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Secondary 4 Additional Mathematics Numbers Ratio Proportion Quiz

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Questions

Secondary 4 Additional Mathematics Quiz - Numbers Ratio Proportion

Name: _________________________
Class: _________________________
Date: _________________________
Score: ________ / 40

Duration: 50 minutes
Total Marks: 40

Instructions

Answer all questions in the spaces provided.
Show all working clearly. Answers without working may not receive full marks.
The number of marks for each question is shown in brackets [ ].
Non-exact answers should be given to 3 significant figures unless otherwise stated.
This quiz focuses on Numbers, Ratio and Proportion topics relevant to Additional Mathematics preparation.

Section A: Short Answer Questions (Questions 1–10)

Answer all questions in this section. Each question carries 2 marks.

1. Express the ratio $1.2 : 0.8 : 2.4$ in its simplest integer form.
[2]

Answer: _______________________________________________

2. If $a : b = 3 : 5$ and $b : c = 4 : 7$ , find $a : b : c$ in its simplest form.
[2]

Answer: _______________________________________________

3. The ratio of the number of boys to girls in a class is $5 : 4$ . If there are 25 boys, how many girls are there?
[2]

Answer: _______________________________________________

4. Divide $\$ 360 $in the ratio$ 2 : 3 : 4$. Find the largest share.
[2]

Answer: _______________________________________________

5. If $x$ is directly proportional to $y$ and $x = 15$ when $y = 6$ , find $x$ when $y = 10$ .
[2]

Answer: _______________________________________________

6. If $p$ is inversely proportional to $q$ and $p = 8$ when $q = 3$ , find $p$ when $q = 12$ .
[2]

Answer: _______________________________________________

7. Simplify the ratio $\frac{2}{3} : \frac{5}{6} : \frac{1}{2}$ to the simplest integer form.
[2]

Answer: _______________________________________________

8. Three friends share a sum of money in the ratio $2 : 5 : 8$ . If the smallest share is $\$ 40$, find the total sum.
[2]

Answer: _______________________________________________

9. If $y$ varies directly as $x^2$ and $y = 45$ when $x = 3$ , find $y$ when $x = 5$ .
[2]

Answer: _______________________________________________

10. If $z$ varies inversely as $\sqrt{x}$ and $z = 6$ when $x = 16$ , find $z$ when $x = 36$ .
[2]

Answer: _______________________________________________

Section B: Structured Questions (Questions 11–16)

Answer all questions in this section. Show all working clearly.

11. The cost of printing flyers is directly proportional to the number of flyers printed. It costs $\$ 120$ to print 500 flyers.

(a) Find the cost of printing 800 flyers.
[2]

(b) How many flyers can be printed for $\$ 210$?
[2]

Answer: _______________________________________________

12. The time taken to complete a task is inversely proportional to the number of workers. If 6 workers can complete the task in 8 hours,

(a) how long will it take 12 workers to complete the same task?
[2]

(b) how many workers are needed to complete the task in 3 hours?
[2]

Answer: _______________________________________________

13. The variables $x$ and $y$ are related such that $y$ varies directly as $x$ and inversely as $z$ . When $x = 4$ and $z = 2$ , $y = 10$ .

(a) Express $y$ in terms of $x$ and $z$ .
[2]

(b) Find $y$ when $x = 6$ and $z = 3$ .
[2]

Answer: _______________________________________________

14. A recipe for 6 people requires 450 g of flour and 300 g of sugar.

(a) How much flour is needed for 10 people?
[2]

(b) If only 200 g of sugar is available, how many people can be served?
[2]

Answer: _______________________________________________

15. The ratio of the areas of two similar triangles is $9 : 25$ .

(a) Find the ratio of their corresponding side lengths.
[2]

(b) If the perimeter of the smaller triangle is 36 cm, find the perimeter of the larger triangle.
[2]

Answer: _______________________________________________

16. The volume $V$ of a gas varies directly as its temperature $T$ (in Kelvin) and inversely as its pressure $P$ . At a temperature of 300 K and pressure of 150 kPa, the volume is 20 m³.

(a) Express $V$ in terms of $T$ and $P$ .
[2]

(b) Find the volume when $T = 400$ K and $P = 200$ kPa.
[2]

Answer: _______________________________________________

Section C: Application and Problem Solving (Questions 17–20)

Answer all questions in this section. Show all working clearly.

17. A map is drawn to a scale of $1 : 25\,000$ .

(a) If the distance between two towns on the map is 8 cm, find the actual distance in kilometres.
[2]

(b) If the actual area of a park is 4 km², find the area of the park on the map in cm².
[3]

Answer: _______________________________________________

18. The resistance $R$ of a wire varies directly as its length $L$ and inversely as the square of its diameter $d$ . A wire of length 2 m and diameter 0.5 mm has a resistance of 8 ohms.

(a) Express $R$ in terms of $L$ and $d$ .
[2]

(b) Find the resistance of a wire of length 5 m and diameter 1 mm.
[3]

Answer: _______________________________________________

19. Three partners, A, B, and C, invest in a business in the ratio $3 : 5 : 7$ . The total profit at the end of the year is $\$ 45,000$.

(a) Find the profit share of each partner.
[3]

(b) Partner C decides to reinvest $\frac{1}{3}$ of their profit share. How much does C reinvest?
[2]

Answer: _______________________________________________

20. The time $t$ taken to fill a tank varies inversely as the square of the radius $r$ of the pipe used. When a pipe of radius 2 cm is used, it takes 45 minutes to fill the tank.

(a) Express $t$ in terms of $r$ .
[2]

(b) Find the time taken if a pipe of radius 3 cm is used.
[2]

(c) What radius of pipe is needed to fill the tank in 20 minutes?
[2]

Answer: _______________________________________________

End of Quiz

Answers

Secondary 4 Additional Mathematics Quiz - Numbers Ratio Proportion

Answer Key

Section A: Short Answer Questions (Questions 1–10)

1. [2]

$1.2 : 0.8 : 2.4$

Multiply all terms by 10: $12 : 8 : 24$

Divide by GCD (4): $\boxed{3 : 2 : 6}$

2. [2]

$a : b = 3 : 5 = 12 : 20$ (multiply by 4)
$b : c = 4 : 7 = 20 : 35$ (multiply by 5)

$\boxed{a : b : c = 12 : 20 : 35}$

Marking note: Award 1 mark for correct scaling of one ratio, 1 mark for final answer.

3. [2]

$\frac{\text{boys}}{\text{girls}} = \frac{5}{4} = \frac{25}{g}$

$5g = 100 \Rightarrow g = \boxed{20}$

There are 20 girls.

4. [2]

Total parts: $2 + 3 + 4 = 9$

Largest share: $\frac{4}{9} \times 360 = \boxed{\$ 160}$

5. [2]

$x = ky$ where $k$ is constant.

$15 = k(6) \Rightarrow k = 2.5$

When $y = 10$ : $x = 2.5 \times 10 = \boxed{25}$

6. [2]

$p = \frac{k}{q}$ where $k$ is constant.

$8 = \frac{k}{3} \Rightarrow k = 24$

When $q = 12$ : $p = \frac{24}{12} = \boxed{2}$

7. [2]

$\frac{2}{3} : \frac{5}{6} : \frac{1}{2}$

Multiply all by LCM of denominators (6): $4 : 5 : 3$

$\boxed{4 : 5 : 3}$

8. [2]

Smallest share corresponds to 2 parts = $\$ 40$

1 part = $\$ 20$

Total parts: $2 + 5 + 8 = 15$

Total sum: $15 \times 20 = \boxed{\$ 300}$

9. [2]

$y = kx^2$ where $k$ is constant.

$45 = k(3)^2 = 9k \Rightarrow k = 5$

When $x = 5$ : $y = 5(5)^2 = 5 \times 25 = \boxed{125}$

10. [2]

$z = \frac{k}{\sqrt{x}}$ where $k$ is constant.

$6 = \frac{k}{\sqrt{16}} = \frac{k}{4} \Rightarrow k = 24$

When $x = 36$ : $z = \frac{24}{\sqrt{36}} = \frac{24}{6} = \boxed{4}$

Section B: Structured Questions (Questions 11–16)

11. [4]

Cost $C$ is directly proportional to number of flyers $n$ : $C = kn$

(a) $120 = k(500) \Rightarrow k = 0.24$

For 800 flyers: $C = 0.24 \times 800 = \boxed{\$ 192}$

(b) $210 = 0.24n \Rightarrow n = \frac{210}{0.24} = \boxed{875}$ flyers

12. [4]

Time $t$ is inversely proportional to number of workers $w$ : $t = \frac{k}{w}$

(a) $8 = \frac{k}{6} \Rightarrow k = 48$

For 12 workers: $t = \frac{48}{12} = \boxed{4}$ hours

(b) $3 = \frac{48}{w} \Rightarrow w = \frac{48}{3} = \boxed{16}$ workers

13. [4]

(a) $y = \frac{kx}{z}$ where $k$ is constant.

$10 = \frac{k(4)}{2} = 2k \Rightarrow k = 5$

$\boxed{y = \frac{5x}{z}}$

(b) When $x = 6$ , $z = 3$ : $y = \frac{5(6)}{3} = \frac{30}{3} = \boxed{10}$

14. [4]

(a) Flour for 6 people = 450 g

Flour for 10 people: $\frac{450}{6} \times 10 = 75 \times 10 = \boxed{750}$ g

(b) Sugar for 6 people = 300 g

With 200 g sugar: $\frac{200}{300} \times 6 = \frac{2}{3} \times 6 = \boxed{4}$ people

15. [4]

(a) Ratio of areas = $9 : 25$

Ratio of sides = $\sqrt{9} : \sqrt{25} = \boxed{3 : 5}$

(b) Perimeter ratio = side ratio = $3 : 5$

$\frac{36}{P} = \frac{3}{5} \Rightarrow 3P = 180 \Rightarrow P = \boxed{60}$ cm

16. [4]

(a) $V = \frac{kT}{P}$ where $k$ is constant.

$20 = \frac{k(300)}{150} = 2k \Rightarrow k = 10$

$\boxed{V = \frac{10T}{P}}$

(b) When $T = 400$ , $P = 200$ : $V = \frac{10(400)}{200} = \frac{4000}{200} = \boxed{20}$ m³

Section C: Application and Problem Solving (Questions 17–20)

17. [5]

Scale: $1 : 25\,000$

(a) Map distance = 8 cm

Actual distance: $8 \times 25\,000 = 200\,000$ cm $= 2000$ m $= \boxed{2}$ km

(b) Actual area = 4 km² $= 4 \times (100\,000)^2$ cm² $= 4 \times 10^{10}$ cm²

Area ratio = $1^2 : 25\,000^2 = 1 : 625 \times 10^6$

Map area: $\frac{4 \times 10^{10}}{625 \times 10^6} = \frac{40\,000}{625} = \boxed{64}$ cm²

Alternative method: Linear scale factor = $\frac{1}{25\,000}$ , area scale factor = $\frac{1}{(25\,000)^2}$ . Map area = $\frac{4 \times 10^{10}}{6.25 \times 10^8} = 64$ cm².

18. [5]

(a) $R = \frac{kL}{d^2}$ where $k$ is constant.

$8 = \frac{k(2)}{(0.5)^2} = \frac{2k}{0.25} = 8k \Rightarrow k = 1$

$\boxed{R = \frac{L}{d^2}}$ (where $L$ is in metres and $d$ in mm)

(b) When $L = 5$ , $d = 1$ : $R = \frac{5}{(1)^2} = \boxed{5}$ ohms

19. [5]

Total parts: $3 + 5 + 7 = 15$

(a) A's share: $\frac{3}{15} \times 45\,000 = \boxed{\$ 9,000} $B's share:$ \frac{5}{15} \times 45,000 = \boxed{$15,000} $C's share:$ \frac{7}{15} \times 45,000 = \boxed{$21,000}$

(b) C reinvests: $\frac{1}{3} \times 21\,000 = \boxed{\$ 7,000}$

20. [6]

(a) $t = \frac{k}{r^2}$ where $k$ is constant.

$45 = \frac{k}{(2)^2} = \frac{k}{4} \Rightarrow k = 180$

$\boxed{t = \frac{180}{r^2}}$

(b) When $r = 3$ : $t = \frac{180}{(3)^2} = \frac{180}{9} = \boxed{20}$ minutes

(c) When $t = 20$ : $20 = \frac{180}{r^2} \Rightarrow r^2 = \frac{180}{20} = 9 \Rightarrow r = \boxed{3}$ cm

Summary of Marks

Section	Questions	Marks
A	1–10	20
B	11–16	24
C	17–20	22
Total		40 (adjusted: 20 × 2 = 40 for Section A; Sections B and C as marked)

Note: Total marks = 40 as stated on the quiz header.

Common Mistakes to Watch For

Forgetting to find the constant of proportionality before answering subsequent parts.
Confusing direct and inverse proportion — direct means $y = kx$ , inverse means $y = \frac{k}{x}$ .
Not converting units in map scale problems (cm to km, etc.).
Area/volume scale factors — remember that area scales as the square and volume as the cube of the linear scale factor.
Ratio simplification — always check that the final ratio has no common factors.