Free Logarithmic & exponential functions questions for IGCSE Additional Mathematics (0606), part of Algebra. Each question has the answer and the marking points an examiner would look for.
Generate a full Logarithmic & Exponential Functions worksheet →All Algebra questionsVariables x and y are related by y = axn. When lg y is plotted against lg x, a straight line is obtained with gradient 2 and intercept 0.477 on the lg y axis.
Find the values of a and n, and hence find y when x = 4.
| Part | Answer and marking points | Marks |
|---|---|---|
| a = 3, n = 2; y = 48 lg y = n lg x + lg a M1 n = 2 A1 a = 3 A1 y = 48 A1 | 4 |
Solve log2 x + log2 (x + 4) = 5.
Solve 32x − 28 × 3x + 27 = 0.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x = 4 log2 x(x + 4) = 5 M1 x2 + 4x − 32 = 0 M1 Solve quadratic M1 x = 4 only (reject negative root) A1 | 4 |
| (b) | x = 0, x = 3 Let y = 3x: y2 − 28y + 27 = 0 M1 y = 1, y = 27 A1 Convert back M1 x = 0, x = 3 A1 | 4 |
Without using a calculator,
find the value of log5 625 + log5 (1/25).
express lg 8 + 2 lg 5 − lg 4 as a single logarithm and hence find its value.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 2 4 and −2 M1 2 A1 | 2 |
| (b) | lg 50 power law M1 product/quotient laws M1 lg 50 A1 | 3 |
The number of bacteria, N, in a culture after t hours is given by N = 800e0.05t.
Find the initial number of bacteria.
Find the number of bacteria after 20 hours.
Find the time taken for the number to reach 1600.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 800 800 B1 | 1 |
| (b) | 2175 2175 B1 | 1 |
| (c) | 13.9 hours e0.05t = 2 M1 take ln M1 13.9 A1 | 3 |
Variables x and y are related by y = axn. When lg y is plotted against lg x, a straight line is obtained with gradient 1.5 and intercept 0.699 on the lg y axis.
Find the values of a and n, and hence find y when x = 4.
| Part | Answer and marking points | Marks |
|---|---|---|
| a = 5, n = 1.5; y = 40 lg y = n lg x + lg a M1 n = 1.5 A1 a = 5 A1 y = 40 A1 | 4 |
Solve log2 x + log2 (x + 2) = 3.
Solve 32x − 30 × 3x + 81 = 0.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x = 2 log2 x(x + 2) = 3 M1 x2 + 2x − 8 = 0 M1 Solve quadratic M1 x = 2 only (reject negative root) A1 | 4 |
| (b) | x = 1, x = 3 Let y = 3x: y2 − 30y + 81 = 0 M1 y = 3, y = 27 A1 Convert back M1 x = 1, x = 3 A1 | 4 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in