AQA GCSE Maths Paper 2: Calculator Higher June 2019 question paper 8300/2H

Circle the point that lies on the curve y = x² – 4x + 1

(–1, 4) (–1, –4) (–1, –2) (–1, 6)

The height of a tree is 12 metres, correct to the nearest metre. Circle the error interval.

3 2 a is five times bigger than b. Circle the ratio a: b

10: 1 1: 10 5: 2 2: 5

Which of these represents the shaded region? Circle your answer.

Using ruler and compasses, show the region inside the grid that is less than 4 cm from A and nearer to B than to C. Label the region R. Show all your construction lines.

Beth drives 200 miles in 4 hours. She drives the first 18 miles at an average speed of 36 mph Work out her average speed for the rest of the journey.

The diagram shows rectangle ABDE and right-angled triangle ABC. AC = 17 cm BC = 8 cm

BC: CD = 1: 2 Work out the area of rectangle ABDE.

On the axes, sketch the curve y = x³ – 2 You must show the coordinates of the y-intercept.

In a sport, injury time is added time played at the end of a match. The table shows the injury time, t (minutes) played in 380 matches.

Injury time, t (minutes)	Frequency
0 t 2	59
2 t 4	158
4 t 6	106
6 t 8	45
8 t 10	12

Circle the two words that describe the data.

continuous discrete grouped ungrouped

Which class interval contains the median? You must show your working.

What percentage of the matches had more than 6 minutes of injury time?

x is an integer.

and

Work out all the possible values of x.

Joe and Kyle share an amount of money in the ratio 7: n Joe gets 35% of the money. Work out the value of n.

A biased coin is thrown 250 times. The relative frequency of Heads is worked out after every 50 throws.

Circle the best estimate of the probability of Heads.

0.3 0.32 0.342 0.4

The amounts spent on clothes by 40 boys and 40 girls in one month were recorded. The table shows information about the amounts spent by the boys.

The mean for the girls was £35 Estimate the mean for the girls as a percentage of the mean for the boys.

Ali and Mel are making 3-digit codes. The digit 0 is not used. Ali only uses odd digits. Mel only uses even digits.

Ali can make x more codes than Mel. Assume that digits cannot be repeated. Work out the value of x.

In fact, digits can be repeated. What does this tell you about the actual value of x ? Tick one box.

Here is line L and the graph of y = x – 1 The scales of the axes are not shown.

Work out the equation of line L.

ABC and ACD are triangles.

The area of ACD is 80.5 cm² Work out the area of ABC. Give your answer to 3 significant figures.

p = 68.3 correct to 1 decimal place. b = 8.7 correct to 1 decimal place. Work out the lower bound for m.

In a bag there are blue discs, green discs and white discs. There are four times as many blue discs as green discs. number of blue discs: number of white discs = 3: 5 One disc is selected at random. Work out the probability that the disc is either blue or white.

Work out the area of the trapezium.

Expressions for consecutive triangular numbers are

Prove that the sum of two consecutive triangular numbers is always a square number.

A solid shape is made by joining two cones. Each cone has the same radius.

One cone has slant height = 2 × radius The other cone has slant height = 3 × radius The total surface area of the shape is 57.8π cm² Curved surface area of a cone = π rl where r is the radius and l is the slant height

Work out the radius.

A and B are similar cuboids. surface area of A: surface area of B = 16: 25 Work out volume of A: volume of B Circle your answer.

4: 5 16: 25 64: 125 256: 625

Here is a sketch of the curve y = x² + 4x – 12

Work out the values of x for which x² + 4x – 12 0 Give your answer as an inequality.

A sample of 50 eggs is taken from Farm A. The table shows information about the masses of the eggs from Farm A.

A sample of 50 eggs is taken from Farm B. The histogram shows information about the masses of the eggs from Farm B.

For medium eggs, 53 g mass 63 g The Farm A sample has more medium eggs than the Farm B sample. Using the table and the histogram, estimate how many more. You must show your working.

(x + 5)(x + 2)(x + a) x³ + bx² + cx – 30 Work out the values of the integers a, b and c.

Work out the value of f^–1(3) + f(–0.5)