GCSE Mathematics

8300/2H Higher Tier Paper 2 Calculator | November 2024

Date: Friday 8 November 2024
Time: 1 hour 30 minutes
Total marks: 80
Materials needed: Calculator, mathematical instruments, formulae sheet
Tier: Higher
Paper: 2 (Calculator)

Instructions & Advice Use black ink or black ball-point pen. Draw diagrams in pencil. Answer all questions. In all calculations, show clearly how you work out your answer. The marks for questions are shown in brackets.

1 Choose a word from the list to complete each sentence. [3 marks]

arc centre circumference diameter radius sector segment tangent

1(a)

The length of the ___ is double the length of the radius.

1(b)

A ___ is a region created by drawing a chord through a circle.

1(c)

A radius meets a ___ at a right angle.

2 Work out an estimate of the mean value. [3 marks]

Here is a grouped frequency table.

Value, v	Frequency	Midpoint
0 ≤ v < 10	16	5
10 ≤ v < 20	22	15
20 ≤ v < 30	13	25
30 ≤ v < 40	9	35
Total	60

Mean =

3 Shade one quarter of the squares so that the grid has exactly two lines of symmetry. [2 marks]

Shade complete squares only. Click squares to shade/unshade.

Shaded: 0 / 4 required

4 Is the actual distance more than 300 m? [3 marks]

A map has a scale of 1 : 4000
On the map, the distance from a station to a museum is 7 cm.
Is the actual distance from the station to the museum more than 300 m?

Yes

Working (e.g. actual distance = m)

5 X is inversely proportional to Y. Circle the correct statement. [1 mark]

X is directly proportional to Y

X is directly proportional to ¹⁄_Y

X is directly proportional to 2Y

X is directly proportional to √Y

6 Show that x = 0.8 using Pythagoras' theorem. [2 marks]

Here is a right-angled triangle with hypotenuse 1.7 cm, base 1.5 cm, and height x cm.

Show your working:

7 Biased coin spins [3 marks]

Beth and Lynn each spin the same biased coin a number of times.

	Beth	Lynn
Number of spins	125	80
Relative frequency of Heads	0.32	0.35

7(a) How many more Heads did Beth spin than Lynn? [2 marks]

More heads =

7(b) Lynn says her estimate must be best because 0.35 > 0.32. Is she correct? [1 mark]

Yes

8 Work out the volume of the oil in litres. [2 marks]

Mass of oil = 537 g | Density = 895 000 g/m³ | 1 m³ = 1000 litres

Volume = litres

9 Complete the error interval for the length of the wall. [2 marks]

The length of a wall is 9 metres to the nearest metre.

m ≤ length < m

10 How many electric cars were sold last year? [3 marks]

384 000 electric cars were sold this year. This is 20% more than last year.

Last year =

11 Work out the three possible fully simplified answers when multiplying pairs of terms. [3 marks]

Terms: xy x² 5y²

Answer 1:

Answer 2:

Answer 3:

12 How many keyboards are there? [4 marks]

At a music festival, four types of instrument are played: guitars, keyboards, drums, trumpets.

• Total instruments = 80
• Half the instruments are guitars
• keyboards : drums : trumpets = 3 : 4 : 1

Keyboards =

13 Work out the size of angle x. [4 marks]

Two right-angled triangles are joined to make a larger triangle.

x = °

14 Is the shop sign correct? [1 mark]

SALE
20% OFF ALL ITEMS

TODAY ONLY 10% OFF THE REDUCED PRICE

THAT MEANS YOU SAVE 30%

Yes

15 Work out the value of x. [4 marks]

AB and CD are straight, parallel lines. P is a point on AB. Q is a point on CD. AP = AQ.
Angle at A on line AB = 2x. Angle at Q on line CD = (5x + 6)°.

x =

16 Solve (x + 2)(x − 5) = 6x [4 marks]

x =

and x =

17 Are lines LM and ST perpendicular? [2 marks]

Line LM: y = 4x − 7 | Line ST: y = (9 − x) / 4

Yes

18 Battery life comparison (cumulative frequency) [7 marks]

Two types of battery, P and Q, were tested. 100 of each were put into clocks.

Number of days, d	Frequency (Type P)	Cumulative Frequency
0 ≤ d < 40	2
40 ≤ d < 80	9
80 ≤ d < 120	26
120 ≤ d < 160	45
160 ≤ d < 200	18

18(b) Compare types P and Q [4 marks]

Type Q: median = 126 days, IQR = 57 days.
Use your cumulative frequency diagram above to read off the median and IQR for type P, then compare.

Median comparison (average statement):

IQR comparison (spread statement):

19 Work out the cost of a phone screen. [5 marks]

A phone screen is similar to a tablet screen.

Phone height: 6 cm | Tablet height: 15 cm
Tablet screen area: 420 cm² | Screen costs £7000 per m²

Cost = £

20 Work out u₁ and u₃ [3 marks]

u_n+1 = 24 / u_n + 4 | u₂ = 8

u₁ =

u₃ =

21 Velocity–time graph of a ball [6 marks]

The graph represents the velocity of a ball as it rolls along the ground.

Graph mode:

📐 Tangent mode: Click two points on or near the curve to draw your tangent line. The gradient (acceleration) will be calculated automatically.

21(a) Estimate the acceleration after 2 seconds. Show your working. [2 marks]

Acceleration ≈ m/s²

21(b) Estimate the total distance covered by the ball. [3 marks]

Distance ≈ m

21(c) Is your estimate an overestimate or underestimate? [1 mark]

Overestimate

Underestimate

22 Show that all terms have two or more digits by completing the square. [3 marks]

The nth term of a sequence is n² − 30n + 236

Completed square form:

23 Circle theorems [6 marks]

23(a) Line DAE is a tangent at A to circle with centre O. Angle OAE = 53°. Work out angle x (angle BOC). [2 marks]

x = °

23(b) Cyclic quadrilateral. f : g = 2 : 3. One angle = 63°. Work out f : h in simplest form. [4 marks]

f : h =

24 Prove that GD bisects angle ADF. [4 marks]

ABCD and AEFG are congruent rectangles. D lies on EF. Angle ADE = x.

This is a proof question. In a real exam you would write a full geometric proof. Here, identify the key angle relationships to show GD bisects angle ADF.

Grade Estimate

–

Answer some questions to see your grade estimate.

Actual AQA Paper 2 boundaries (Nov 2023 proxy): Grade 9 ≥ 68 · 8 ≥ 58 · 7 ≥ 48 · 6 ≥ 37 · 5 ≥ 26 · 4 ≥ 15 · 3 ≥ 9 (out of 80)
Jun 2024 for comparison: 9≥72, 8≥62, 7≥52, 6≥40, 5≥29, 4≥18, 3≥12

Question Summary

Q	Topic	Marks	Your score