AQA GCSE Maths Paper 2: Calculator Higher June 2023 question paper 8300/2H

Write 30: 12 in the form n: 1

Four consecutive triangular numbers are 6 10 15 21 Write down the next triangular number.

The price of a toy increases by 12.5% to £19.53 Work out the original price of the toy.

Jess saves 2p, 5p and 10p coins. She has

• 45 10p coins

• 8 times as many 2p coins as 10p coins

• £17.70 in total.

Work out total value of 2p coins: total value of 5p coins Give your answer in its simplest form.

6

Assume that the polygon is an octagon. Work out the size of an exterior angle.

In fact, the polygon has more sides than an octagon. What does this mean about the size of an exterior angle? Tick one box.

In a game,

an ordinary fair six-sided dice is rolled

the fair spinner shown is spun.

The score is the dice number substituted into the spinner expression.

Complete the table to show all of the possible scores.

A player wins the game if their score is 10 or more. Work out the probability that they win the game.

The game is played 711 times. Estimate the number of games that are won.

(a – 3) x² + 2b ≡ 5x² + 12 Work out the values of a and b.

A (1, 3) and B (2, 9) are points on a centimetre grid.

ABCD is a parallelogram. AD and BC are horizontal and each has length 5 cm The diagonals of ABCD cross at E. Work out the two possible pairs of coordinates of E.

Write down the translation vector that maps shape A onto shape B .

A bowl is a hemisphere with radius 12 cm

Water is poured into the bowl at a rate of 325 cm³ per second for 8 seconds. Does the water fill more than 70% of the bowl? You must show your working.

Show that these two rectangles are similar.

A factory packs x boxes of teabags per hour. Each box contains 80 teabags. Show that the factory packs teabags per minute.

A company has 123 employees. Information about their hourly rates of pay is shown in the table.

Hourly rate, £p	Number of employees
10 p 14	66
14 p 20	32
20 p 40	15
40 p 100	10
	Total = 123

The owner of the company uses the data to make two statements.

Statement A “Over 30% of employees have an hourly rate that is more than £17”

Statement B “The average hourly rate of pay is more than £20”

Show working that supports Statement A.

Why might Statement A not be true?

Work out an estimate of the mean to support Statement B.

Why is the mean not the best average to represent the data?

Expand (x² – 9xy)(2x + 5y)

Line A has equation y = ax – 1 passes through the point (7, 13) Line B has equation 5 y – 3 x = 4 Show that line A has a greater gradient than line B.

Work out the size of angle x.

Here are the first four terms of a quadratic sequence. 3 20 47 84 Work out an expression for the n th term of the sequence.

P, Q and R are points on a circle.

Assume that S is the centre of the circle. Work out the size of angle x.

x = °

In fact, the centre of the circle is on PS but not at S. What does this mean about the size of angle x ? Tick one box.

For a different circle, AB is a tangent at A C and D are on the circumference of the circle

Here is Simon’s method to work out the size of angle y. Angle ADC = 70 ° (alternate segment theorem) Therefore y = 70 ° (angles in an isosceles triangle)

Is he correct? Give a reason for your answer.

Magana decides to put £500 into an account that pays compound interest. She wants to have at least £560 in the account after 3 years. Work out to 1 decimal place the minimum annual interest rate she needs.

An approximate value of a root of an equation, x, can be found using the iterative formula

Work out the values of x₂ and x₃

By continuing the iteration, show that the value of x is more than 4.25

Here are three sets of cards.

In a game, a player has two options.

The cards are picked at random. The player wins if the total of their two cards is exactly 10

Which option gives a better chance of winning?

Show working to support your answer.

a = 65 to the nearest integer b = 30 to 1 significant figure Work out the upper bound for 2a² – b² You must show your working.

simplifies to where a and b are integers.

Here is a sketch of y = x²

The minimum point of y = x² is at (0, 0) Write down the coordinates of the minimum point of y = x² + 2

The graph y = x² is reflected in the x axis. Write down the equation of the graph after this transformation.

y = x² is now transformed to give y = (x + 3)² Describe fully this single transformation.