10 questions · Form 4 Additional Mathematics Bab 4: Indices, Surds and Logarithms
10 questions · plays in fullscreen
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. 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.
2. Solve the logarithmic equation log₂ (x + 2) + log₂ (x - 2) = 3.
Answer: A
Combine logs: log₂ [(x+2)(x-2)] = 3 => log₂ (x² - 4) = 3 => x² - 4 = 2³ = 8 => x² = 12 => x = √12 = 2√3. (Reject x = -2√3 since log domain x > 2).
3. 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.
4. 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.
5. Rationalise the denominator of 6 / √3.
Answer: A
Multiply numerator and denominator by √3: 6 × √3√3 × √3 = 6√33 = 2√3.
6. 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.
7. Which of the following numbers is an example of a surd?
Answer: C
√16 = 4, √(94) = 32, and ∛27 = 3 are all rational numbers. √7 is irrational and cannot be expressed as a ratio of integers, making it a surd.
8. 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.
9. Find the conjugate surd of (3 - √5) and simplify their product.
Answer: A
The conjugate of (3 - √5) is (3 + √5). Product: (3 - √5)(3 + √5) = 3² - (√5)² = 9 - 5 = 4.
10. Evaluate log₂ 32 - log₂ 4.
Answer: A
By the Quotient Law: log₂ (324) = log₂ 8 = log₂ (2³) = 3.