Secondary 2 Mathematics Numbers Ratio Proportion Quiz

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Secondary 2 Mathematics Quiz - Numbers Ratio Proportion

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

Duration: 50 minutes
Total Marks: 40

Instructions:

• Answer all 20 questions.
• Show your working clearly where required.
• Write your answers in the spaces provided.
• Calculators may be used.

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Section A: Ratio Basics (Questions 1–5)

1. Write the ratio $12 : 18 : 30$ in its simplest form. [1]

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2. The ratio of boys to girls in a class is $3 : 5$. If there are 24 boys, how many girls are there? [2]

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3. Express the ratio $0.6 : 1.5$ in the form $a : b$ where $a$ and $b$ are whole numbers. [1]

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4. A recipe uses flour, sugar and butter in the ratio $4 : 2 : 3$. If 360 g of the mixture is made, find the mass of sugar used. [2]

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5. The ratio of $x$ to $y$ is $5 : 7$. Find the value of $x$ when $y = 21$. [1]

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

6. Express 45 as a percentage of 60. [1]

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7. A shirt originally costs $80. It is sold at a 15% discount. Find the sale price. [2]

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8. After a 20% increase, a book costs $24. Find its original price. [2]

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9. $y$ is directly proportional to $x$. When $x = 4$, $y = 10$. Find the equation connecting $y$ and $x$. [2]

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10. $P$ is inversely proportional to the square of $Q$. When $Q = 3$, $P = 18$. Find $P$ when $Q = 6$. [2]

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Section C: Mixed Problems (Questions 11–15)

11. The map scale is $1 : 25\,000$. Two towns are 8 cm apart on the map. Find the actual distance in km. [2]

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12. A car travels 240 km in 3 hours. Find its average speed in km/h. [1]

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13. The ratio of red to blue marbles is $3 : 7$. If there are 50 marbles altogether, how many are red? [2]

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14. A worker's salary is increased by 12% to $4480. What was the salary before the increase? [2]

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15. Three numbers are in the ratio $2 : 3 : 5$. Their sum is 100. Find the largest number. [2]

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Section D: Application and Reasoning (Questions 16–20)

16. A mixture of paint is made by mixing red, yellow and white in the ratio $2 : 3 : 5$. If 4 litres of red paint are used, find the total volume of the mixture. [2]

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17. The table below shows the number of students who prefer different sports.

Sport	Boys	Girls
Football	18	12
Badminton	10	20

Find the ratio of boys who prefer Football to girls who prefer Badminton. [2]

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18. A shop buys a toy at $50 and sells it at a profit of 30%. Find the selling price. [2]

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19. $A$ is directly proportional to $\sqrt{B}$. When $B = 16$, $A = 12$. Find $A$ when $B = 64$. [3]

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20. The ratio of the lengths of two sides of a rectangle is $5 : 2$. The longer side is 20 cm. Find the perimeter of the rectangle. [3]

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

Total Marks: 40
Topic: Numbers, Ratio & Proportion

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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

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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.

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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.

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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.