Secondary 1 Mathematics Numbers Ratio Proportion Quiz

Secondary 1 Mathematics Quiz - Numbers Ratio Proportion

Answer Key

Total Marks: 40

Section A: Basic Concepts [10 marks]

1. Solve the inequality $-4q > 12$ and illustrate the solution on the number line below. [2 marks]

Solution: $-4q > 12$ $q < -3$ (dividing by -4 reverses the inequality sign) [1 mark]

Number line: Open circle at -3, arrow pointing left [1 mark]

    |    |    |    |    |    |    |    |
   -6   -5   -4   -3   -2   -1    0    1
              ←---○

2. Find the HCF of 84 and 126 using prime factorisation. [2 marks]

Prime factorisation of 84: $2^2 \times 3 \times 7$ [1 mark] Prime factorisation of 126: $2 \times 3^2 \times 7$

HCF = $2 \times 3 \times 7 = 42$ (lowest powers of common primes) [1 mark]

3. Express 0.375 as a fraction in its simplest form. [2 marks]

$0.375 = \frac{375}{1000} = \frac{3}{8}$ [2 marks] (Award 1 mark for $\frac{375}{1000}$, 1 mark for simplifying to $\frac{3}{8}$)

4. A recipe for 6 people requires 450g of flour. How much flour is needed for 8 people? [2 marks]

$\frac{450}{6} \times 8 = 75 \times 8 = 600$g [2 marks] (Award 1 mark for correct method, 1 mark for correct answer)

5. Calculate 15% of $240. [2 marks]

\frac{15}{100} \times 240 = \36$ [2 marks] (Award 1 mark for method, 1 mark for answer)

Section B: Ratios and Proportions [10 marks]

6. The ratio of boys to girls in a school is 3:4. If there are 168 girls, how many boys are there? [2 marks]

Ratio boys:girls = 3:4 If girls = 168, then boys = $\frac{3}{4} \times 168 = 126$ boys [2 marks]

7. A water tank is filled at a rate of 250 litres per minute. How many tanks of capacity 1500 litres each can be filled completely in 2 hours? [2 marks]

Time = 2 hours = 120 minutes Total water filled = $250 \times 120 = 30,000$ litres [1 mark] Number of tanks = $\frac{30,000}{1500} = 20$ tanks [1 mark]

8. Find the percentage increase in temperature from 15°C at 6am to 27°C at 2pm. [2 marks]

Increase = $27 - 15 = 12$°C [1 mark] Percentage increase = $\frac{12}{15} \times 100\% = 80\%$ [1 mark]

9. In a survey of 80 students, 35 students prefer Mathematics, 28 prefer Science, and the rest prefer English. Calculate the percentage of students who prefer English. [2 marks]

Students who prefer English = $80 - 35 - 28 = 17$ [1 mark] Percentage = $\frac{17}{80} \times 100\% = 21.25\%$ [1 mark]

10. Express the ratio 24:36:48 in its simplest form. [2 marks]

HCF of 24, 36, 48 = 12 [1 mark] Simplest form = $24÷12 : 36÷12 : 48÷12 = 2:3:4$ [1 mark]

Section C: Problem Solving [10 marks]

11. [2 marks]

Let the original number of blue marbles = $x$ Original number of red marbles = $3x$ After increase, number of blue marbles = $1.6x$

Total marbles after increase: $3x + 1.6x = 92$ $4.6x = 92$ $x = 20$ [1 mark]

Original red marbles = $3 \times 20 = 60$ marbles [1 mark]

12. A man invests $5000 in a bank account at 4.1% simple interest per year. How much simple interest would he earn in one year? [2 marks]

Simple interest = \frac{5000 \times 4.1 \times 1}{100} = \205$ [2 marks]

13. Share $420 among three children in the ratio 2:3:5. Find the largest share. [2 marks]

Total ratio parts = $2 + 3 + 5 = 10$ [1 mark] Largest share = \frac{5}{10} \times 420 = \210$ [1 mark]

14. A car travels 180 km in 2.5 hours. At this rate, how far will it travel in 4 hours? [2 marks]

Speed = $\frac{180}{2.5} = 72$ km/h [1 mark] Distance in 4 hours = $72 \times 4 = 288$ km [1 mark]

15. Find the LCM of 84 and 126 using prime factorisation. [2 marks]

84 = $2^2 \times 3 \times 7$ 126 = $2 \times 3^2 \times 7$ [1 mark] LCM = $2^2 \times 3^2 \times 7 = 252$ [1 mark]

Section D: Extended Problems [10 marks]

16. [3 marks]

(a) Sale price = 3.20 - (25\% \times 3.20) = 3.20 - 0.80 = \2.40$ per kg [1 mark]

(b) Cost of 2.5 kg = 2.40 \times 2.5 = \6.00$ [2 marks]

17. [2 marks]

Increase = $75 - 45 = 30$ books [1 mark] Percentage increase = $\frac{30}{45} \times 100\% = 66.67\%$ [1 mark]

18. [2 marks]

If flour = 150g and ratio is 5:3:2 Sugar = $\frac{3}{5} \times 150 = 90$g Butter = $\frac{2}{5} \times 150 = 60$g [1 mark] Total mass = $150 + 90 + 60 = 300$g [1 mark]

19. Express 2.45 as a mixed number in its simplest form. [1 mark]

$2.45 = 2\frac{45}{100} = 2\frac{9}{20}$ [1 mark]

20. [2 marks]

Primary:Secondary = 3:4 Total parts = 7 Primary students = $\frac{3}{7} \times 420 = 180$ Secondary students = $\frac{4}{7} \times 420 = 240$ [1 mark] Difference = $240 - 180 = 60$ students [1 mark]

Marking Notes:

• Award partial marks for correct method even if arithmetic errors occur
• For inequalities, both algebraic solution and correct number line representation required
• Prime factorisation must show working, not just final factors
• Percentage problems require clear identification of original and new values
• Ratio problems must show proportional reasoning clearly