10 questions · Form 4 Additional Mathematics Bab 4: Indices, Surds and Logarithms
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Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Simplify √20 + √45 - √5.
Answer: A
Simplify each surd: √20 = 2√5, √45 = 3√5. Then 2√5 + 3√5 - 1√5 = (2 + 3 - 1)√5 = 4√5.
2. Given that log_b 3 = 0.5 and log_b 5 = 0.7, calculate log_b 45.
Answer: A
log_b 45 = log_b (3² × 5) = 2 log_b 3 + log_b 5 = 2(0.5) + 0.7 = 1.0 + 0.7 = 1.7.
3. Express log_a (x³ / y²) in terms of log_a x and log_a y.
Answer: A
Apply Quotient Law and Power Law: log_a (x³) - log_a (y²) = 3 log_a x - 2 log_a y.
4. If 3^(x + 2) = 27^(x - 1), find the value of x.
Answer: A
Express base as 3: 3^(x + 2) = (3³)^(x - 1) => 3^(x + 2) = 33x - 3) => x + 2 = 3x - 3 => 2x = 5 => x = 52.
5. Simplify the expression (2³ × 4⁻¹) ÷ 81/3).
Answer: A
Express all terms with base 2: (2³ × 2⁻²) ÷ (2³)1/3) = 23 - 2) ÷ 2¹ = 2¹ ÷ 2¹ = 1.
6. Express 12 + √3 with a rational denominator.
Answer: A
Multiply by conjugate (2 - √3): 1 × (2 - √3)(2 + √3)(2 - √3) = 2 - √34 - 3 = 2 - √3.
7. Simplify the surd √72 into its simplest form a√b.
Answer: C
Find the largest perfect square factor: √72 = √36 × 2 = √36 × √2 = 6√2.
8. Convert the logarithmic equation log₃ 81 = 4 into index form.
Answer: B
Using log_a N = x ≤> a^x = N, log₃ 81 = 4 converts directly to 3⁴ = 81.
9. Simplify (3√2 + √5)(3√2 - √5).
Answer: A
Use difference of squares (a + b)(a - b) = a² - b²: (3√2)² - (√5)² = (9 × 2) - 5 = 18 - 5 = 13.
10. Use the change of base formula to evaluate log₄ 64.
Answer: A
log₄ 64 = log₁₀ 64 / log₁₀ 4 = log₁₀ (4³) / log₁₀ 4 = 3 log₁₀ 4 / log₁₀ 4 = 3.