Grade 4 Maths Quizzes

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Score: 0 / 10

Question 1 4E Inequalities on a number line

[2 marks]

Here is a number line.

Write down the inequality shown on the number line.

Worked Solution & Answer

Filled circle at –3 means –3 ≤ p M1
open circle at 1 means p < 1 → –3 ≤ p < 1 A1

Answer: -3 ≤ p < 1

Question Paper (PDF) • Mark Scheme (PDF)

Question 2 4H nth term of a linear sequence

[2 marks]

Here is a sequence of patterns made from grey square tiles.

(a) On the grid below, draw Pattern number 5 [1 mark]

(b) Complete the table. [1 mark]

Worked Solution & Answer

(a)

L-shape with 5 squares along top and 5 squares down left (9 squares total)

Answer (a): L-shape with 5 squares along top and 5 squares down left (9 squares total)

(b)

Number of squares increases by 2 each time: 1, 3, 5, 7, 9, 11 B1

Answer (b): 9, 11

Question Paper (PDF) • Mark Scheme (PDF)

Question 3 4K Pythagoras theorem AQA Jun 2017 2H Q15

[2 marks]

Sami is trying to work out the exact value of y using Pythagoras’ theorem.
Here is her working:
(2y)² = 6² + 8²
2y² = 36 + 64
2y² = 100
y² = 100 ÷ 2
y² = 50
y = √(50)

(a) What error has she made in her working? [1 mark]

(b) Kai works out that y = 5 Mel says,
“y cannot be 5 because the hypotenuse should be the longest side and the other sides are longer than 5 cm”
Is Mel correct? Tick a box
[ ] Yes [ ] No Give a reason for your answer. [1 mark]

Worked Solution & Answer

(a)

(2y)² = 4y²
She did not square the 2. B1

Answer (a): She wrote (2y)² as 2y² instead of 4y²

(b)

No, because the hypotenuse is 2y = 2 × 5 = 10 cm, which is longer than both 6 cm and 8 cm. C1

Answer (b): No

Question Paper (PDF) • Mark Scheme (PDF)

Question 4 4A Compound interest

[3 marks]

Anil wants to invest £25 000 for 3 years in a bank.

Which bank will give Anil the most interest at the end of 3 years?
You must show all your working.

Worked Solution & Answer

Personal Bank: 25000 × 1.02³ = £26 530.20 (interest = £1530.20) M1
Secure Bank: 25000 × 1.043 × 1.009² = £26 546.46 (interest = £1546.46) M1
Secure Bank gives more interest. A1

Answer: Secure Bank (£26 546.46 vs £26 530.20, or £1546.46 vs £1530.20 interest)

Question Paper (PDF) • Mark Scheme (PDF)

Question 5 4B Indices AQA Nov 2024 1H Q22

[3 marks]

@@TABULAR₀@@
Match each expression on the left to the correct expression on the right.
One has been done for you.

Given 7ⁿ = x, match 7⁻ⁿ, 7²ⁿ, 7ⁿ⁺¹, 7 {}^{1/2 n}) to 7x, 1/x, 1/2 x, √x, x². [3 marks]

Worked Solution & Answer

7²ⁿ = (7ⁿ)² = x². M1
7ⁿ⁺¹ = 7¹ × 7ⁿ = 7x. M1
7 {}^{1/2 n}) = (7ⁿ) {}^1/2) = √x. A1

Answer: 7²ⁿ → x², 7ⁿ⁺¹ → 7x, 7^(1/2 n) → √x

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 4G Forming and solving equations

[3 marks]

The diagram shows triangle AOB.

Angle AOB is **not** an obtuse angle.
Find the greatest value of x.
You must show all your working.

Worked Solution & Answer

Not obtuse ⇒ Angle AOB ≤ 90° M2
2x + 3x + 10 ≤ 90 ⇒ 5x ≤ 80 ⇒ x ≤ 16, so greatest value of x is 16. A1

Answer: 16

Question Paper (PDF) • Mark Scheme (PDF)

Question 7 4D Real life graphs

[3 marks]

A train travels from Derby to Sheffield.
The travel graph shows information about the train’s journey.

(a) Work out the speed of the train.
Give your answer in miles per hour. [2 marks]

miles per hour

(b) Show this information on the travel graph. [1 mark]

Worked Solution & Answer

(a)

(Average speed = distance ÷ time)
Distance = 35 miles, Time = 30 minutes = 0.5 hours M1
Speed = 35 ÷ 0.5 = 70 mph A1

Answer (a): 70 miles per hour

(b)

(Average speed = distance ÷ time)
Draw horizontal line at distance 35 from t = 30 to t = 45 B1

Answer (b): Horizontal line from (30, 35) to (45, 35)

Question Paper (PDF) • Mark Scheme (PDF)

Question 8 4F Solving inequalities IGCSE Jun 2019 2HR Q1 / 2FR Q17

[3 marks]

(a) Write down the inequality shown on the number line. (1) (b) Solve 4y – 13 ≤ y + 8. (2)

(a) Write down the inequality shown on the number line. [1 mark]

(b) Solve the inequality 4y - 13 ≤ y + 8 [2 marks]

Worked Solution & Answer

(a)

x > –3

Answer (a): x > –3

(b)

3y ≤ 21 M1
⇒ y ≤ 7 A1

Answer (b): y ≤ 7

Question Paper (PDF) • Mark Scheme (PDF)

Question 9 4J Expanding and factorising

[3 marks]

(a) Factorise 4m + 12. (1) (b) Complete: 5y is a [term] in the [expression] 3x + 5y. (2)

(a) Factorise 4m + 12 [1 mark]

(b) Choose two words from the box above to make this statement correct. [2 marks]

Worked Solution & Answer

(a)

4(m + 3)

Answer (a): 4(m + 3)

(b)

5y is a term in the expression 3x + 5y M1 A1

Answer (b): term, expression

Question Paper (PDF) • Mark Scheme (PDF)

Question 10 4C Prime factors HCF and LCM Eduqas Nov 2018 2F Q23

[7 marks]

Gregor owns a restaurant.

(a) The diagram shows a circular place mat. [2 marks]

The radius of the circular place mat is 14 cm.
Calculate the circumference of the circular place mat.

(b) Gregor plans to buy some spoons and forks.
A bag of 24 spoons costs £19.95.
A box of 18 forks costs £15.55.
Bags and boxes cannot be split.
Gregor decides to buy the same number of spoons as forks.
He places an order to buy the smallest number of each that he can.
Complete the details on the order form shown below.
You must show all your working.
@@TABULAR₀@@ [5 marks]

Worked Solution & Answer

(a)

C = 2 * π * r = 2 * π * 14 = 28π ≈ 87.96 cm (or 2 * 3.14 * 14 = 87.92 cm). M1 A1

Answer (a): 87.96 cm (or 88 cm, 87.92 cm)

(b)

Smallest common multiple of 24 and 18 is 72 M1
Bags of spoons = 72 / 24 = 3 bags M1
Cost of spoons = 3 * 19.95 = £59.85 M1
Boxes of forks = 72 / 18 = 4 boxes M1
Cost of forks = 4 * 15.55 = £62.20
Total cost = 59.85 + 62.20 = £122.05. A1

Answer (b): 3 bags of spoons (£59.85), 4 boxes of forks (£62.20), Total = £122.05

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 31 marks)

Grade 4 Quizzes by Topic

24 Topics

4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction