Secondary 1 Mathematics Semestral Assessment 2 (End of Year) Paper 5

TuitionGoWhere Exam Practice (AI) - Mathematics Secondary 1

SA2 Practice Paper Version 5 — Answer Key

Total Marks: 60

Section A: Numbers and Operations

1. [2 marks]
Prime factorisation of 84:
$84 = 2 \times 42 = 2 \times 2 \times 21 = 2 \times 2 \times 3 \times 7 = 2^2 \times 3 \times 7$
Answer: $2^2 \times 3 \times 7$
Teaching note: Divide by smallest prime repeatedly until result is 1.

2. [2 marks]
$36 = 2^2 \times 3^2$, $48 = 2^4 \times 3$
HCF uses lowest power of common primes: $2^2 \times 3 = 12$
Answer: 12

3. [2 marks]
$|-7| = 7$, $(-3) \times 2 = -6$
$7 + (-6) = 1$
Answer: 1

4. [1 mark]
0.04739 → 3 sig figs: look at 4,7,3 then next digit 9 rounds 3 up → 0.0474
Answer: 0.0474

5. [2 marks]
Convert: $-\frac{3}{4} = -0.75$, $\frac{2}{3} \approx 0.667$
Order: $-1,\ -0.75,\ 0.5,\ 0.667$
Answer: $-1,\ -\frac{3}{4},\ 0.5,\ \frac{2}{3}$

Section B: Ratio and Proportion

6. [1 mark]
$18:24 = 3:4$ (divide by 6)
Answer: 3 : 4

7. [2 marks]
Boys : Girls = 3 : 5
3 units = 24 → 1 unit = 8
Girls = 5 units = $5 \times 8 = 40$
Answer: 40

8. [2 marks]
Flour : Sugar = 5 : 2
5 units = 350 g → 1 unit = 70 g
Sugar = 2 units = 140 g
Answer: 140 g

9. [2 marks]
Red = $\frac{3}{4}$ Blue → Red : Blue = $3 : 4$
Answer: 3 : 4

10. [3 marks]
Ratio 2 : 3 : 5 → total 10 units
10 units = 280 → 1 unit = 28
Cai = 5 units = $5 \times 28 = 140$
Answer: $140
Marking: 1 mark ratio total, 1 mark per unit, 1 mark Cai value

11. [3 marks]
Stamps : Coins = 1 : 2
Let stamps = $x$, coins = $2x$, total = $3x$
New stamps = $1.6x$, coins = $2x$, new total = $3.6x$
Increase = $3.6x - 3x = 0.6x$
% increase = $\frac{0.6x}{3x} \times 100\% = 20\%$
Answer: 20%

12. [2 marks]
$x:y = 4:7$ → 11 units = 88 → 1 unit = 8
$y = 7 \times 8 = 56$
Answer: 56

Section C: Percentage, Rate and Speed

13. [1 mark]
$15\% \times 240 = 0.15 \times 240 = 36$
Answer: 36

14. [2 marks]
Increase = $25\% \times 40 = 10$
New price = $40 + 10 = 50$
Answer: $50

15. [2 marks]
Badminton = 8, Total = 30
$\frac{8}{30} \times 100\% = 26\frac{2}{3}\%$ or 26.7%
Answer: $26\frac{2}{3}\%$ (accept 26.7%)

16. [3 marks]
Rate = 500 g/s, time = 1 h = 3600 s
Total mass = $500 \times 3600 = 1\,800\,000$ g = 1800 kg
Bag = 2 kg → $1800 \div 2 = 900$
Answer: 900 bags

17. [2 marks]
Increase = $27 - 18 = 9$
% increase = $\frac{9}{18} \times 100\% = 50\%$
Answer: 50%

18. [3 marks]
$-4q > 12$ → divide by -4 (reverse sign): $q < -3$
Number line: open circle at -3, arrow left.
Marking: 1 mark equation, 1 mark reverse sign, 1 mark correct plot

19. [2 marks]
Speed = distance ÷ time = $150 \div 2 = 75$ km/h
Answer: 75 km/h

20. [4 marks]
Let stamps = $x$, coins = $2x$, total = $3x$
New stamps = $1.75x$, coins = $2x$, new total = $3.75x$
Coins as fraction of new total = $\frac{2x}{3.75x} = \frac{8}{15}$
Original coins as fraction of old total = $\frac{2x}{3x} = \frac{2}{3}$
Decrease relative to new total interpretation: coins unchanged but total grew, so coins dropped from 66.7% to 53.3% of total → decrease of $13\frac{1}{3}$ percentage points; as % of original coin share: $\frac{2/3 - 8/15}{2/3} = \frac{2}{15} \div \frac{2}{3} = 20\%$ decrease in proportional representation.
Answer: 20% decrease (in share)
*Marking: 1 mark setup, 1 mark new total, 1 mark comparison, 1 mark final %