WJEC GCSE Mathematics Unit 1: Non-calculator Higher June 2022 question paper 3300U50-1

The table below shows some of the values of y x² x 4 for values of x from –3 to 3.

x	–3	–2	–1	0	1	2	3
y x2 x 4	2	–2		– 4		2	8

Complete the table by finding the values of y for x = –1 and for x = 1.

The children in year 5 and year 6 in a primary school took part in a survey.

The children were asked, “How many pets do you have?” The results are shown in the pie chart and bar chart below. No child in either year had more than 5 pets.

There are 36 children in year 5.

One child is chosen at random from all the children in year 5 and year 6.

What is the probability that this child has no more than 1 pet?

A and B are independent events.

The probability of event A occurring is 0·6. The probability of event A and event B occurring is 0·48.

Calculate the probability of neither event A nor event B occurring.

In the diagram: • AB and ED are parallel • triangles ABC and DEC are similar.

Calculate the length of CE.

Calculate the length of AB.

Solve the following simultaneous equations using an algebraic (not graphical) method.

You must show all your working.

Circle the correct answer for each of the following statements.

7·2 m³ is equal to

720 cm³ 72 000 cm³ 7·2 10⁵cm³ 7·2 10³cm³ 7·2 10⁶cm³

Write your answer as a decimal.

Sketch the curve y sinx, for values of x in the range x 0 to x 360.

Sketch the curve y tanx, for values of x in the range x 0 to x 360.

Rearrange the following formula to make x the subject.

You must show all your working.

The wavelength of a sound wave, W metres, is inversely proportional to its frequency,

f hertz (Hz).

Richard is measuring the wavelengths of different sound waves. The wavelength is 0·5 m when the frequency is 1200 Hz.

What is the frequency when the wavelength is 10 m?

Enlarge the triangle below by a scale factor of –2.

Use the origin as the centre of enlargement.

Marian is competing in a race.

The race is (6x + 5) miles long. She completes the race in x hours. Her average speed during the race is (2x + 3) miles per hour.

Calculate how long Marian takes to complete the race.

You must use an algebraic method (not trial and improvement).

Simplify your answer.

The following diagram shows a sketch of the curvey f x.

The curve is transformed, as shown below.

Using function notation, complete the equation of the transformed curve.

The following diagram shows a sketch of the curve y f x.

The curve is transformed, as shown below.

Using function notation, complete the equation of the transformed curve.

A bag contains 10 balls. 5 of the balls are blue, 4 of the balls are red and 1 ball is green. Three balls are chosen at random, one at a time, without replacement.

Calculate the probability that the first ball is blue, the second ball is red and the third ball is green.

You must show all your working.

Calculate the probability that at least one blue ball is chosen.

You must show all your working.