O Level Elementary Mathematics Numbers Ratio Proportion Quiz

O-Level Elementary Mathematics Quiz - Numbers Ratio Proportion: Answer Key

Total Marks: 40
Topic: Numbers, Ratio and Proportion

Section A: Numbers and Operations

1. [2 marks]
Standard form: $A \times 10^n$ where $1 \le A < 10$.
$0.000\,384 = 3.84 \times 10^{-4}$.
Answer: $3.84 \times 10^{-4}$
Teaching note: Move decimal point 4 places right to get 3.84, so power is $-4$.

2. [2 marks]
$180 = 18 \times 10 = (2 \times 9) \times (2 \times 5) = 2 \times 3^2 \times 2 \times 5 = 2^2 \times 3^2 \times 5$.
Answer: $2^2 \times 3^2 \times 5$
Teaching note: Divide by smallest primes: 180÷2=90, ÷2=45, ÷3=15, ÷3=5, ÷5=1.

3. [2 marks]
$8^3 = 512$, so $\sqrt[3]{512} = 8$.
Answer: $8$
Teaching note: Cube root asks "what number cubed gives 512".

4. [2 marks]
$0.0746$: first non-zero digit is 7, second is 4, next is 6 (round up). → $0.075$.
Answer: $0.075$
Teaching note: 2 sig figs means keep 7 and 4, round because next digit 6 ≥ 5.

5. [2 marks]
$2^3 \times 2^4 \div 2^2 = 2^{3+4-2} = 2^5 = 32$.
Answer: $32$
Teaching note: Law of indices: $a^m \times a^n = a^{m+n}$, $a^m \div a^n = a^{m-n}$.

Section B: Ratio and Proportion

6. [2 marks]
HCF of 24, 36, 60 is 12. $24÷12=2$, $36÷12=3$, $60÷12=5$.
Answer: $2 : 3 : 5$
Teaching note: Divide all parts by common factor.

7. [2 marks]
Map 1 cm = 25 000 cm actual. $8 \times 25\,000 = 200\,000$ cm = $2$ km.
Answer: $2$ km
Teaching note: 1 km = 100 000 cm.

8. [2 marks]
$3$ units = 24 boys → 1 unit = 8. Girls = $5 \times 8 = 40$.
Answer: $40$
Teaching note: Ratio part method.

9. [3 marks]
$y = kx$. $15 = k \times 5 \Rightarrow k = 3$. Then $y = 3 \times 12 = 36$.
Answer: $36$
Marking: 1 mark for $k=3$, 2 marks for final.

10. [3 marks]
$p = \frac{k}{q}$. $8 = \frac{k}{3} \Rightarrow k = 24$. $6 = \frac{24}{q} \Rightarrow q = 4$.
Answer: $4$
Marking: 1 mark constant, 2 marks final.

11. [2 marks]
Length ratio $1 : 40\,000$, area ratio $1^2 : 40\,000^2 = 1 : 1.6 \times 10^9$. Actual : map = $1.6 \times 10^9 : 1$.
Answer: $1\,600\,000\,000 : 1$
Teaching note: Area scales as square of length scale.

12. [2 marks]
A:B:C = 2:3:5. C − A = 3 units = \200$→ 1 unit =$$66.67$? Wait: 5−2=3 units = 200, 1 unit = 200/3. Total = 10 units =$2000/3 ≈ 666.67$. Use exact: total =$\frac{10}{3} \times 200 = \frac{2000}{3}$. **Answer:**$$666.67$(or$$\frac{2000}{3}$)
Teaching note: Difference in ratio units gives unit value.

Section C: Percentage, Rate and Speed

13. [2 marks]
$\frac{45}{120} \times 100\% = 37.5\%$.
Answer: $37.5\%$

14. [2 marks]
Discount = $15\% \times 80 = 12$. Sale = $80 - 12 = 68$.
Answer: \68$

15. [3 marks]
Increase = $600$. % increase = $\frac{600}{4000} \times 100\% = 15\%$.
Answer: $15\%$
Marking: 1 mark increase, 2 marks percentage.

16. [2 marks]
Speed = $\frac{150}{2.5} = 60$ km/h.
Answer: $60$ km/h

17. [3 marks]
$72$ km/h = $72\,000$ m / $3\,600$ s = $20$ m/s.
Answer: $20$ m/s
Marking: 1 mark conversion, 2 marks final.

Section D: Mixed Application

18. [3 marks]
Ratio 4:2:1 → total 7 units = 1400 g. 1 unit = 200 g. Sugar = 2 units = 400 g.
Answer: $400$ g
Marking: 1 mark unit, 2 marks final.

19. [3 marks]
$120\% \rightarrow 960$. $100\% = \frac{960}{1.2} = 800$.
Answer: \800$
Marking: 1 mark equation, 2 marks answer.

20. [3 marks]
Daily = $15 \times 7 = 105$. Total = $105 \times 5 = 525$. Daily average rate = \105$per day. **Answer:** Total$$525$, daily avg$$105$
Marking: 1 mark total, 1 mark daily, 1 mark rate.