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?
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?
Working (e.g. actual distance =
m)
5
X is inversely proportional to Y. Circle the correct statement.
[1 mark]
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]
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
• 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%
20% OFF ALL ITEMS
TODAY ONLY 10% OFF THE REDUCED PRICE
THAT MEANS YOU SAVE 30%
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)°.
Angle at A on line AB = 2x. Angle at Q on line CD = (5x + 6)°.
x =