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

The line with equation y = 2 x + 7 intersects the y-axis at A. Complete the coordinates of A.

Write down a fraction equivalent to 1.875

Solve 5 x + 11 = 3 x + 19

x =

A map has a scale of 1: 5000 How many metres are represented by a length of 4.5 cm on the map?

The number of hedgehogs in England is expected to reduce by 4% each year. Assume there are now 1 000 000 hedgehogs in England. Work out the expected number of hedgehogs in England after five years. You must show your working.

Here is cuboid A.

Cuboid B is made from two of cuboid A.

volume of A: volume of B = 1: 2 Matthew says, “surface area of A: surface area of B must be 1: 2 because B is made of 2 of A.” Is Matthew correct? Tick one box.

Give a reason for your answer.

Complete the table of values for y = x² + 2x

Draw the graph of y = x² + 2x for values of x from –3 to 1

Jing has £2450 She saves some and gives the rest to her four brothers. money saved: money given to brothers = 2: 5 She gives each of her four brothers the same amount. Does each brother receive more than £430 ? You must show your working.

There were 132 more people on Friday than on Thursday. Work out the number of people on Saturday.

Use trigonometry to work out the value of x.

Millie is estimating the value of

She rounds each decimal number to 1 significant figure.

Work out Millie’s estimate. You must show your working.

Millie says, “My estimate must be more than the exact value.” Without working out the exact value, give a reason how she can know this.

Here is a biased spinner.

Ali, Ben and Cary want to know the probability of spinning red on the biased spinner. They each spin it and count how many times it lands on red and divide by the total number of spins.

Who had the best estimate for the probability of spinning red? Give a reason for your answer.

Dev spins the spinner 80 times. He says, “My relative frequency of red is 0.185” Give a reason why his relative frequency must be wrong.

Elena spins the spinner 125 times. The relative frequency of red is 0.32 Work out how many times the spinner landed on green.

Charlie is driving 293 miles home. He

• leaves at 9.00 am

• travels the first 176 miles at an average speed of 48 mph

• drives the rest of the way at an average speed of 65 mph

Will he be home by 2.30 pm? You must show your working.

Kiran paid Income Tax and National Insurance on her annual salary.

Income Tax 0% of the first £12 570 of her annual salary 20% of the rest of her annual salary

National Insurance 0% of the first £9880 of her annual salary 13.25% of the rest of her annual salary

Kiran paid £5186 Income Tax. How much National Insurance did she pay?

180 runners started a marathon. Some of the runners did not complete it.

The histogram represents the times of the runners who did complete the marathon.

How many runners did not complete the marathon?

The table shows information about the runners who did not complete the marathon.

Draw a box plot to represent the information.

In this right-angled triangle, a = 16 cm a: c = 4: 5 Work out the area of the triangle.

f(x) = x² + 6x g(x) = 2 x + 4

Show that fg(x) = 4x² + 28x + 40

Solve fg(x) = – 5

Two integers have a difference of 6 The integers are multiplied together. 9 is then added. Prove algebraically that the result is always a square number.

The graph shows the values of D and E for 2 D 6

Choose one point on the graph and state if Sunil’s equation is correct for that point.

G is directly proportional to the square root of H. G: H = 3: 2 when H = 16 Work out G: H when H = 100

A solid shape is made from centimetre cubes. The front elevation and side elevation of the shape are shown.

the maximum possible number of cubes in the shape and the minimum possible number of cubes in the shape.

Shape A and shape B are shown on the grid.

Describe the single transformation that maps shape A to shape B.

A boat sails 35 km North from A to B. From B the boat sails to C and then back to A.

Show that the distance the boat sails from C to A is 79 km to the nearest km You must show your working.

Work out the bearing of A from C.