WJEC GCSE Mathematics Unit 2: Calculator-allowed Higher November 2018 question paper 3300U60-1

A number is decreased by 12% of its value. This is done 3 times, each time decreasing the previous value by 12%.

Circle the multiplier that you would use to find the value after the 3 decreases.

Calculate the percentage change when 42.5 is increased to 45.9. (b)

Display the following information in a Venn diagram.

• Universal Set (ε): Integers between 74 and 80 inclusive.

• Set A: Even numbers.

• Set B: Multiples of 3.

The table below shows some of the values of y = x² + 4x − 1 for values of x from –5 to 2.

Complete the table by finding the value of y for x = –2 and for x = 2.

On the graph paper opposite, draw the graph of y = x² + 4x − 1 for values of x from

–5 to 2.

Draw the line y = 2 on the graph paper.

Write down the values of x where the line y = 2 cuts the curve y = x² + 4x − 1.

Values of x are_........ and_........

Jonathan writes a whole number on a card.

• The number is between 55 and 83 inclusive.

• The square root of the number is greater than 8 but less than 9.

• The highest common factor (HCF) of 49 and the number is 7.

What number is on Jonathan’s card?

The number on Jonathan’s card is_{………........ ……………..}

A solution of the equation

lies between 5 and 6.

Use the method of trial and improvement to find this solution correct to 1 decimal place.

You must show all your working.

What is the gradient of the straight line with equation 6 y = 3 x + 7 ?

Circle the correct answer.

What is the value of y at the point where the line 5x + y + 3 = 0 crosses the y-axis?

Circle the correct answer.

What are the coordinates of the point where the lines with equations x + y = 7 and x − y = 3 intersect?

Circle the correct answer.

(4, 3)
(7, 4)
(5, 2)
(3, 7)
(−5, 2)

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

The perimeter of a square is 76.4 m.

Calculate the length of its diagonal.

You must show all your working.

Alwena regularly travels from Anglesey to Cardiff to attend meetings.

For each meeting, she chooses one of three ways to travel: by plane, train or car. The probability of a meeting being held on a Saturday is 0.08. The probability that Alwena travels by plane to a meeting is 0.15. The probability that she travels by train is 0.45. Her decision on how to travel is independent of the day on which the meeting is held.

Complete the following tree diagram.

A meeting is chosen at random. Calculate the probability that the meeting is held on a Saturday and that Alwena travels

by plane or by car.

The diagram below shows two right-angled triangles ABC and APQ.

= 8.2 cm, = 6.4 cm and = 7.9 cm. AB BC PQ CAQ = 90°.

Calculate the size of angle x.

Calculate the length AQ.

A googol is the number 1 × 10¹⁰⁰.

Circle the value that is 90% of a googol.

Sketch the curve y = tan x, for values of x in the range x = – 180° to x = 180°.

Calculate the total surface area of a solid hemisphere with a base radius of 29 cm.

Fully factorise the expression c³ – cd².

Factorise and simplify 5(e – 1)² + 3(e – 1).

The diagram below shows a cuboid with HG = 3 cm, AE = 5 cm and EH = 7 cm.

Calculate the length of the line AG.

Give your answer correct to 2 decimal places.

Three unbiased 6-sided dice are rolled at the same time.

Calculate the probability they will all land on a 5.

Four unbiased 6-sided dice are now rolled.

Calculate the probability that at least three of the dice will land on a 5.

The graph of y = 18 + 3x – x², for values of x from x = 0 to x = 6, is drawn below.

Use the trapezium rule, with the ordinates x = 0, x = 1, x = 2, x = 3, x = 4, x = 5 and x = 6, to estimate the area of the region bounded by the curve, the positive x-axis and the positive

y-axis.

The diagram below shows two triangles ABE and BCD, which are constructed from the straight lines AD and EC crossing at point B.

AE = 11 cm, EB = 13 cm, BC = 10 cm and BD = 7 cm. EAB = 37°.

Diagram not drawn to scale.

Calculate the length CD.

Give your answers correct to 2 decimal places.

You must show all your working.