YEAR 11 · EXPONENTIALS AND LOGARITHMS

Topic review.

Connect the key ideas, then choose a practice paper.

01 / 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.

02 / PRACTICE TESTS

Choose a paper and show your working.

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

SACE Board of South Australia

Stage 1 Mathematics: exponential and logarithmic functions, growth models and numerical/algebraic prerequisites.