve with equation y = f(x). The maximum point of this curve has coordinates (−2, 5).

On the same diagram, sketch the curve y = f(x − 6). Mark clearly the coordinates of any point where the new curve crosses an axis.

Complete the following sentence.

The maximum point of the curve y = f(x − 6) has coordinates_........