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Question 1

Topic – C1.4

Write $\frac{8}{10}$ as a decimal.

▶️ Answer/Explanation

Solution

Ans: 0.8

To convert $\frac{8}{10}$ to a decimal, divide the numerator by the denominator.

8 ÷ 10 = 0.8

Question 2

Topic – C1.16

Asha works in a café.
Her wage is calculated using the formula $ \text{wage} = \text{hourly rate} \times \text{number of hours} + \text{bonus} $.
Her hourly rate is $11.52.
One week Asha works 25 hours and receives a bonus of $5.40.

Work out her wage for this week.

▶️ Answer/Explanation

Solution

Ans: $293.40

Using the formula: wage = hourly rate × hours + bonus

= $11.52 × 25 + $5.40

= $288.00 + $5.40 = $293.40

Question 3

Topic – C2.7

These are the first four terms in a sequence.

-3 4 11 18

(a) Find the next term.

(b) Explain how you worked out your answer.

▶️ Answer/Explanation

Solution

Ans: (a) 25 (b) Added 7

(a) Looking at the differences between terms: 4 – (-3) = 7, 11 – 4 = 7, 18 – 11 = 7

So the next term is 18 + 7 = 25

(b) The pattern is adding 7 each time.

Question 4

Topic – C1.4

Work out $\frac{2}{5}$ of 180.

▶️ Answer/Explanation

Solution

Ans: 72

To find $\frac{2}{5}$ of 180:

First divide 180 by 5 to get $\frac{1}{5}$: 180 ÷ 5 = 36

Then multiply by 2: 36 × 2 = 72

Question 5

Topic – C1.5

Write these numbers in order, starting with the smallest:

$\frac{3}{16}$, 18.7%, 0.19, $\frac{9}{50}$

▶️ Answer/Explanation

Solution

Ans: $\frac{9}{50}$ < 18.7% < $\frac{3}{16}$ < 0.19

Convert all to decimals: $\frac{9}{50}$ = 0.18, 18.7% = 0.187, $\frac{3}{16}$ ≈ 0.1875, 0.19

Order: 0.18, 0.187, 0.1875, 0.19

Question 6

Topic – C1.6

Write down the number that is 9 greater than -23.

▶️ Answer/Explanation

Solution

Ans: -14

-23 + 9 = -14

Adding 9 moves the number 9 places to the right on the number line.

Question 7

Topic – C9.4

For 16 days, Safia records the number of dresses she sells:

24, 6, 18, 14, 27, 37, 9, 16

22, 17, 16, 16, 24, 20, 15, 32

(a) Complete the stem-and-leaf diagram.

(b) Write down the mode.

▶️ Answer/Explanation

Solution

Ans:

(a) Stem-and-leaf:

(b) Mode = 16 (appears most frequently)

Question 8

Topic – C1.10

Write 24.07839

(a) correct to 2 decimal places

(b) correct to the nearest 10

▶️ Answer/Explanation

Solution

Ans:

(a) 24.08 (look at 3rd decimal 8 ≥5, so round up)

(b) 20 (look at units digit 4 <5, so round down)

Question 9

Topic – C2.5

Given v = u + at, find the value of v when u = 30, a = -2 and t = 7.

▶️ Answer/Explanation

Solution

Ans: 16

v = 30 + (-2)×7

v = 30 – 14

v = 16

Question 10

Topic – C5.1

Change 62,000 millimetres into kilometres.

▶️ Answer/Explanation

Solution

Ans: 0.062 km

First convert mm to m: 62,000 ÷ 1,000 = 62 m

Then convert m to km: 62 ÷ 1,000 = 0.062 km

Question 11

Topic – C4.6

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

▶️ Answer/Explanation

Solution

Ans: 64

1. The angle adjacent to 114° is 66° (180° – 114°).

2. In the triangle formed, the third angle is 64° (180° – 50° – 66°).

3. x is equal to this angle because they are vertically opposite angles.

Markscheme:

B1 for any of these angles labelled on the diagram.

Question 12

Topic – C1.1

(a) Explain why 111 is not a prime number.

(b) Find a prime number between 110 and 120.

▶️ Answer/Explanation

Solution

Ans: (a) It’s divisible by 3 (b) 113

(a) 111 is divisible by 3 (1+1+1=3, which is divisible by 3).

(b) Checking numbers between 110-120: 113 isn’t divisible by 2, 3, 5, 7, or 11, making it prime.

Question 13

Topic – C4.6

Find the bearing of Q from P.

▶️ Answer/Explanation

Solution

Ans: 231°

1. The angle between North and the line PQ is 39°.

2. The bearing is measured clockwise from North.

3. 180° (South) + 90° (East) – 39° = 231°.

Question 14

Topic – C9.5

(a) As the age of a car increases, the selling price decreases. What type of correlation is this?

(b) Write down the type of correlation between the height of a driver and the value of their car.

▶️ Answer/Explanation

Solution

Ans: (a) Negative (b) No correlation

(a) As one variable increases while the other decreases, this shows negative correlation.

(b) There’s no logical connection between a driver’s height and car value, so no correlation exists.

Question 15

Topic – C4.6

Calculate the interior angle of a regular 9-sided polygon.

▶️ Answer/Explanation

Solution

Ans: 140°

1. Sum of interior angles = (9-2) × 180° = 1260°.

2. Each interior angle = 1260° ÷ 9 = 140°.

Alternatively: 180° – (360° ÷ 9) = 140°.

Question 16

Topic – C1.13

Filip invests $4000 for 3 years at a rate of 2.5% per year simple interest.

Calculate the value of his investment at the end of the 3 years.

▶️ Answer/Explanation

Solution

Ans: $4300

First calculate the interest: $4000 × 2.5% × 3 = $300

Then add to principal: $4000 + $300 = $4300

Question 17

Topic – C4.7

A, B and C are points on a circle, center O.

(a) Draw a tangent to the circle at point A.

(b) The circumference of the circle is 22.3 cm. Calculate the radius of the circle.

▶️ Answer/Explanation

Solution

Ans:

(a) A line perpendicular to radius OA at point A

(b) r = C/(2π) = 22.3/(2×3.142) ≈ 3.55 cm

Question 18

Topic – C2.2

Expand and simplify.

2(t + w) + 3(w – t)

▶️ Answer/Explanation

Solution

Ans: 5w – t

First expand: 2t + 2w + 3w – 3t

Then combine like terms: (2t – 3t) + (2w + 3w)

Final simplification: -t + 5w or 5w – t

Question 19

Topic – C1.4

Without using a calculator, work out 3⅛ – 1¾.

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

▶️ Answer/Explanation

Solution

Ans: 1⅜

Convert to improper fractions: 25/8 – 7/4

Find common denominator: 25/8 – 14/8

Subtract: 11/8

Convert to mixed number: 1⅜

Question 20

Topic – C1.2

ξ = {students in a class}
C = {students who play cricket}
F = {students who play football}

There are 36 students in the class.
15 students play cricket.
20 students play football.

(a) Complete the Venn diagram.

(b) Write down n(C ∪ F).

▶️ Answer/Explanation

Solution

Ans:

(a) Intersection: 15 + 20 – 36 = 11 (overlap), C only: 4, F only: 16

(b) n(C ∪ F) = 4 + 11 + 16 = 31 (all students who play either sport)

Question 21

Topic – C6.2

ABC is a right-angled triangle.

Calculate AC.

▶️ Answer/Explanation

Solution

AC = 21.7 cm

Using cosine ratio: cos(34°) = adjacent/hypotenuse = BC/AC

cos(34°) = 18/AC

AC = 18/cos(34°)

AC ≈ 18/0.829 ≈ 21.7 cm

Question 22

Topic – C3.1

Point A and line L are shown on the grid.

(a) Write down the coordinates of point A.

(b) On the grid, plot the point (-2, 4).

▶️ Answer/Explanation

Solution

(a) (1, -2)

(b) Point plotted at (-2, 4)

(c) y = 2x + 3

For (a): Read directly from the grid.

For (c): The line passes through (0,3) giving y-intercept 3. The slope is 2 (rise/run = 2/1).

Question 23

Topic – C1.6

Bell A rings every 22 minutes.
Bell B rings every 14 minutes.
Both bells ring at 09:00.

Work out the next time both bells ring together.

▶️ Answer/Explanation

Solution

11:34

Find LCM of 22 and 14 minutes.

Prime factors: 22 = 2×11, 14 = 2×7

LCM = 2×7×11 = 154 minutes

154 minutes = 2 hours 34 minutes

09:00 + 2:34 = 11:34

Question 24

Topic – C4.4

Triangle ABC is mathematically similar to triangle DEF.

Calculate the value of x.

▶️ Answer/Explanation

Solution

x = 5.84 cm

Find the scale factor: DF/AB = 4.4/5.5 = 0.8

Apply to BC: x = 7.3 × 0.8 = 5.84 cm

Alternatively: x/7.3 = 4.4/5.5

x = (4.4 × 7.3)/5.5 = 5.84 cm

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