WJEC GCSE Mathematics Unit 2: Calculator-allowed Higher November 2020 question paper 3300U60-1

Caryl has two fair dice.

Dice A is a cube. It shows the numbers 1 to 6. Dice B is a tetrahedron. It shows the numbers 1 to 4.

Caryl throws both dice.

What is the probability that she throws a 5 on dice A and a 3 on dice B?

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

The diagram shows two right-angled triangles, joined together along a common side. AB = 10·8 cm, BC = 14·4 cm and CD = 24 cm.

Calculate the area of triangle ACD.

You must show all your working.

A solution of the equation

lies between 7∙2 and 7∙3.

Use the method of trial and improvement to find this solution correct to 2 decimal places.

You must show all your working.

Data for different values of t are shown in the table below.

t	Frequency
0 t 5	8
5 t 10	0
10 t 15	7
15 t 20	5

Calculate an estimate for the mean value of t.

Calculate the value of (3·2 × 10⁷) × (8·3 × 10⁻²).

Give your answer in standard form.

The lengths of the sides of a rectangle are given as 24 cm and 15 cm.

Each measurement is given correct to the nearest centimetre.

Calculate the difference between the greatest possible perimeter of the rectangle and the least

possible perimeter of the rectangle.

The diagram below shows a circle with centre at point O.

A, B, C and D are all points on the circumference of the circle. AB = 7·5 cm and BC = 4·7 cm.

Calculate the size of angle x.

Write down the size of angle y.

State the circle theorem you have used to find your answer.

Circle theorem used:_........

Write 16¹⁰⁰ in the form 2ⁿ.

Calculate the perpendicular height of a cone with a volume of 5533 cm³ and a base area of

825 cm².

Factorise 4x² – 81.

Factorise 7x² + 10x – 8.

Factorise (x + 2)³ + 5(x + 2)².

In the following diagram, triangle ABC has been enlarged to triangle DEF, with the centre of enlargement at O.

Write down the scale factor of the enlargement.

The first four terms of a sequence are

Find the 100th term of the sequence.

An amount written correct to the nearest £10 is £7180. This amount is increased by 23·5%, correct to the nearest 0·1%. Calculate the least possible value of the increased amount.

Give your answer correct to the nearest pound.

Sketch the curve y = cos x, for values of x in the range x = 0° to x = 360°.

You must indicate any important values on the axes.

Solve the equation cosx = 0.7.

Give all solutions in the range x = 0° to x = 360°.

A large number of people took part in a survey that was carried out to find the popularity of three different walks in West Wales.

Each person surveyed was asked, independently, to select their one favourite walk. The table below shows the results of the survey.

Three girls, Constance, Scarlett and Clementine, were chosen at random from all of the people surveyed. They were asked which walk they had selected.

Calculate the probability that the three girls had each selected a different walk.

Use the quadratic formula to solve (5 x + 3)(5 x – 3) = 19 x.

Give your answers correct to 2 decimal places.

You must show all your working.