WJEC GCSE Mathematics Unit 1: Non-calculator Higher June 2023 question paper 3300U50-1

Write down the column vector that will reverse the translation in part (a).

Express 675 as a product of its prime factors in index form.

360 expressed as a product of its prime factors in index form is 2³ × 3² × 5.

What is the smallest whole number that 360 can be multiplied by to give a square

number?

Smallest whole number is_........

Simplify each of the following. Circle your answer in each case.

m⁴ m³

Write down an expression for the nth term of the following sequence.

List all of the integers that satisfy the following inequality.

13 < 2 n < 19

R is a point on the line LM.

Using only a ruler and a pair of compasses, construct an angle of 90° at point R.

Using only a ruler and a pair of compasses, construct a perpendicular line from the point

P to the line XY.

Two time periods are measured as 4 hours 40 minutes and 2 hours 50 minutes.

Each measurement is correct to the nearest 10 minutes.

What is the least possible sum of these two time periods?

Give your answer in hours and minutes.

Answer =_........ hours_........ minutes

Whitney walks, cycles or travels on the bus to work each day.

On any randomly chosen day: • the probability that she walks to work is 0·25 • the probability that she cycles to work is 0·45.

At work, the probability that there will be a fire drill on any randomly chosen day is 0·04.

How Whitney travels to work is independent of whether or not there is a fire drill.

Complete the tree diagram shown below.

On a randomly chosen day, what is the probability that Whitney walks to work and there

is a fire drill?

Express 0·0076 in standard form.

Calculate the value of (3 × 10¹⁷) × (2 × 10⁻¹²).

Give your answer in standard form.

Calculate the value of (2·3 × 10⁴) + (5 × 10³).

Give your answer in standard form.

What percentage of the whole circle is shaded?

You must show how you calculated your answer.

What tangent property of circles did you use in order to answer part (a)?

Given that y is inversely proportional to x and that y = 0·2 when x = 160, find an

expression for y in terms of x.

Use the expression you found in part (a) to complete the following table.

A sphere has a diameter of 6 cm.

A cone has a base radius of 10 cm and a height of 9 cm.

Find the ratio of the volume of the sphere to the volume of the cone.

Give your answer in its simplest form.

Volume of the sphere: Volume of the cone

Show that 16x² 8x 3 0.

Solve the equation 16x² 8x 3 0.

You must use an algebraic method.

Find the length of BC.

You must justify any decision that you make.

Complete the table by finding the value of y for x = 0·5.

Use your graph to solve the equation x + = 3.

A box contains 5 blue discs and 3 yellow discs. Three discs are to be chosen at random, without replacement.

Calculate the probability that the three discs chosen will all be the same colour.

Calculate the probability that exactly one blue disc is selected.

The following diagram shows a sketch of y sin x for values of x from 0° to 360°.

Given that sin62° = 0·8829, correct to 4 decimal places, write down all the solutions of the equation

for values of x from 0° to 360°.

Use the following axes to sketch the graph of y –sin x for values of x from 0° to

360°. You must indicate any important values on the y-axis.

Use the following axes to sketch the graph of y sin x + 1 for values of x from 0°

to 360°. You must indicate any important values on the y-axis.

Write down an integer value of x that is greater than 5, for which and

are both rational.