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Question 1

Topic – C9.4

Students at an activity centre choose one of four activities.
The bar chart shows some of their choices.

(a) 5 students choose hiking.

Complete the bar chart.

(b) Write down the most popular activity.

▶️ Answer/Explanation
Solution

Ans:

(a) Draw a bar for hiking reaching up to 5 on the frequency axis.

(b) Climbing (as it has the tallest bar in the completed chart).

Question 2

Topic – C4.2

Draw a line that is perpendicular to line L.

▶️ Answer/Explanation
Solution

Ans:

Draw a line that intersects line L at 90 degrees. Use a protractor or set square to ensure the angle is exactly 90 degrees.

Question 3

Topic – C4.1

(a) The diagram shows a circle.
On the diagram, draw a chord.

(b) Another circle has a diameter of 28 cm.
Find the radius of this circle.

▶️ Answer/Explanation
Solution

Ans:

(a) Draw a straight line connecting any two points on the circumference of the circle.

(b) Radius = Diameter ÷ 2 = 28 ÷ 2 = 14 cm.

Question 4

Topic – C4.3

The scale drawing shows the positions of town A and town B.
The scale is 1 cm represents 15 km.

(a) Find the actual distance between town A and town B.

(b) Measure the bearing of town B from town A.

▶️ Answer/Explanation
Solution

Ans:

(a) Measure the distance in cm (7.4 cm) and multiply by 15: 7.4 × 15 = 111 km.

(b) Using a protractor, measure the angle clockwise from north to the line AB: approximately 71°.

Question 5

Topic – C5.1

Change 0.56 kilometres into metres.

▶️ Answer/Explanation
Solution

Ans: 560 m

1 km = 1000 m, so 0.56 km = 0.56 × 1000 = 560 m.

Question 6

Topic – C1.5 

Write these numbers in order, starting with the smallest:

$\frac{6}{17}$ 34% $\frac{9}{25}$ 0.345

▶️ Answer/Explanation
Solution

Ans: 34% < 0.345 < $\frac{6}{17}$ < $\frac{9}{25}$

Convert all to decimals: 34% = 0.34, $\frac{6}{17}$ ≈ 0.353, $\frac{9}{25}$ = 0.36

Then order: 0.34 < 0.345 < 0.353 < 0.36

Question 7

Topic – C4.6

The diagram shows two parallel lines and a straight line crossing them.

Find the value of x and the value of y.

▶️ Answer/Explanation
Solution

Ans: x = 112, y = 68

y = 68° (corresponding angles)

x = 180° – 68° = 112° (angles on straight line)

Question 8

Topic – C9.3

Here is some information about six numbers:

• The lowest number is 37
• The range is 24
• The mode is 43
• The median is 46
• One number is a multiple of 11

Find the other five numbers.

▶️ Answer/Explanation
Solution

Ans: 37, 43, 43, 49, 55, 61 (in any order except 37 must be first)

Range 24 → highest = 37 + 24 = 61

Mode 43 → appears at least twice

Median 46 → average of 3rd and 4th numbers is 46

Multiple of 11 → likely 55

Question 9

Topic – C1.7

Calculate $4^5 – 5^4$.

▶️ Answer/Explanation
Solution

Ans: 399

$4^5 = 4 × 4 × 4 × 4 × 4 = 1024$

$5^4 = 5 × 5 × 5 × 5 = 625$

$1024 – 625 = 399$

Question 10

Topic – C1.15

Jason starts a run at 10.05 am and finishes at 1.02 pm.

Work out the time Jason takes to complete the run.

▶️ Answer/Explanation
Solution

Ans: 2 hours 57 minutes

From 10:05 am to 1:02 pm is 2 hours and 57 minutes

10:05 am → 1:05 pm = 3 hours

Subtract 3 minutes to get to 1:02 pm

Question 11

Topic – C1.4

Calculate $\frac{1 – 0.7}{0.45 – 0.38}$, giving your answer correct to 4 significant figures.

▶️ Answer/Explanation
Solution

Ans: 4.286

Numerator: 1 – 0.7 = 0.3

Denominator: 0.45 – 0.38 = 0.07

Division: 0.3 ÷ 0.07 ≈ 4.285714…

Rounded to 4 significant figures: 4.286

Question 12

Topic – C1.16

Kirsty changes $380.80 into pounds (£) when £1 = $1.19.

Calculate the amount Kirsty receives.

▶️ Answer/Explanation
Solution

Ans: £320

Divide dollars by exchange rate: £ = $380.80 ÷ 1.19

Calculation: 380.80 ÷ 1.19 = 320

Kirsty receives £320.

Question 13

Topic – C8.1

A 4-sided spinner is numbered 1, 2, 3 and 4.
The table shows the probability of the spinner landing on 1, 2 and 4.

Number1234
Probability0.270.18 0.32

Complete the table.

▶️ Answer/Explanation
Solution

Ans: 0.23

Total probability must equal 1.

Sum of known probabilities: 0.27 + 0.18 + 0.32 = 0.77

Missing probability: 1 – 0.77 = 0.23

Question 14

Topic – C1.4

Without using a calculator, work out $\frac{3}{7} – \frac{2}{21}$.

You must show all your working and give your answer as a fraction in its simplest form.

▶️ Answer/Explanation
Solution

Ans: $\frac{1}{3}$

Find common denominator (21): $\frac{3}{7} = \frac{9}{21}$

Subtract fractions: $\frac{9}{21} – \frac{2}{21} = \frac{7}{21}$

Simplify: $\frac{7}{21} = \frac{1}{3}$

Question 15

Topic – C6.2

The diagram shows a right-angled triangle ABC.
AC = 15 cm and angle BAC = 38°.

Calculate BC.

▶️ Answer/Explanation
Solution

Ans: 9.23 cm

Use sine ratio: sin(38°) = opposite/hypotenuse = BC/15

Rearrange: BC = 15 × sin(38°)

Calculate: 15 × 0.6157 ≈ 9.2355 cm

Rounded to 3 significant figures: 9.23 cm

Question 16

Topic – C2.1 

v = 3 – 5t

(a) Work out the value of v when t = 4.

(b) Make t the subject of the formula.

▶️ Answer/Explanation
Solution

(a) Ans: -17

Substitute t = 4 into the formula: v = 3 – 5(4) = 3 – 20 = -17

(b) Ans: t = (3 – v)/5

Rearrange the formula: v = 3 – 5t → 5t = 3 – v → t = (3 – v)/5

Question 17

Topic – C8.2

Kim has a 6-sided spinner numbered 1 to 6. She spins it 63 times and her scores are shown in the table.

Score123456
Frequency1271511810

(a) Find the relative frequency of scoring a 5 with this spinner.

(b) Work out the mean score.

▶️ Answer/Explanation
Solution

(a) Ans: 8/63 or 0.127

Relative frequency = Frequency of 5 / Total spins = 8/63 ≈ 0.127

(b) Ans: 3.41

Mean = (1×12 + 2×7 + 3×15 + 4×11 + 5×8 + 6×10)/63 = 215/63 ≈ 3.41

Question 18

Topic – C2.2 

Factorise completely.

14xy – 7y²

▶️ Answer/Explanation
Solution

Ans: 7y(2x – y)

Identify common factor: 7y is common to both terms.

Factor out 7y: 7y(2x) – 7y(y) = 7y(2x – y)

Question 19

Topic – C1.13

Lin invests $16,000 at a rate of r% per year simple interest.
After 5 years, she has $17,920. 

Find the value of r.

▶️ Answer/Explanation
Solution

Ans: 2.4

Interest earned = 17,920 – 16,000 = $1,920

Simple interest formula: I = PRT → 1,920 = 16,000 × r/100 × 5

Solve for r: r = (1,920 × 100)/(16,000 × 5) = 2.4%

Question 20

Topic – C2.7

22, 17, 12, 7, 2, …

(a) Find the next term.

(b) Find the nth term.

▶️ Answer/Explanation
Solution

(a) Ans: -3

The sequence decreases by 5 each time: 2 – 5 = -3

(b) Ans: 27 – 5n

First term (a) = 22, common difference (d) = -5

nth term = a + (n-1)d = 22 + (n-1)(-5) = 27 – 5n

Question 21

Topic – C1.1

Write down an irrational number with a value between 10 and 20.

▶️ Answer/Explanation
Solution

Ans: Any irrational number between 10 and 20 (e.g., √2×10 ≈ 14.142, π×4 ≈ 12.566, etc.)

An irrational number cannot be expressed as a simple fraction and has non-repeating decimal digits. Examples include √2, π, or √3. Multiply these by appropriate numbers to get values between 10 and 20.

Question 22

Topic – C1.8

The table shows the population and area of three countries in 2020.

(a) Calculate the difference in population between Nigeria and Vietnam.

(b) Which of Comoros or Vietnam has the greater population density? Show your working. 
[Population density = \(\frac{population}{area(km^{2})}\)]

▶️ Answer/Explanation
Solution

Ans (a): 1.087 × 10⁸ or 108,700,000

Difference = Nigeria population (2.06×10⁸) – Vietnam population (9.73×10⁷) = 1.087×10⁸

Ans (b): Comoros

Comoros density = 8.70×10⁵ ÷ 1.86×10³ ≈ 468/km²

Vietnam density = 9.73×10⁷ ÷ 3.10×10⁵ ≈ 314/km²

Comoros has higher population density.

Question 23

Topic – C5.2 

Work out the area of this trapezium.

▶️ Answer/Explanation
Solution

Ans: 21,600 mm²

Area of trapezium = ½ × (sum of parallel sides) × height

= ½ × (204 + 72) × 180

= ½ × 276 × 180

= 138 × 180 = 24,840 mm²

(Note: There seems to be discrepancy between the answer and calculation)

Question 24

Topic – C4.4

Triangle ABC is mathematically similar to triangle PQR. Calculate QR.

▶️ Answer/Explanation
Solution

Ans: 4.5 cm

Since triangles are similar, corresponding sides are proportional.

AB/PQ = AC/PR = BC/QR

8/6 = 6/QR → 4/3 = 6/QR

QR = (6 × 3)/4 = 18/4 = 4.5 cm

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