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Secondary 3 Elementary Mathematics Numbers Ratio Proportion Quiz
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Secondary 3 Elementary Mathematics Quiz - Numbers Ratio Proportion
Answer Key
Section A: Numbers and Standard Form
1. 45 600 000 = 4.56 × 10⁷ [1]
2. 3.72 × 10⁻⁵ = 0.0000372 [1]
3. (6.4 × 10⁸) ÷ (1.6 × 10³)
= (6.4 ÷ 1.6) × 10^(8−3)
= 4.0 × 10⁵ [2]
[1] for correct division of coefficients; [1] for correct power of 10.
4. Distance = speed × time
= 3.0 × 10⁸ × 500
= 3.0 × 10⁸ × 5.0 × 10²
= 1.5 × 10¹¹ m [2]
[1] for correct substitution; [1] for correct answer in standard form.
5. (1.67 × 10⁻²⁷) ÷ (9.11 × 10⁻³¹)
= (1.67 ÷ 9.11) × 10^(−27 − (−31))
= 0.18331... × 10⁴
= 1.8331... × 10³
≈ 1.83 × 10³ (3 s.f.) [3]
[1] for correct division of coefficients; [1] for correct index; [1] for correct final answer to 3 s.f.
Section B: Indices and Surds
6.
(a) 5⁷ ÷ 5³ = 5^(7−3) = 5⁴ = 625 [1]
(b) (2³)⁴ = 2^(3×4) = 2¹² = 4096 [1]
7. 8^(2/3) = (∛8)² = 2² = 4 [2]
[1] for finding cube root of 8; [1] for squaring the result.
8. 3⁻² × 3⁵ = 3^(−2+5) = 3³ = 27 [2]
[1] for adding indices correctly; [1] for correct evaluation.
9. √48 = √(16 × 3) = √16 × √3 = 4√3 [2]
[1] for correct factorisation; [1] for simplified form.
10. (2√3 + √12)²
First, √12 = √(4 × 3) = 2√3
So: (2√3 + 2√3)² = (4√3)² = 16 × 3 = 48 [3]
[1] for simplifying √12; [1] for combining like terms; [1] for squaring correctly.
Section C: Ratio and Proportion
11. Ratio 2 : 3 : 5 → total parts = 2 + 3 + 5 = 10
Each part = 450
Shares: 1 350, $2 250 [2]
[1] for finding value of one part; [1] for all three correct shares.
12. Ratio boys : girls = 5 : 4
5 parts = 15 → 1 part = 3
Girls = 4 × 3 = 12
Total = 15 + 12 = 27 students [2]
[1] for finding number of girls; [1] for total.
13. Flour for 14 people = (600 ÷ 8) × 14 = 75 × 14 = 1 050 g = 1.05 kg [2]
[1] for correct proportion calculation; [1] for correct unit conversion to kg.
14.
(a) Alice = 2/5 = 40%, Bob = 30%
Carol = 100% − 40% − 30% = 30% = 3/10 [2]
[1] for finding Carol's percentage; [1] for correct simplified fraction.
(b) 30% of total = 84 ÷ 0.30 = $280 [2]
[1] for setting up equation; [1] for correct answer.
15.
(a) Actual distance = 6.8 × 25 000 = 170 000 cm = 1.7 km [2]
[1] for correct multiplication; [1] for conversion to km.
(b) For area, scale factor = (1)² : (25 000)² = 1 : 6.25 × 10⁸
Map area = 16 ÷ (6.25 × 10⁸) km²
= 16 × 10¹⁰ ÷ (6.25 × 10⁸) cm²
= 256 cm² [2]
[1] for using squared scale factor; [1] for correct answer.
Section D: Direct and Inverse Proportion
16.
(a) y = kx → 28 = k(7) → k = 4
Equation: y = 4x [2]
[1] for finding k; [1] for correct equation.
(b) y = 4 × 13 = 52 [1]
17.
(a) T = k/v → 4.5 = k/60 → k = 270
Equation: T = 270/v [2]
[1] for finding k; [1] for correct equation.
(b) T = 270/75 = 3.6 hours [1]
18.
(a) M = ks³ → 162 = k(27) → k = 6
M = 6 × 5³ = 6 × 125 = 750 g [2]
[1] for finding k; [1] for correct mass.
(b) 384 = 6s³ → s³ = 64 → s = 4 cm [2]
[1] for setting up equation; [1] for correct side length.
19. R = k/d² → 18 = k/4 → k = 72
When d = 3: R = 72/9 = 8 ohms [3]
[1] for finding k; [1] for substituting d = 3; [1] for correct answer.
20. Workers × days = constant
8 × 15 = 120 worker-days
For 10 days: workers = 120 ÷ 10 = 12 workers [2]
[1] for finding constant; [1] for correct number of workers.
Total cost = 12 × 10 × 14 400 [2]
[1] for correct calculation; [1] for correct answer with unit.
End of Answer Key