AQA GCSE Maths Paper 3: Calculator Higher November 2018 question paper 8300/3H

In which direction does the shape move? Circle your answer.

up down left right

What is 1.75 kilometres as a fraction of 700 metres? Circle your answer.

The first 4 terms of a linear sequence are 3 11 19 27 Circle the expression for the n th term.

8 – 5 n n + 8 8 n + 3 8 n – 5

Work out the lowest common multiple (LCM) of 20, 30 and 40 Circle your answer.

10 120 240 24 000

The length of a table is 110 cm to the nearest cm Complete the error interval.

A music festival has taken place each year from 2011 The table shows the number of people who attended each year.

The festival organisers draw a time series graph to represent the data. The first four years have been plotted.

Complete the graph.

Use the graph to estimate the number of people who will attend the festival in 2019

k = n² + 9n + 1 Mo says, “ k will be a prime number for all integer values of n from 1 to 9” Show that Mo is wrong. You must show that your value of k is not prime.

Doug owes an amount of £600 He wants to pay off this amount in five months. He says, “Each month, I will pay back 20% of the amount I still owe.” Show working to check if his method is correct.

A motor racing circuit consists of two parallel straight sections, each of length 0.75 km a semicircle of diameter 0.9 km three equal, smaller semicircles.

The length of a motor race must be greater than 305 km What is the lowest number of full laps needed at this circuit? You must show your working.

Use trigonometry to work out the size of angle x.

Lewis wants to draw the graph y = x³ for values of x from –2 to 2 Here is his graph.

Make one criticism of his graph.

The probability of Heads when a biased coin is thrown is 0.6 The coin is thrown 500 times. Circle the expected number of Tails. 20 200 250 300

The mean mass of a squad of 19 hockey players is 82 kg A player of mass 93 kg joins the squad. Work out the mean mass of the squad now.

A company makes two types of lampshade using fabric on wire frames. Lampshade A Fabric is used to make the curved surface of a cylinder. The cylinder has radius 8 cm and height 22 cm

Lampshade B Fabric is used to make the four triangular faces of a pyramid.

Each triangular face has base 15 cm and perpendicular height 24 cm

Work out the ratio cost of one lampshade A: cost of one lampshade B Give your answer in the form n: 1

In a running club there are 50 females and 80 males. If a female is chosen at random, the probability she has blue eyes is 0.38 If a male is chosen at random, the probability he has blue eyes is 0.6 One person is chosen at random. Show that the probability the person has blue eyes is more than 0.5

Circle the expression for w²

Here is some information about the ages of people at a concert.

Age, x (years)	Frequency
10 x 15	8
15 x 25	24
25 x 40	30
40 x 70	39

Draw a histogram to represent the information.

The length of a roll of ribbon is 30 metres, correct to the nearest half-metre. A piece of length 5.8 metres, correct to the nearest 10 centimetres, is cut from the roll. Work out the maximum possible length of ribbon left on the roll.

Curve P has equation y = 2(x – 1)² – 5 Curve Q is a reflection in the y-axis of curve P. Work out the equation of curve Q. Give your answer in the form y = ax² + bx + c where a, b and c are integers.

Priya and Joe travel the same 16.8 km route. Priya starts at 9.00 am and walks at a constant speed of 6 km/h Joe starts at 9.30 am and runs at a constant speed. Joe overtakes Priya at 10.20 am At what time does Joe finish the route?

An approximate solution to an equation is found using the iterative formula

Work out the values of x₂ and x₃

Work out the solution to 5 decimal places.

x =

The diagram shows the side view of a step ladder with a horizontal strut of length 48 cm The strut is one third of the way up the ladder. The symmetrical cross section of the ladder shows two similar triangles.

Work out the vertical height, h cm, of the ladder.

24

A sphere has radius 2 x cm A cone has radius 3 x cm perpendicular height h cm The sphere and the cone have the same volume. Work out radius of cone: perpendicular height of cone Give your answer in the form a: b where a and b are integers.

ABCD is a quadrilateral.

The quadrilateral is reflected in the line x = 4 Which vertices are invariant? Circle your answer.

A and D C and D B and C B and D

Work out f^–1(x)

The line y = 3x + p and the circle x² + y² = 53 intersect at points A and B. p is a positive integer.

Show that the x-coordinates of points A and B satisfy the equation

The coordinates of A are (2, 7) Work out the coordinates of B. You must show your working.

Here is a sketch of a quadratic curve. The turning point is (3, –2)

Circle the correct statement about the gradient of the curve for x < 3

gradient is positive gradient is negative

gradient is zero gradient could be any value