Grade 6 Maths Quizzes

Question 1 6C The product rule

[2 marks]

Harris is buying a shirt and a tie.
He has a choice of three colours of shirt and a choice of three styles of tie.

Harris is going to choose one shirt and one tie.
List all the possible combinations Harris can choose.

Worked Solution & Answer

3 × 3 = 9 combinations: WP, WS, WC, BP, BS, BC, GP, GS, GC M1 C1

Answer: WP, WS, WC, BP, BS, BC, GP, GS, GC

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Question 2 6J Negative scale factors

[2 marks]

Enlarge shape P by scale factor –1/2 with centre of enlargement (0, 0). Label your image Q.

Enlarge shape **P** by scale factor -12 with centre of enlargement (0, 0).
Label your image **Q**.

Worked Solution & Answer

(2, 3) → (–1, –1.5) M1
(4, 3) → (–2, –1.5)
(2, 7) → (–1, –3.5) A1

Answer: Triangle Q with vertices (–1, –1.5), (–2, –1.5) and (–1, –3.5)

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Question 3 6E Triple brackets IGCSE Nov 2023 2H Q16

[3 marks]

Expand and simplify (2x + 3)(x - 5)(x + 4)

Worked Solution & Answer

(2x + 3)(x² − x − 20) = 2x³ − 2x² − 40x + 3x² − 3x − 60 = 2x³ + x² − 43x − 60. M2 A1

Answer: 2x³ + x² - 43x - 60

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Question 4 6F Parallel and perpendicular AQA Nov 2019 1H Q22

[3 marks]

(-3, 10) is a point on line L.
(4, 0) and (6, 10) are points on line M.
L and M are parallel.

Work out the equation of line L.
Give your answer in the form y = mx + c

Answer

Worked Solution & Answer

Gradient of M = 10 - 06 - 4 = 102 = 5 M1
Since L is parallel to M, gradient of L is also 5.
Equation of L using (-3, 10): M1
y - 10 = 5(x - (-3)) = 5(x + 3) = 5x + 15
y = 5x + 25. A1

Answer: Answer y = 5x + 25

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Question 5 6G Inequalities on Graphs

[3 marks]

On the grid, shade the region R that satisfies all the following inequalities.
x ≤ 2 y ≥ -3 y ≤ 2x + 1 3x + 2y ≤ 6
Label the region R.

Worked Solution & Answer

Plot boundary lines x = 2, y = –3, y = 2x + 1 (through (–2,–3), (0,1), (2,5)), and 3x + 2y = 6 (through (0,3), (2,0)) M2
Shade interior region R. A1

Answer: Quadrilateral region R bounded by x = 2, y = –3, y = 2x + 1 and 3x + 2y = 6 with vertices (–2, –3), (2, –3), (2, 0) and (6/7, 19/7)

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Question 6 6H Similar shapes (area and vol)

[3 marks]

Here are two similar solid shapes.

surface area of shape **A** : surface area of shape **B** = 3 : 4
The volume of shape **B** is 10 cm³
Work out the volume of shape **A**.
Give your answer correct to 3 significant figures.

cm³

Worked Solution & Answer

Length ratio = √3 : √4 = √3 : 2. Volume ratio = (√3)³ : 2³ = 3√3 : 8. Volume of A = 10 × (√3 / 2)³ = 10 × 0.649519 = 6.50 cm³ (3 s.f.). M2 A1

Answer: 6.50 cm³

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Question 7 6K Circle theorems IGCSE Nov 2021 2H Q11

[3 marks]

B, D, E and F are points on a circle, centre O.
ABC is a tangent to the circle.
ODC is a straight line.
BOE is a diameter of the circle.
Angle BCD = 48°
Find the size of angle DFE.

°

Worked Solution & Answer

(Angles on a straight line add up to 180°)
∠OBC = 90° (tangent-radius) ⇒ ∠BOD = 180 – 90 – 48 = 42° M1
Since BOE is a diameter, ∠DOE = 180 – 42 = 138° M1
Angle at circumference ∠DFE = 138 ÷ 2 = 69° A1

Answer: 69 °

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Question 8 6B Harder indices

[3 marks]

Work out
(a) Write down the value of 100 {}^1/2) (1) (b) Find the value of 125 {}^2/3) (2)

(a) Write down the value of 100^{12} [1 mark]

(b) Find the value of 125^{23} [2 marks]

Worked Solution & Answer

(a)

√100 = 10 B1

Answer (a): 10

(b)

(∛125)² = 5² = 25 M1 A1

Answer (b): 25

Question Paper (PDF) • Mark Scheme (PDF)

Question 9 6A Recurring decimals OCR Jun 2024 5H Q17

[5 marks]

The diagram shows a number line.

P = 1.2̇ and Q = 123.
Q is the midpoint of PR.
Find the value of R.
Give your answer as a mixed number in its simplest form.
You must show your working.

Worked Solution & Answer

P = 1.2̇ = 1 2/9 = 11/9. M2
Q = 1 2/3 = 1 6/9 = 15/9. M1
Step from P to Q = 15/9 − 11/9 = 4/9. M1
R = Q + 4/9 = 15/9 + 4/9 = 19/9 = 2 1/9. A1

Answer: 219

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Question 10 6D Repeated change OCR Jun 2024 5H Q12

[5 marks]

(a) Sasha invests £1000 at a rate of 5% per year compound interest.
Sasha says:
"After one year, my investment will get £50 in interest and will be worth £1050.
Therefore, after two years, my investment will get another £50 in interest and will be worth £1100."
Is Sasha correct?
Give a reason for your answer.
(b) Sasha buys a car.
The value, £V, of the car after n years is given by the formula
V = a × bⁿ.
The graph shows some information about the value of the car.

(a) Sasha invests £1000 at a rate of 5% per year compound interest.
Sasha says:
"After one year, my investment will get £50 in interest and will be worth £1050.
Therefore, after two years, my investment will get another £50 in interest and will be worth £1100."
Is Sasha correct?
Give a reason for your answer. [1 mark]

(b) Sasha buys a car.
The value, £V, of the car after n years is given by the formula
V = a × bⁿ.
The graph shows some information about the value of the car. [4 marks]

Find the value of a and the value of b.

Worked Solution & Answer

(a)

Compound interest is calculated on the new amount (£1050) in year 2, not the original £1000. C1

Answer (a): No, because in the second year the 5% interest is calculated on £1050 (giving £52.50 interest, total £1102.50).

(b)

When n = 0, V = 8000 ⇒ a = 8000 M3
When n = 1, V = 6400 ⇒ 8000 × b = 6400 ⇒ b = 6400 ÷ 8000 = 0.8. A1

Answer (b): a = 8000, b = 0.8

Question Paper (PDF) • Mark Scheme (PDF)

6A - Recurring decimals	6B - Harder indices
6C - The product rule	6D - Repeated change
6E - Triple brackets	6F - Parallel and perpendicular
6G - Inequalities on graphs	6H - Similar shapes (area and vol)
6J - Negative scale factors	6K - Circle theorems
6L - Cumulative frequency	6M - Box plots
6N - Combined transformations	6P - Capture recapture

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