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Question 1

Topic – C1.1

Write the number two million eight hundred and forty thousand three hundred and twenty-seven in figures.

▶️ Answer/Explanation

Solution

Ans: 2,840,327

Break it down: two million (2,000,000) + eight hundred forty thousand (840,000) + three hundred (300) + twenty-seven (27) = 2,840,327.

Question 2

Topic – C4.6

Write down the mathematical name of this type of angle.

▶️ Answer/Explanation

Solution

Ans: Obtuse

An obtuse angle is any angle greater than 90° but less than 180°. The diagram shows an angle in this range.

Question 3

Topic – C4.2

Draw a line perpendicular to this line.

▶️ Answer/Explanation

Solution

Ans: A perpendicular line forms a 90° angle with the original line. Use a protractor or right angle tool to draw it accurately.

Question 4

Topic – C4.2

In triangle PQR, PR = 5 cm and QR = 4 cm.

Using a ruler and compasses only, construct triangle PQR.
Leave in your construction arcs.
The side PQ has been drawn for you.

▶️ Answer/Explanation

Solution

Ans: [Correct triangle constructed]

1. From point P, draw an arc with radius 5 cm. From point Q, draw an arc with radius 4 cm.

2. The intersection point of these arcs is point R. Connect P to R and Q to R to complete the triangle.

Question 5

Topic – C1.1

Write down a common multiple of 18 and 24.

▶️ Answer/Explanation

Solution

Ans: 72 (or any multiple of 72)

The LCM of 18 (2×3²) and 24 (2³×3) is 2³×3² = 72. Any multiple of 72 (e.g., 72, 144, 216) is a correct answer.

Question 6

Topic – C1.11

Write 32 cm as a fraction of 2 m.
Give your answer in its simplest form.

▶️ Answer/Explanation

Solution

Ans: 4/25

First convert 2m to cm: 2m = 200cm. The fraction is 32/200. Simplify by dividing numerator and denominator by 8: 32÷8=4, 200÷8=25.

Question 7

Topic – C1.5

The temperature, in °C, is recorded at the same time in six cities.

London	Helsinki	Oslo	Paris	Madrid	Berlin
6	-2	-5	7	9	2

(a) Which city has the coldest temperature?

(b) What is the difference in temperature between Helsinki and Paris?

▶️ Answer/Explanation

Solution

Ans: (a) Oslo (b) 9°C

(a) The coldest temperature is -5°C in Oslo.

(b) Difference = Paris (7°C) – Helsinki (-2°C) = 7 – (-2) = 9°C.

Question 8

Topic – C4.6

The diagram shows two straight lines intersecting two parallel lines. Find the value of x.

▶️ Answer/Explanation

Solution

Ans: 54

Angles in a triangle add up to 180°. Given two angles are 71° and 55°, so x = 180 – 71 – 55 = 54°.

Question 9

Topic – C1.11

Divide $200 in the ratio 7:3.

▶️ Answer/Explanation

Solution

Ans: $140, $60

Total parts = 7 + 3 = 10. Value per part = $200 ÷ 10 = $20. First share = 7 × $20 = $140, second share = 3 × $20 = $60.

Question 10

Topic – C9.4

The birth weights, in kg, of 11 babies are recorded:

2.1 1.6 2.7 4.2 4.0 2.2 3.1 1.7 2.6 3.3 3.7

(a) Complete the stem-and-leaf diagram to show this information.

(b) Find the median.

▶️ Answer/Explanation

Solution

Ans: (a) Stem-and-leaf completed (b) 2.7 kg

(a) Stem-and-leaf:

(b) Ordered data: 1.6,1.7,2.1,2.2,2.6,2.7,3.1,3.3,3.7,4.0,4.2. Median is the 6th value = 2.7 kg.

Question 11

Topic – C9.4

Victoria records the colour of each of 240 cars leaving a car park. Some of this information is shown in the pie chart.

(a) Show that 60 cars are blue.

(b) The rest of the cars are either red or white.
110 cars are red.

Complete the pie chart to show this information.

▶️ Answer/Explanation

Solution

(a) The blue sector is 90° out of 360°, so fraction is 90/360 = 1/4. 1/4 of 240 cars = 60 cars.

(b) Total remaining cars = 240 – 60 – 110 = 70 white cars. Red sector angle = (110/240)×360 = 165°, white sector angle = (70/240)×360 = 105°.

Question 12

Topic – C1.13

The price of a computer is $520.
This price is reduced by 15% in a sale.

Work out the sale price.

▶️ Answer/Explanation

Solution

Original price = $520

15% reduction = 0.15 × 520 = $78

Sale price = 520 – 78 = $442

Question 13

Topic – C1.4

Without using a calculator, work out $\frac{1}{3} + \frac{5}{6}$.

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

▶️ Answer/Explanation

Solution

Find common denominator (6):

$\frac{1}{3} = \frac{2}{6}$

$\frac{2}{6} + \frac{5}{6} = \frac{7}{6}$

Convert to mixed number: $1\frac{1}{6}$

Question 14

Topic – C8.1

Mario tests new cars. The probability that a car is faulty is 0.04.

(a) Find the probability that a car is not faulty.

(b) In one week Mario tests 850 cars. Find the number of cars that are expected to be faulty.

▶️ Answer/Explanation

Solution

(a) P(not faulty) = 1 – P(faulty) = 1 – 0.04 = 0.96

(b) Expected faulty cars = 850 × 0.04 = 34 cars

Question 15

Topic – C1.4

A café sells 330 sandwiches.
This is $\frac{11}{14}$ of the sandwiches they make.

Work out the number of sandwiches the café makes.

▶️ Answer/Explanation

Solution

Let total sandwiches be x

$\frac{11}{14}x = 330$

$x = 330 × \frac{14}{11}$

$x = 420$ sandwiches

Question 16

Topic – C2.10

(a) Complete the table of values for $ y = \frac{5}{x}$

x	-5	-4	-2.5	-2	-1	1	2	2.5	4	5
y	-1		-2	-2.5	-5	5	2.5	2		1

(b) On the grid, draw the graph of $ y = \frac{5}{x}$ for -5 ≤ x ≤ -1 and 1 ≤ x ≤ 5.

▶️ Answer/Explanation

Solution

(a) Missing values: -1.25 (x=-4), 1.25 (x=4)

Calculated by y = 5/x: 5/-4 = -1.25 and 5/4 = 1.25

(b) Hyperbola graph

Plot all points from the table and draw two smooth curves (one in negative x, one in positive x) approaching but never touching the axes.

Question 17

Topic – C2.7

(a) 3, 9, 27, 81, …

Write down the term to term rule for this sequence.

(b) 13, 17, 21, 25, …

Find the nth term of this sequence.

▶️ Answer/Explanation

Solution

(a) ×3

Each term is multiplied by 3 to get the next term.

(b) 4n + 9

The common difference is 4, and the first term minus the difference gives 9 when n=1.

Question 18

Topic – C1.2

The Venn diagram shows elements of sets ξ, P and Q. Complete the statements.

(a) Write down the elements of set P.

(b) Find n(P ∪ Q).

▶️ Answer/Explanation

Solution

(a) {a, b, c, d}

These are the elements shown inside circle P.

(b) 6

Counting all elements in P or Q gives 6 elements.

Question 19

Topic – C4.6

The bearing of A from B is 137°. Find the bearing of B from A.

▶️ Answer/Explanation

Solution

317°

To find the reverse bearing, add 180° to 137°.

137° + 180° = 317°.

Question 20

Topic – C1.8

(a) Write 0.00273 in standard form.

(b) Sam has to answer this question.

Sam writes $ 42.1 \times 10^{6}$ as his answer to this question.
What two errors has Sam made?

▶️ Answer/Explanation

Solution

(a) 2.73 × 10⁻³

Move decimal 3 places right for standard form.

(b) 1) 42.1 is incorrectly rounded [to 3 significant figures]

2) $ 42.1 \times 10^{6}$ is not correct standard form

Question 21

Topic – C4.4

Triangle ABC is mathematically similar to triangle DEF.

Find BC.

▶️ Answer/Explanation

Solution

Ans: 34 cm

Since triangles are similar, corresponding sides are proportional.

Scale factor = AB/DE = 51/6 = 8.5

Therefore, BC = EF × scale factor = 4 × 8.5 = 34 cm

Question 22

Topic – C6.2

The diagram shows a right-angled triangle.

Show that the value of x is 15.8, correct to 3 significant figures.

▶️ Answer/Explanation

Solution

Ans: 15.8 cm

Using tangent function: tan(48°) = opposite/adjacent = x/17.5

Therefore, x = 17.5 × tan(48°) ≈ 17.5 × 1.1106 ≈ 19.435

Alternatively, tan(42°) = 17.5/x → x ≈ 17.5/0.9004 ≈ 19.435

Rounding to 3 significant figures gives x ≈ 19.4 cm

Question 23

Topic – C2.5

Natalie buys 4 tomato plants and 3 pepper plants for $9.35 .
Samir buys 2 tomato plants and 11 pepper plants for $16.55 .

Write down a pair of simultaneous equations and solve them to find the cost of one tomato plant and the cost of one pepper plant.
You must show all your working.

▶️ Answer/Explanation

Solution

Ans: Tomato plant $1.41, Pepper plant $1.25

Let t = tomato plant price, p = pepper plant price.

Equation 1: 4t + 3p = 9.35

Equation 2: 2t + 11p = 16.55

Multiply Equation 2 by 2: 4t + 22p = 33.10

Subtract Equation 1: 19p = 23.75 → p = 1.25

Substitute p into Equation 1: 4t + 3.75 = 9.35 → t = 1.40

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