WJEC GCSE Mathematics Unit 2: Calculator-allowed Higher November 2017 question paper 3300U60-1

Simplify each of the following and circle the correct answer in each case.

6p⁶ × 3p³

3·4g⁸ ÷ 13·6g²

A solution of the equation

x³ + 2x = 91

lies between 4 and 5.

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

You must show all your working.

ABC is an isosceles triangle with AB = AC.

Calculate the value of y.

A triangular prism of length 2 metres is shown below.

AC = 21 cm, BC = 35 cm and BAC = 90°.

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing. Calculate the area of triangle ABC. Give your answer in cm².

You must show all your working.

Calculate the volume of the prism.

You must give the units of your answer.

Find the answer to the following number problem.

‘(the LCM of 12, 18 and 24) ÷ (the HCF of 36 and 54)’.

Rearrange the following formula to make x the subject.

Give your answer in its simplest form.

2(x + y) = 7 y – 3

Write down the nth term of the following sequence.

3, 6, 11, 18, 27, …

The diagram shows two right-angled triangles, joined together along a common side.

SPQ = 90°, SQR = 90°, SQP = 38°, PS = 8 cm and QR = 15 cm.

Calculate the size of angle x.

All the members of a farming club visited the Royal Welsh Agricultural Show.

They all travelled to the show either by bus or by car. None of them visited the show on more than one day. The decision to travel by car or by bus was independent of the day of the visit. A member of the club was selected at random. The probability that this member travelled by bus was 0·87. The probability that this member visited the show on the first day was.

What is the probability that a member, chosen at random, was not one of those who

travelled by bus on the first day of the show?

Show that (10w + 3)(w – 1) – (2 – 3w)² w² + 5w – 7.

Use the quadratic formula to solve the equation w² + 5w – 7 = 0.

Give your answers correct to 2 decimal places.

The line GH is a tangent to the circle at point Y.

The line EF is parallel to the line GH. The vertices of triangle EFY lie on the circle. EYG = 60°.

Prove that EFY is an equilateral triangle.

Give a reason for each step to justify your proof.

A cone is joined to a cylinder, as shown below.

The cone has a base radius of 11 cm and a slant height of 13 cm. The cylinder has the same radius, 11 cm, and a height of 17 cm.

Calculate the total surface area of the composite solid.

The area of a rectangle is 137 cm², correct to the nearest cm².

Its width is 11 cm, correct to the nearest cm.

Calculate the greatest possible length of the rectangle.

Give your answer correct to 3 significant figures.

A bag contains 5 red counters and 5 blue counters.

Three counters are drawn at random from the bag at the same time.

Calculate the probability that the three counters will be the same colour.

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

Solve each of the following equations. Give all answers in the range x = 0° to x = 360°.

sinx = 0.3

sinx + 1 = 0

Two similar pyramids have volumes of 3970 cm³ and 3100 cm³ respectively. The height of the larger pyramid is 25 cm.

Calculate the height of the smaller pyramid.

Each of the two graphs below is described by one of the equations on the right.

Put a tick in the box next to the equation which correctly describes each graph.

ABC represents the sector of a circle with radius 7 cm and centre A, as shown below. BAC = x°, AD = 3 cm and BD = 6 cm.

Find the area of the shaded region BCD.