A Level H1 Mathematics Numbers Ratio Proportion Quiz

<!-- TuitionGoWhere generation metadata: stage=5-1; model=tencent/hy3:free; model_label=Tencent HY3 Free; generated=2026-07-09; Sources: Stage 4-0 LLM templates, syllabus context, and Stage 2 evidence where available. -->

A-Level Maths H1 Quiz - Numbers Ratio Proportion

Name: ___________________________
Class: ___________________________
Date: ___________________________
Score: _______ / 40

Duration: 50 minutes
Total Marks: 40
Topic: Numbers, Ratio & Proportion

Instructions:

• Answer all 20 questions.
• Show your working clearly where applicable.
• Use a calculator if needed.
• Write your answers in the spaces provided.

---

Section A: Basic Number and Ratio (Questions 1–5)

1. [2 marks] Simplify the ratio $24 : 36 : 60$ to its simplest form.

Answer: ________________________________________________

2. [2 marks] A recipe uses flour and sugar in the ratio $3 : 2$. If 450 g of flour is used, how much sugar is needed?

Answer: ________________________________________________ g

3. [2 marks] Express the fraction $\frac{7}{8}$ as a percentage.

Answer: ________________________________________________ %

4. [2 marks] Divide $840 between Ali and Bala in the ratio $5 : 3$. How much does each receive?

Ali: $__________
Bala: $__________

5. [2 marks] A number is increased by 25% and then decreased by 20%. What is the overall percentage change from the original?

Answer: ________________________________________________ %

---

Section B: Proportion and Applications (Questions 6–10)

6. [2 marks] If 6 workers can complete a task in 10 days, how many days will 15 workers take at the same rate?

Answer: ________________________________________________ days

7. [2 marks] $y$ is directly proportional to $x$. Given $y = 18$ when $x = 3$, find $y$ when $x = 7$.

Answer: ________________________________________________

8. [2 marks] $P$ is inversely proportional to $Q$. If $P = 12$ when $Q = 4$, find $P$ when $Q = 6$.

Answer: ________________________________________________

9. [2 marks] A map has scale $1 : 25\,000$. Two towns are 8 cm apart on the map. What is the actual distance in km?

Answer: ________________________________________________ km

10. [2 marks] The ratio of boys to girls in a class is $4 : 5$. If there are 36 students, how many boys are there?

Answer: ________________________________________________

---

Section C: Mixtures, Rates and Multi-Step (Questions 11–15)

11. [3 marks] A mixture of orange and apple juice is in the ratio $2 : 5$. If 14 litres of orange juice are used, find the total volume of the mixture.

Answer: ________________________________________________ L

12. [3 marks] A car travels 240 km in 3 hours. Another travels the same distance at a speed 20 km/h faster. Find the time taken by the second car.

Answer: ________________________________________________ h

13. [3 marks] Three partners invest in a business in the ratio $3 : 4 : 5$ and share profit in the same ratio. If total profit is $4800, find the largest share.

Answer: $________________________________________________

14. [3 marks] The mass of an object is proportional to the cube of its radius. If mass is 64 kg when radius is 2 cm, find mass when radius is 3 cm.

Answer: ________________________________________________ kg

15. [3 marks] A solution is made by mixing acid and water in the ratio $1 : 7$. How much acid must be added to 56 L of water to keep the same ratio?

Answer: ________________________________________________ L

---

Section D: Problem Solving and Interpretation (Questions 16–20)

16. [2 marks] The table below shows the number of customers at a cafe on two days.

Day	Men	Women	Children
Mon	12	18	6
Tue	15	20	5

Find the ratio of men to women on Tuesday.

Answer: ________________________________________________

17. [2 marks] A shop offers 30% discount followed by additional 10% off the discounted price. What is the total percentage discount from original?

Answer: ________________________________________________ %

18. [3 marks] A and B can finish a job in 6 days together. A alone takes 10 days. How long does B alone take?

Answer: ________________________________________________ days

19. [3 marks] The number of bacteria doubles every 3 hours. If there are 200 at 9 am, how many at 6 pm the same day?

Answer: ________________________________________________

20. [2 marks] The ratio of red to blue marbles is $3 : 8$. After adding 10 blue marbles, the ratio becomes $3 : 10$. How many red marbles are there?

Answer: ________________________________________________

<!-- TuitionGoWhere generation metadata: stage=5-1; model=tencent/hy3:free; model_label=Tencent HY3 Free; generated=2026-07-09; Sources: Stage 4-0 LLM templates, syllabus context, and Stage 2 evidence where available. -->

A-Level Maths H1 Quiz - Numbers Ratio Proportion (Answer Key)

Topic: Numbers, Ratio & Proportion
Total Marks: 40

---

Section A: Basic Number and Ratio

1. [2 marks] Simplify $24 : 36 : 60$.

• Find GCD of 24, 36, 60 = 12.
• Divide each by 12: $24/12 = 2$, $36/12 = 3$, $60/12 = 5$.
• Answer: $2 : 3 : 5$
• Teaching note: Ratios simplify by dividing all terms by common factor. Mark: 2 for correct simplified ratio.

2. [2 marks] Flour : Sugar = $3 : 2$. Flour = 450 g.

• 3 parts = 450 g → 1 part = 150 g.
• Sugar = 2 parts = $2 \times 150 = 300$ g.
• Answer: 300 g
• Common mistake: reversing ratio. Mark: 2 for correct value with working.

3. [2 marks] $\frac{7}{8}$ as percentage.

• $\frac{7}{8} = 0.875$.
• $0.875 \times 100 = 87.5\%$.
• Answer: 87.5%
• Mark: 1 for decimal, 1 for percentage.

4. [2 marks] $840 in ratio $5 : 3$.

• Total parts = 8.
• Ali: $\frac{5}{8} \times 840 = 525$.
• Bala: $\frac{3}{8} \times 840 = 315$.
• Answer: Ali $525, Bala $315
• Mark: 1 each.

5. [2 marks] Increase 25% then decrease 20%.

• Let original = 100. After +25% → 125. After -20% of 125 → $125 \times 0.8 = 100$.
• Overall change = 0%.
• Answer: 0%
• Teaching: successive % changes not additive. Mark: 2 for correct.

---

Section B: Proportion and Applications

6. [2 marks] Workers-days constant: $6 \times 10 = 60$. For 15 workers: $60 / 15 = 4$ days.

• Answer: 4 days
• Mark: 2.

7. [2 marks] $y \propto x$, $y = kx$. $18 = k \cdot 3 \Rightarrow k = 6$. $y = 6 \times 7 = 42$.

• Answer: 42
• Mark: 1 for k, 1 for y.

8. [2 marks] $P \propto 1/Q \Rightarrow PQ = c$. $12 \times 4 = 48$. $P = 48 / 6 = 8$.

• Answer: 8
• Mark: 2.

9. [2 marks] Scale $1 : 25\,000$. 8 cm → $8 \times 25\,000 = 200\,000$ cm = 2 km.

• Answer: 2 km
• Mark: 1 for cm, 1 for km.

10. [2 marks] Boys : Girls = $4 : 5$, total 36. Parts = 9. Boys = $4/9 \times 36 = 16$.

• Answer: 16
• Mark: 2.

---

Section C: Mixtures, Rates and Multi-Step

11. [3 marks] Orange : Apple = $2 : 5$. Orange = 14 L → 1 part = 7 L. Total = 7 parts = 49 L.

• Answer: 49 L
• Mark: 1 part, 2 total.

12. [3 marks] Car1 speed = $240/3 = 80$ km/h. Car2 speed = 100 km/h. Time = $240/100 = 2.4$ h.

• Answer: 2.4 h
• Mark: 1 speed1, 1 speed2, 1 time.

13. [3 marks] Ratio $3:4:5$, total 12 parts. Largest = $5/12 \times 4800 = 2000$.

• Answer: $2000
• Mark: 1 parts, 2 share.

14. [3 marks] $m \propto r^3$, $m = kr^3$. $64 = k \cdot 8 \Rightarrow k = 8$. At r=3: $m = 8 \cdot 27 = 216$ kg.

• Answer: 216 kg
• Mark: 1 k, 2 m.

15. [3 marks] Acid : Water = $1 : 7$. Water = 56 L → 1 part = 8 L acid already? To keep ratio with 56 L water need acid = $56/7 = 8$ L. If currently only water given, add 8 L.

• Answer: 8 L
• Mark: 2 ratio, 1 answer.

---

Section D: Problem Solving

16. [2 marks] Tue men = 15, women = 20 → ratio $15 : 20 = 3 : 4$.

• Answer: $3 : 4$
• Mark: 2.

17. [2 marks] Original 100. After 30% → 70. After extra 10% → $70 \times 0.9 = 63$. Total discount = 37%.

• Answer: 37%
• Mark: 2.

18. [3 marks] Together rate = 1/6. A rate = 1/10. B rate = $1/6 - 1/10 = 1/15$. B alone = 15 days.

• Answer: 15 days
• Mark: 1 eq, 2 solve.

19. [3 marks] 9 am to 6 pm = 9 h. Doubles every 3 h → 3 periods. $200 \times 2^3 = 1600$.

• Answer: 1600
• Mark: 1 time, 2 calc.

20. [2 marks] Red = 3k, Blue = 8k. After +10 blue: $3k : (8k+10) = 3 : 10$. Cross: $30k = 24k + 30 \Rightarrow 6k = 30 \Rightarrow k=5$. Red = 15.

• Answer: 15
• Mark: 2.