AQA GCSE Maths Paper 2: Calculator Higher November 2021 question paper 8300/2H

Circle the factor of x² – 5x

x – 1 – 5 x x – 5 5 x

A is half of B. Work out the ratio A: B Circle your answer.

1: 2 2: 1 1: 3 3: 1

The first three terms of a geometric progression are Circle the fourth term.

Circle the reason why these triangles are congruent.

ASA RHS SAS SSS

Solve 10 x = 62.4 – 3 x

x =

Lines A, B, C, D and E intersect as shown. Lines A and B are parallel.

Work out the size of angle x.

7 102 boys and 85 girls took a test. The table shows information about the mean marks.

The pass mark for the test was 70 Was the mean mark for all of these students greater than the pass mark? You must show your working.

Describe fully the single transformation that maps triangle ABC to triangle ADE.

A ball contains 5000 cm³ of air. More air is pumped into the ball at a rate of 160 cm³ per second. The ball is full of air when it becomes a sphere with radius 15 cm

Does it take less than 1 minute to fill the ball? You must show your working.

p is a positive number. n is a negative number. For each statement, tick the correct box.

250 trains arrived at a station. The number of trains that were late was recorded after every 50 trains. The table shows some information about the results.

Complete the relative frequency graph.

Write down the best estimate of the probability that a train arriving at the station is late.

A, B and C are three points on a circle. The radii from A, B and C are shown.

Is AC a diameter of the circle? You must show your working.

A straight line has gradient 6 and passes through the point (3, 19) Work out the equation of the line. Give your answer in the form y = mx + c

The population of butterflies in a park is 4200

Assume that the population increases by 12% each day. Show that after 20 days the population would be greater than 40 000

In fact, the population increases by 13% each day for 19 days then decreases by 8% for 1 day. After the 20 days, is the actual population greater than 40 000 ?

Show working to support your answer.

The expected number of visitors to the park each day depends on the temperature.

On each of the 30 days in June the park is open the probability that the temperature is less than 21°C is 0.4 Work out the total number of expected visitors to the park in June.

L is directly proportional to D² L = 85 when D = 10

Work out an equation connecting L and D.

Work out the value of L when D = 5

Here is a cube with edge length x cm One diagonal is shown.

Circle the length, in centimetres, of the diagonal.

The total length, in centimetres, of the edges of the cube is a multiple of 18 Circle the correct statement.

x is a x is not a x might be a whole number whole number whole number

20 people were asked which device they used more often, laptop or phone. The table shows the results.

One male and one female are chosen at random. Work out the probability that exactly one of them said laptop.

Two males are chosen at random. Work out the probability that they both said phone.

On the grid, identify the region represented by

Label the region R.

The graph shows the height above ground of a toy rocket for 10 seconds.

For how long is the rocket in the air? Circle your answer.

10 seconds 9 seconds 6 seconds 4 seconds

Using the graph, estimate the speed of the rocket after 6 seconds. State the units of your answer.

A square has an area of 0.25 square metres. Circle the length, in centimetres, of one side of the square.

0.5 cm 5 cm 50 cm 500 cm

x is an integer. Prove that 35 + (3x + 1)² – 2x(4x – 3) is a square number.

Liam is trying to remember a 3-digit code. He knows the rule that the first digit is a cube number the second digit is a factor of 16 the third digit is an odd number. Liam tries at random a code that matches the rule. Work out the probability that this is the correct code.

A ship sails from P to Q and then from Q to R. Q is 12 miles from P, on a bearing of 080° R is 28 miles from Q, on a bearing of 155°

Work out the direct distance from P to R.

The flight of a plane was in two stages. The table shows information about the flight.

	Distance (miles)	Speed (mph)	Time (hours)
1st stage	731	x	731 x
2nd stage	287	x – 24	287 x 24

In total, the flight lasted 2 hours. Work out the value of x.

The equation of a curve is y = x² + 14x + 52 By completing the square, work out the coordinates of the turning point. You must show your working.