Exponentials and logarithms — Topic Review | Year 11

QUICK RECAP

Connect the ideas

Index laws describe products, quotients and powers; fractional powers name roots and negative powers name reciprocals.

Keep surds exact until an approximation is requested, and preserve denominator/domain restrictions.

An exponential model has a constant multiplier for equal time steps; the multiplier is not the percentage rate itself.

Transformations control the asymptote, intercepts and range; check features by substitution.

Logs answer exponent questions and apply only to positive real arguments with a valid base.

Use full-precision log ratios to solve exponential equations, then interpret time, units and constraints in context.

Complete each paper and show your working.

Exponential and logarithmic functions — Practice test 1
10 questions · 47 marks · 70 minutes · Scientific calculator
Build from exact powers and radicals to graph features, logarithmic equations and contextual model checks.
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Exponential and logarithmic functions — Practice test 2
10 questions · 46 marks · 70 minutes · Scientific calculator
Interpret tables, transformed curves and inverse relationships before analysing two competing models.
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Exponential and logarithmic functions — Practice test 3
10 questions · 50 marks · 75 minutes · Scientific calculator
Develop and compare models with different time periods, background levels and practical thresholds.
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Exponential and logarithmic functions — Practice test 4
10 questions · 48 marks · 75 minutes · Scientific calculator
Test the reasoning behind algebraic rules, domains, graph features and model selection.
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Exponential and logarithmic functions — Applications test
10 questions · 53 marks · 75 minutes · Scientific calculator
Apply exact algebra and logarithmic models to medicine, finance, calibrated scales and the reliability of forecasts.
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