Secondary 2 Mathematics Numbers Ratio Proportion Quiz

Secondary 2 Mathematics Quiz - Numbers Ratio Proportion (Answer Key)

Total Marks: 40
Topic: Numbers, Ratio & Proportion

Section A: Ratio Basics

Q1. [1 mark]
Simplify $12 : 18 : 30$ by dividing each term by the highest common factor 6.
$12 \div 6 = 2$, $18 \div 6 = 3$, $30 \div 6 = 5$.
Answer: $2 : 3 : 5$
Teaching note: Always divide all parts by the same number to keep ratio equivalent.

Q2. [2 marks]
Ratio boys : girls = $3 : 5$.
$3$ units = 24 boys → $1$ unit = $24 \div 3 = 8$.
Girls = $5$ units = $5 \times 8 = 40$.
Answer: 40 girls
Marks: M1 for finding 1 unit = 8, A1 for 40.

Q3. [1 mark]
$0.6 : 1.5$ → multiply by 10 → $6 : 15$ → divide by 3 → $2 : 5$.
Answer: $2 : 5$

Q4. [2 marks]
Ratio flour : sugar : butter = $4 : 2 : 3$, total units = $4+2+3=9$.
$9$ units = 360 g → $1$ unit = 40 g.
Sugar = $2$ units = $2 \times 40 = 80$ g.
Answer: 80 g
Marks: M1 for 1 unit = 40 g, A1 for 80 g.

Q5. [1 mark]
$x : y = 5 : 7$, so $x = \frac{5}{7}y = \frac{5}{7} \times 21 = 15$.
Answer: 15

Section B: Percentage and Proportion

Q6. [1 mark]
$\frac{45}{60} \times 100\% = 75\%$.
Answer: 75%

Q7. [2 marks]
Discount = 15\% \times 80 = 0.15 \times 80 = \12$. Sale price =$80 - 12 = $68$. **Answer:**$68
Marks: M1 for discount $12, A1 for$68.

Q8. [2 marks]
Let original price be $P$. After 20% increase: $1.2P = 24$.
$P = 24 \div 1.2 = 20$.
Answer: $20 *Marks: M1 for equation$1.2P=24$, A1 for$20.*
Common mistake: subtracting 20% of 24 instead of reversing increase.

Q9. [2 marks]
$y = kx$. When $x=4, y=10$: $10 = 4k \Rightarrow k = 2.5$.
Equation: $y = 2.5x$.
Answer: $y = 2.5x$
Marks: M1 for $y=kx$ and finding k, A1 for equation.

Q10. [2 marks]
$P = \frac{k}{Q^2}$. When $Q=3, P=18$: $18 = \frac{k}{9} \Rightarrow k = 162$.
When $Q=6$: $P = \frac{162}{36} = 4.5$.
Answer: 4.5
Marks: M1 for finding k=162, A1 for 4.5.

Section C: Mixed Problems

Q11. [2 marks]
Scale $1 : 25\,000$ means 1 cm = 25 000 cm = 0.25 km.
Map distance 8 cm → actual = $8 \times 0.25 = 2$ km.
Answer: 2 km
Marks: M1 for converting scale to km, A1 for 2 km.

Q12. [1 mark]
Average speed = $\frac{240}{3} = 80$ km/h.
Answer: 80 km/h

Q13. [2 marks]
Red : blue = $3 : 7$, total 10 units = 50 → 1 unit = 5.
Red = $3 \times 5 = 15$.
Answer: 15
Marks: M1 for 1 unit = 5, A1 for 15.

Q14. [2 marks]
Let original be $S$. $1.12S = 4480 \Rightarrow S = 4480 \div 1.12 = 4000$.
Answer: $4000 *Marks: M1 for$1.12S=4480$, A1 for 4000.*

Q15. [2 marks]
Ratio $2:3:5$, total 10 units = 100 → 1 unit = 10.
Largest = $5 \times 10 = 50$.
Answer: 50
Marks: M1 for 1 unit = 10, A1 for 50.

Section D: Application and Reasoning

Q16. [2 marks]
Red : yellow : white = $2:3:5$. Red = 2 units = 4 L → 1 unit = 2 L.
Total = 10 units = $10 \times 2 = 20$ L.
Answer: 20 L
Marks: M1 for 1 unit = 2 L, A1 for 20 L.

Q17. [2 marks]
Boys Football = 18, Girls Badminton = 20.
Ratio = $18 : 20 = 9 : 10$.
Answer: $9 : 10$
Marks: M1 for reading correct values, A1 for simplified ratio.

Q18. [2 marks]
Profit = $30\% \times 50 = 15$. Selling price = $50 + 15 = 65$.
Answer: $65
Marks: M1 for profit 15, A1 for 65.

Q19. [3 marks]
$A = k\sqrt{B}$. When $B=16, A=12$: $12 = k \times 4 \Rightarrow k=3$.
When $B=64$: $A = 3 \times \sqrt{64} = 3 \times 8 = 24$.
Answer: 24
Marks: M1 form $A=k\sqrt{B}$, M1 k=3, A1 for 24.

Q20. [3 marks]
Ratio $5:2$, longer side = 5 units = 20 cm → 1 unit = 4 cm.
Shorter side = 2 units = 8 cm.
Perimeter = $2(20+8) = 56$ cm.
Answer: 56 cm
Marks: M1 for 1 unit = 4 cm, M1 for shorter side 8 cm, A1 for 56 cm.