Secondary 4 Elementary Mathematics Numbers Ratio Proportion Quiz

Secondary 4 Elementary Mathematics Quiz - Numbers Ratio Proportion (Answer Key)

Topic: Numbers, Ratio & Proportion
Version: 1 of 5
Total Marks: 40

Teaching notes are provided for each question to help a student new to the topic.

Section A: Direct Ratio and Proportion

1. (2 marks)
Flour : Sugar = $3 : 2$.
$3$ parts flour = $240$ g → $1$ part = $240 \div 3 = 80$ g.
Sugar = $2$ parts = $2 \times 80 = 160$ g.
Answer: 160 g
Concept: In a ratio, divide the known quantity by its ratio number to find one part, then multiply.

2. (2 marks)
Boys : Girls = $5 : 4$, total parts = $5 + 4 = 9$.
$9$ parts = $36$ students → $1$ part = $36 \div 9 = 4$.
Boys = $5 \times 4 = 20$.
Answer: 20
Concept: Total students correspond to sum of ratio parts.

3. (2 marks)
$45 : 30$ → divide both by $15$ → $3 : 2$.
Answer: 3 : 2
Concept: Simplify by dividing by highest common factor.

4. (2 marks)
Ratio $2 : 3 : 5$, total parts = $10$.
$10$ parts = \480$→$1$part =$$48$. C gets$5$parts =$5 \times 48 = $240. **Answer: \240**
Common mistake: forgetting to add all parts before dividing.

5. (2 marks)
Scale $1 : 25\,000$ means $1$ cm = $25\,000$ cm = $250$ m = $0.25$ km.
$8$ cm = $8 \times 0.25 = 2$ km.
Answer: 2 km
Concept: Convert cm to km (÷100 000).

Section B: Percentages, Fractions and Proportion

6. (2 marks)
Discount = $15\%$ of \60$=$0.15 \times 60 = $9$. Sale price =$60 - 9 = $51. **Answer: \51**
Alternative: $60 \times 0.85 = 51$.

7. (2 marks)
Increase = 52 - 40 = \12$. Percentage increase =$(12 \div 40) \times 100% = 30%$.
Answer: 30%
Concept: % increase = (change ÷ original) × 100%.

8. (2 marks)
Filled = $\frac{3}{8}$, empty = $1 - \frac{3}{8} = \frac{5}{8}$.
Answer: $\frac{5}{8}$
Concept: Whole is 1 or $\frac{8}{8}$.

9. (2 marks)
$0.6 = \frac{6}{10} = 60\%$.
Answer: 60%
Concept: Multiply decimal by 100 to get percentage.

10. (2 marks)
Speed = distance ÷ time = $120 \div 2 = 60$ km/h.
Answer: 60 km/h
Concept: Average speed formula.

Section C: Ratio in Geometry and Mixtures

11. (2 marks)
Length ratio $2 : 5$ → area ratio = $2^2 : 5^2 = 4 : 25$.
Answer: 4 : 25
Concept: Area scale factor = (length scale factor)².

12. (2 marks)
Orange : Water = $3 : 7$.
$7$ parts water = $2$ L → $1$ part = $2/7$ L.
Orange = $3 \times (2/7) = 6/7$ L.
Answer: $\frac{6}{7}$ litres
Common mistake: flipping the ratio.

13. (2 marks)
Ratio $2 : 3 : 4$, total = $9$ parts.
Sum of angles = $180°$ → $1$ part = $20°$.
Largest = $4 \times 20 = 80°$.
Answer: 80°

14. (2 marks)
Scale $1 : 18$ → model length = $4.5 \text{ m} \div 18 = 0.25 \text{ m} = 25 \text{ cm}$.
Answer: 25 cm
Concept: Model is smaller; divide actual by scale.

15. (2 marks)
Volume ratio $1 : 27$ → length ratio = $\sqrt[3]{1} : \sqrt[3]{27} = 1 : 3$.
Answer: 1 : 3
Concept: Length scale factor = cube root of volume scale factor.

Section D: Applied Problems

16. (2 marks)
Ali : Bala = $4 : 7$.
$4$ parts = \80$→$1$part =$$20$. Total =$11$parts =$11 \times 20 = $220. **Answer: \220**

17. (2 marks)
Cost of 12 kg @ $8 = $96.
Cost of 8 kg @ $10 = $80.
Total cost = $176, total mass = 20 kg.
Cost per kg = 176 \div 20 = \8.80. **Answer: \8.80/kg**
Concept: Weighted average.

18. (2 marks)
Red : Blue = $5 : 9$, difference = $4$ parts = $28$ → $1$ part = $7$.
Red = $5 \times 7 = 35$.
Answer: 35

19. (2 marks)
$112\%$ of original = \448$. Original =$448 \div 1.12 = $400. **Answer: \400**
Concept: New = original × (1 + % increase).

20. (2 marks)
Scale $1 : 500$ → 1 cm = 5 m.
Room actual = $6 \times 5$ m by $4 \times 5$ m = $30$ m by $20$ m.
Area = $30 \times 20 = 600$ m².
Answer: 600 m²
Common mistake: using cm² without converting.