WJEC GCSE Mathematics Unit 1: Non-calculator Higher November 2019 question paper 3300U50-1

The exterior angle of a regular polygon is 36°.

How many sides does the polygon have?

Calculate the sum of all the interior angles of this regular polygon.

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

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

Write down the first three terms of the sequence whose nth term is given by n² – 6.

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

5, 11, 17, 23, …

Circle the correct answer for each of the following.

81 =

2·1⁵ =

32·5 10·5 40·84101 30·84101 32·1

6·48 3·6 4·32 3·3 2·16

Using only a ruler and a pair of compasses, construct a line from the point A that is

perpendicular to the line LM.

Dylan is having a weekend break in Wrexham.

The probability that he will visit Erddig Gardens is 0·7. The probability of Dylan going to the Bersham Heritage Centre is independent of him visiting Erddig Gardens.

The probability that he visits Erddig Gardens and goes to the Bersham Heritage Centre is 0·28.

Complete the following tree diagram.

Calculate the probability that Dylan visits Erddig Gardens but does not go to the Bersham

Heritage Centre.

Factorise x² + 4x – 21. Hence, solve x² + 4x – 21 = 0.

Write down the greatest possible value of length a.

Give your answer in mm.

Calculate the greatest possible value of length b.

Give your answer in mm.

Calculate the least possible value of length c.

Give your answer in mm.

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

The diagrams below show a solid cone and a solid hemisphere.

The cone has a base radius of 9 cm and a vertical height of 12 cm. The hemisphere has a radius of 8 cm.

Which of the two solids has the greater curved surface area? You should express any areas in terms of .

You must show all your working.

The illuminance of light, I, from a lamp depends on the distance, d, from the lamp. The unit used to measure the illuminance of light is the lux.

It is known that I is inversely proportional to the square of d.

Carys has a desk lamp in her room. For her lamp, Carys measures the illuminance, I, to be 5 lux when the distance, d, is 2 m.

What is the illuminance of light from this lamp at a distance of 0·5 m?

The points A, B, C and D lie on the circumference of a circle. The straight line EDF is a tangent to the circle at D. BAC = x and CDE = 2x, where x is measured in degrees.

Find the size of BCD in terms of x. Express your answer in its simplest form.

You must give a reason for each step of your solution.

Show that

6 x (8 x + 1) – 3(4 x + 1)(4 x – 1) ≡ 6 x + 3.

Hence, write down the value of x for which 6x(8x + 1) – 3(4x + 1)(4x – 1) = 0.

Circle the correct answer for the following statement.

The graph of y = 16 − x² has been drawn below, for values of x from x = 0 to x = 4.

Use the trapezium rule, with the ordinates x = 0, x = 1, x = 2, x = 3 and x = 4, to estimate

the area of the shaded region shown above.

Simplify the following expression.

Sixteen balls are placed in a bag.

Ten of the balls are green and six are yellow. Two balls are selected at random and not replaced.

Benjamin states that the probability of selecting two balls of the same colour is equal to the probability of selecting two balls of different colours.

Is Benjamin correct?

You must show all your working to justify your answer.