Secondary 1 Mathematics Numbers Ratio Proportion Quiz

Secondary 1 Mathematics Quiz - Numbers Ratio Proportion (Answer Key)

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Section A: Basic Calculations (2 marks each)

1. Find the HCF and LCM of 48 and 72 using prime factorization.

Answer: HCF = 24, LCM = 144

Working:

• 48 = 2⁴ × 3¹
• 72 = 2³ × 3²
• HCF = 2³ × 3¹ = 8 × 3 = 24
• LCM = 2⁴ × 3² = 16 × 9 = 144

Marking: 1 mark for correct prime factorization, 1 mark for correct HCF and LCM

2. Calculate $2\frac{3}{4} - 1.6 + \frac{5}{8} \times (-2)$

Answer: $\frac{3}{20}$

Working:

• $2\frac{3}{4} = \frac{11}{4}$, $1.6 = \frac{8}{5}$
• $\frac{5}{8} \times (-2) = -\frac{5}{4}$
• $\frac{11}{4} - \frac{8}{5} - \frac{5}{4} = \frac{11-5}{4} - \frac{8}{5} = \frac{6}{4} - \frac{8}{5} = \frac{3}{2} - \frac{8}{5}$
• $= \frac{15-16}{10} = -\frac{1}{10}$

Correction: $\frac{11}{4} - \frac{8}{5} - \frac{5}{4} = \frac{55-32-25}{20} = -\frac{2}{20} = -\frac{1}{10}$

Marking: 1 mark for correct order of operations, 1 mark for correct final answer

3. Express 0.375 as a fraction in its simplest form.

Answer: $\frac{3}{8}$

Working: $0.375 = \frac{375}{1000} = \frac{3}{8}$ (dividing by 125)

Marking: 1 mark for conversion to fraction, 1 mark for simplification

4. A recipe for 6 people requires 450g of flour. How much flour is needed for 8 people?

Answer: 600g

Working: $\frac{450}{6} \times 8 = 75 \times 8 = 600$g

Marking: 1 mark for correct method, 1 mark for correct answer

5. Find 35% of $240.

Answer: $84

Working: $35\% \times 240 = 0.35 \times 240 = 84$

Marking: 1 mark for method, 1 mark for correct answer

6. What percentage is 72 out of 160?

Answer: 45%

Working: $\frac{72}{160} \times 100\% = 45\%$

Marking: 1 mark for correct fraction, 1 mark for correct percentage

7. Increase $150 by 20%.

Answer: $180

Working: $150 \times 1.20 = 180$ or $150 + (20\% \times 150) = 150 + 30 = 180$

Marking: 1 mark for method, 1 mark for correct answer

8. A shirt originally costs $80. After a 15% discount, what is the sale price?

Answer: $68

Working: $80 \times 0.85 = 68$ or $80 - (15\% \times 80) = 80 - 12 = 68$

Marking: 1 mark for method, 1 mark for correct answer

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Section B: Problem Solving (3 marks each)

9. The ratio of boys to girls in a class is 3:4. If there are 12 boys, how many girls are there?

Answer: Girls = 16, Total = 28

Working:

• If boys:girls = 3:4 and boys = 12
• 3 parts = 12, so 1 part = 4
• Girls = 4 parts = 16
• Total = 12 + 16 = 28

Marking: 1 mark for finding 1 part = 4, 1 mark for girls = 16, 1 mark for total = 28

10. A car travels 240 km in 3 hours. Calculate its average speed.

Answer: 80 km/h

Working: Speed = Distance ÷ Time = 240 ÷ 3 = 80 km/h

Marking: 1 mark for formula, 1 mark for substitution, 1 mark for correct answer

11. Sarah's monthly salary increased from $2400 to$2640. Calculate the percentage increase.

Answer: 10%

Working:

• Increase = $2640 -$2400 = $240
• Percentage increase = $\frac{240}{2400} \times 100\% = 10\%$

Marking: 1 mark for finding increase, 1 mark for correct formula, 1 mark for correct answer

12. A tank can be filled by Pipe A in 6 hours and by Pipe B in 4 hours. If both pipes work together, how long will it take?

Answer: 2.4 hours or 2 hours 24 minutes

Working:

• Rate of A = $\frac{1}{6}$ tank/hour
• Rate of B = $\frac{1}{4}$ tank/hour
• Combined rate = $\frac{1}{6} + \frac{1}{4} = \frac{2+3}{12} = \frac{5}{12}$ tank/hour
• Time = $\frac{1}{\frac{5}{12}} = \frac{12}{5} = 2.4$ hours

Marking: 1 mark for individual rates, 1 mark for combined rate, 1 mark for correct time

13. The price of petrol increased by 25% to $1.50 per litre. What was the original price?

Answer: $1.20 per litre

Working:

• Let original price = $x
• $x \times 1.25 = 1.50$
• $x = \frac{1.50}{1.25} = 1.20$

Marking: 1 mark for setting up equation, 1 mark for correct method, 1 mark for correct answer

14. In a survey of 200 students, the ratio is Math:Science:English = 5:3:2. How many prefer each subject?

Answer: Math: 100, Science: 60, English: 40

Working:

• Total parts = 5 + 3 + 2 = 10
• 1 part = 200 ÷ 10 = 20
• Math = 5 × 20 = 100
• Science = 3 × 20 = 60
• English = 2 × 20 = 40

Marking: 1 mark for finding 1 part = 20, 2 marks for all three correct answers

15. A recipe has flour:sugar:butter = 6:3:2. If 450g flour is used, find sugar and butter masses.

Answer: Sugar: 225g, Butter: 150g

Working:

• If flour = 6 parts = 450g, then 1 part = 75g
• Sugar = 3 parts = 3 × 75 = 225g
• Butter = 2 parts = 2 × 75 = 150g

Marking: 1 mark for finding 1 part = 75g, 1 mark for sugar, 1 mark for butter

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Section C: Advanced Applications (4 marks each)

16. A shop increases prices by 15% then decreases by 10%. Final price is $92.70. Find original price.

Answer: $90

Working:

• Let original price = $x
• After 15% increase: $1.15x
• After 10% decrease: $1.15x \times 0.90 = 1.035x
• $1.035x = 92.70$
• $x = \frac{92.70}{1.035} = 90$

Marking: 1 mark for 15% increase, 1 mark for 10% decrease, 1 mark for equation setup, 1 mark for correct answer

17. Two numbers are in ratio 7:5. Their sum is 144. Find the numbers.

Answer: Larger: 84, Smaller: 60

Working:

• Let numbers be 7x and 5x
• 7x + 5x = 144
• 12x = 144
• x = 12
• Numbers are 84 and 60

Marking: 1 mark for setting up 7x and 5x, 1 mark for equation 12x = 144, 1 mark for x = 12, 1 mark for final answers

18. Tank has 180L, capacity 540L, filling at 12L/min. Time to fill completely?

Answer: 30 minutes

Working:

• Amount needed = 540 - 180 = 360L
• Time = 360 ÷ 12 = 30 minutes

Marking: 1 mark for finding amount needed, 1 mark for correct division, 2 marks for correct answer with units

19. Time is inversely proportional to workers. 8 workers take 15 days. How many workers for 10 days?

Answer: 12 workers

Working:

• Time × Workers = constant
• 15 × 8 = 120
• For 10 days: 10 × workers = 120
• Workers = 12

Marking: 1 mark for inverse proportion concept, 1 mark for finding constant = 120, 1 mark for equation setup, 1 mark for correct answer

20. Mixture has oil:vinegar = 3:2. Add 150ml oil to 200ml mixture. Find new ratio.

Answer: 9:4

Working:

• Original mixture: 200ml with ratio 3:2
• Oil in mixture = $\frac{3}{5} \times 200 = 120$ml
• Vinegar in mixture = $\frac{2}{5} \times 200 = 80$ml
• New oil amount = 120 + 150 = 270ml
• Vinegar remains 80ml
• New ratio = 270:80 = 27:8

Correction: 270:80 = 27:8, which simplifies to 27:8, not 9:4

Actual Answer: 27:8

Marking: 1 mark for finding original oil and vinegar amounts, 1 mark for adding 150ml oil, 1 mark for new amounts, 1 mark for simplified ratio

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Total: 60 marks