AQA GCSE Maths Paper 3: Calculator Higher November 2023 question paper 8300/3H

The first four terms of a linear sequence are

6 13 20 27

Write down the expression for the n th term.

Square A is enlarged to square B.

Write down the scale factor of the enlargement as a fraction.

The length of a line is 8 cm to the nearest centimetre.

Complete the error interval.

At what point does the graph y = x³ – 1 cross the y axis?

Carly’s total annual pay = salary + bonus

Work out the percentage change in her total annual pay. State whether it is an increase or a decrease.

An exhibition was open for 240 hours and had 29 760 visitors. For of the time the exhibition was open, there were 172 visitors per hour.

For the remaining time, how many visitors per hour were there?

The first two cube numbers are 1 and 8

Show that the 3rd cube number can be written as the sum of three different prime numbers.

Circle the largest number.

Use trigonometry to work out the size of angle w.

Two bags contain only green discs and yellow discs. Bag A contains 1 green disc and 4 yellow discs. Bag B contains 3 green discs and 7 yellow discs. One disc is picked at random from each bag.

Complete the tree diagram with the correct probabilities.

Work out the probability that both discs are green.

Solve these simultaneous equations.

7 x + 2 y = 100 3 x + 2 y = 48

AF, BC, DE and DF are straight lines. BC and DE are parallel.

p is three times r.

Work out the size of angle p.

100 people were asked about the distance they travel from home to work. The table shows information about the results.

Distance, d (miles)	Frequency
0 d 5	21
5 d 10	24
10 d 20	37
20 d 40	18

Write down the greatest possible number of people who work from home.

One person is chosen at random.

Work out the probability that the person travels at least 10 miles.

The table is repeated.

Distance, d (miles)	Frequency
0 d 5	21
5 d 10	24
10 d 20	37
20 d 40	18

Draw a histogram to represent the results.

A solid trophy consists of a stand and a player.

The stand is made by removing a small pyramid from a large pyramid.

Large pyramid Square base, edge 8 cm Perpendicular height 16 cm Small pyramid Square base, edge 5 cm Perpendicular height 10 cm

Show that the volume of the stand is 258 cm³

The trophy is made from a metal of density 7.5 grams per cm³ The total mass of the trophy is 2340 grams.

Work out the volume of the player.

m 4 15 a = b = 3 p The diagram shows the vector 2 a + b

Work out the values of m and p.

PQ is a diameter of a circle. QR is a tangent to the circle. PQ = QR PR = 10 cm

Work out the radius of the circle. Give your answer as a decimal.

Here is a sketch of the quadratic graph y = f(x) The graph crosses the x-axis at x = a and x = b

Write an expression for the x-coordinate of the turning point.

Give your answer in the form ax² + bx + c where a, b and c are integers.

AC is a diameter of a circle, centre E. E is the midpoint of BD.

Prove that triangle ABE is congruent to triangle CDE.

Solve 2 x (x + 10) = 5 x – 18

Water flows from a tap at a constant rate. A container is filled with water from the tap in 40 seconds.

The graph shows the height, h centimetres, of the water after time, t seconds.

The container is one of these shapes.

Circle the letter of the correct shape.

By drawing a tangent on the graph, estimate the rate at which the height is increasing when t = 10

Write – as a single fraction in its simplest form.

A chocolate box in the shape of a prism is being designed. All lengths are in centimetres. The cross section is a regular hexagon with side x The length is 5 x

The total surface area of the box must be less than 650 cm²

Work out the largest possible integer value of x. You must show your working.

Work out the area of triangle ABC.

a is three quarters of c 6 b = 5 c

Work out the ratio a: b: c Give your answer in its simplest form, where a, b and c are integers.

In a game, these numbered tiles are in a bag.

Choose tiles at random one at a time and do not replace the tiles. You win if at any stage the total of the numbers on your tiles is 10

Amber plays the game once.

Work out the probability that she wins.

The graph of y = x³ is translated to the graph of y = (x – 2)³

Write down the translation vector.

The graph of y = 5 x + 4 is reflected in the y-axis.

Write down the equation of the reflected graph.