GCSE Mathematics
8300/3H Higher Tier Paper 3 Calculator | November 2024
- Date
- Monday 11 November 2024
- Time
- 1 hour 30 minutes
- Total marks
- 80
- Materials needed
- Calculator, mathematical instruments, formulae sheet
- Tier
- Higher
- Paper
- 3 (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.
Questions 1 – 3
1Reciprocals2
Work out the reciprocal of 103.
Give your answer as a decimal.
Give your answer as a decimal.
Answer
Show working space
2Line Graphs / Extrapolation3
The table shows information about the number of houses with solar panels in a town.
| Year | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 |
|---|---|---|---|---|---|---|
| Number of houses | 50 | 65 | 115 | 210 | 275 | 350 |
2 (a) Complete the graph. [2 marks]
Points for 2017, 2018 and 2019 are already plotted. Click the graph to plot 2020, 2021 and 2022, then join all points with straight lines.
2 (b) Use the graph to estimate the number of houses with solar panels in 2023. [1 mark]
Switch to Extend line → 2023 mode and click the graph, or type your reading below.
Answer
3Plans and Elevations4
A building in the shape of a cylinder has diameter 40 m and height 55 m.
3 (a) On the centimetre grid, draw a plan of the building. Use a scale of 1 cm to 10 m. [2 marks]
Diameter (cm)
3 (b) On this centimetre grid, draw the front elevation of the building. Use a scale of 1 cm to 10 m. [2 marks]
Width × Height (cm)
Show working space
Questions 4 – 7
4Bounds / Show That3
To the nearest pound, Rosie has £12. She wants to buy 6 drinks. Each drink costs £1.89.
Show that Rosie definitely has enough money to buy the 6 drinks.
Show that Rosie definitely has enough money to buy the 6 drinks.
Working
Show working space
5Formulae2
The total cost of a taxi ride is calculated by adding a fixed charge of £4 and a charge of £2 per mile.
Write a formula to work out the total cost, £C, of a journey of m miles.
Write a formula to work out the total cost, £C, of a journey of m miles.
C =
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6Best Buy / Percentage Discount5
Three shops sell shirts.
At which shop is it cheapest to buy 6 shirts? Show working to support your answer.
Cost of 6 — A: £
B: £
C: £
Cheapest shop
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7Ratio / Rounding4
7 (a) [3 marks]
At a school there are 912 students. The ratio of students to teachers is 15.2 : 1.
The number of students stays the same. The number of teachers increases by 2.
Work out the new ratio of students to teachers. Give your answer in the form n : 1
The number of students stays the same. The number of teachers increases by 2.
Work out the new ratio of students to teachers. Give your answer in the form n : 1
: 1
7 (b) [1 mark]
On a school trip, one teacher is needed for every group of 10 or fewer students.
72 students want to go on the trip. Lexi tries to work out how many teachers are needed.
72 students want to go on the trip. Lexi tries to work out how many teachers are needed.
What is wrong with her answer?
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Questions 8 – 11
8Coordinate Geometry4
A triangle is drawn using the lines
y = x
x = −2
y = 4
Work out the coordinates of the three vertices of the triangle.
Vertex 1
Vertex 2
Vertex 3
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9Number / Remainders2
When x is divided by 2 the remainder is 1
When x is divided by 3 the remainder is 1
When x is divided by 4 the remainder is 1
Work out two possible values of x.
When x is divided by 3 the remainder is 1
When x is divided by 4 the remainder is 1
Work out two possible values of x.
Value 1
Value 2
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10Reciprocal Graphs / Speed–Distance–Time3
A car will travel 60 miles. Draw a graph to show the average speed of the car for times taken between 1 hour and 6 hours.
| Time taken (t hours) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Average speed (mph) | 60 | 30 | 10 |
Fill in the table above, then click the graph to plot your points at t = 3, 4 and 5. Join all six points with a smooth curve.
Show working space
11Algebra — Factorising2
Factorise fully 12t + 4t3
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Questions 12 – 15
12Compound Percentage Change4
The population of a country is now 67 200 000.
The population is predicted to increase by 1% per year for 6 years and then decrease by 1.2% per year for 2 years.
Work out the predicted population of the country 8 years from now. Give your answer to 3 significant figures.
The population is predicted to increase by 1% per year for 6 years and then decrease by 1.2% per year for 2 years.
Work out the predicted population of the country 8 years from now. Give your answer to 3 significant figures.
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13Probability — Without Replacement2
A bag contains one £5 note, one £10 note, one £20 note and one £50 note.
Amaan picks two of the notes at random without replacement.
Work out the probability that he has picked at least £30.
Amaan picks two of the notes at random without replacement.
Work out the probability that he has picked at least £30.
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14Probability — Tree Diagrams6
A test consists of two sections, A and B.
• 85% of people pass section A.
• 78% of people who pass section A also pass section B.
• 36% of people who fail section A also fail section B.
• 85% of people pass section A.
• 78% of people who pass section A also pass section B.
• 36% of people who fail section A also fail section B.
14 (a) Complete the tree diagram. [2 marks]
14 (b) 40% of people who fail at least one section take the test again. 5000 people take the test. How many are expected to take the test again? [4 marks]
Show working space
15Proportionality — Matching3
Match each equation to a statement to show what happens when the value of x is doubled.
One has been done for you.
One has been done for you.
✓ Already matched: y = 8x → The value of y is doubled
y = 1x2
y = 10x
y = 3x2
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Questions 16 – 19
16Algebra — Rearranging3
Rearrange y = √(x2 + 1) to make x the subject.
x =
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17Direct Proportion — d ∝ t24
A stone falls vertically from 300 metres above ground.
• The stone falls d metres in t seconds.
• d is directly proportional to the square of t (d ∝ t2).
• The stone falls 20 metres in the first 2 seconds.
Work out the total time taken for the stone to reach the ground.
• The stone falls d metres in t seconds.
• d is directly proportional to the square of t (d ∝ t2).
• The stone falls 20 metres in the first 2 seconds.
Work out the total time taken for the stone to reach the ground.
seconds
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18Statistics — Histograms4
The table shows information about the height of 40 plants. Complete the table and draw a histogram to represent the heights.
| Height, h (cm) | Frequency | Class width | Frequency density |
|---|---|---|---|
| 0 ≤ h < 5 | 6 | ||
| 5 ≤ h < 15 | 15 | ||
| 15 ≤ h < 25 | 9 | ||
| 25 ≤ h < 50 | 10 |
On the grid below, click a class interval and drag up or down to draw each bar. Bar height is frequency density.
Show working space
19Trigonometry — Sine Rule3
Use the sine rule to work out length x. You must show your working.
Not drawn accurately
x =cm
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Questions 20 – 24
20Algebra — Factorising Quadratics2
Factorise fully 3x2 + 23x + 30
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21Probability — Without Replacement3
A bag contains 25 discs. 11 are red, 9 are blue and 5 are yellow.
Ashley picks three of the discs at random without replacement.
Ashley's first disc is red.
Work out the probability that all three discs are different colours.
Ashley picks three of the discs at random without replacement.
Ashley's first disc is red.
Work out the probability that all three discs are different colours.
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22Volume / Density / Sphere4
The metal used to make a sphere costs £4320.
The metal costs £3.60 per gram.
Each cubic centimetre of metal has a mass of 17.3 grams.
Work out the radius, r, of the sphere.
The metal costs £3.60 per gram.
Each cubic centimetre of metal has a mass of 17.3 grams.
Work out the radius, r, of the sphere.
Volume of a sphere = 43πr3
r =cm
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23Exponential Graphs3
The distance of a particle from a point is d metres after t seconds. Work out the values of a and b.
d = a × bt where a and b are constants
a =
b =
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24Algebra — Simultaneous Equations (Curve & Line)5
A curve has the equation y = x2 + 4x − 4
A straight line has the equation y = 3x − 2
Work out the two points of intersection of the curve and the straight line.
A straight line has the equation y = 3x − 2
Work out the two points of intersection of the curve and the straight line.
Point 1
Point 2
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