Set 4 — 2026 past papers
- 4.01: Logarithmic and exponential equations
- 4.02: Logarithmic equations
- 4.03: Logarithmic manipulation and equation
- 4.04: Linearised exponential relationship
Set 3 — 2021–2025 past papers
- 3.47: Log equation and exponential equation
- 3.48: Single lg and reciprocal-base log equation
- 3.49: Sketch y = 5 ln(4x + 3)
- 3.20: x-intercepts of a cubic curve
- 3.21: Domain and equation with log_5(12x − 4)
- 3.22: Derivative of ln quotient at x = 0
- 3.23: Polynomial factors via remainder theorem
- 3.24: Equation combining lg and log
- 3.25: Shaded area between chord and curve
- 3.26: Completed square and logarithmic function g
- 3.7: Equation with log base 2 and reciprocal base
- 3.8: Straight line for e^y against x²
- 3.40: Integral equal to ln 16
- 3.41: Log and exponential equations
- 3.42: Single base-2 logarithm
- 3.43: Base-2 log and lg = log_x 10
- 3.44: Log equation for p
- 3.45: Find p from combined logs
- 3.46: Log and exponential equations
- 3.18: Single lg and equation with log base x+1
- 3.19: Exponential equation with e^{2x}
- 3.51: Log equation for rs
- 3.4: Log laws for a and reciprocal-base equation
- 3.5: Normal to y = ln(x³ + 3)
- 3.6: Definite integrals with fractional powers and ln
- 3.38: Single lg expression from Q6 stem
- 3.39: Single lg and quadratic in log_a 4
- 3.15: Differentiate and integrate (3x+1) ln(3x+1)
- 3.16: Composite with ln and inverse sketch data
- 3.17: Single lg and quadratic in log_c 3
- 3.53: Exponential equations
- 3.3: Single lg and equation with reciprocal logs
- 3.32: Definite integral as a single logarithm
- 3.33: Solve for y in terms of p
- 3.34: Definite integral equal to ln 5
- 3.35: Composite fg and gg with ln
- 3.36: Normal constants a and b
- 3.37: Log equation with base 3
- 3.13: Partial fractions integral with ln
- 3.14: Normal to y = ln(x² + 2x + 1) form curve
- 3.50: Exponential equation and sketch
- 3.2: Difference of logs base 5
- 3.27: Index form and exponential quadratic
- 3.28: Single lg and equation in log_a 4
- 3.29: Values of m with no intersection
- 3.30: Logarithmic exponential and log equations
- 3.31: Three logarithmic/exponential equations
- 3.9: Definite integral in the form a + ln b
- 3.10: Find p and solve exponential and log equations
- 3.52: Log domain and exact equation
- 3.11: Index form and logarithms to base a
- 3.12: Sketch of y = ln(3x − 4)
- 3.1: Quadratic in ln 5x
Set 2
- 2.7: Write as a single logarithm
- 2.14: Equation with powers of 2, matching indices
- 2.15: Bacteria model with constants P and Q — part (a)
- 2.16: Bacteria model with constants P and Q — parts (b), (c)
- 2.19: Simultaneous logarithmic equations leading to a cubic
- 2.2: Binomial expansion applied to an exponential equation
- 2.10: Index equation; solve log a b minus half equals log b a
- 2.6: Exponential equation; lg equation with two factors
- 2.5: Exponential equations in base 3 and base e
- 2.13: Exponential equation; log equation with reciprocal
- 2.4: Log equation with base 5
- 2.12: Equation with fractional indices
- 2.9: Logs from a power relation; two index equations
- 2.17: Exponential equation solved to 2 decimal places
- 2.3: Equation in lg x
- 2.11: Equation in lg x (repeat)
- 2.18: Equation with e^3x and e^x
- 2.1: Logarithm evaluations without a calculator
- 2.8: Difference of base-2 logarithms
Set 1
- 1.11: Value of xy; exponential equation by substitution
- 1.14: Logarithms in terms of p and q; exponential equation
- 1.3: Logarithmic equations with bases 3, 9 and 4
- 1.8: Value of a two-term exponential expression
- 1.5: Single logarithm; hence solve a log equation
- 1.13: Show log 9 4 equals log 3 2; hence solve
- 1.1: Exponential population model
- 1.2: Single logarithm and a quadratic in log a 5
- 1.6: Doubling time of an exponential population
- 1.7: Common logarithms; hence solve for a
- 1.9: Exponential population model (repeat)
- 1.10: Single logarithm and a quadratic in log a 5 (repeat)
- 1.4: Quadratic in log base 3 by substitution
- 1.12: Simultaneous equations in log x and log y