Units 1 & 2 (Foundation of Indices and Exponents)
Focus on understanding and applying the laws of indices and properties of exponential expressions, including simplification, solving exponential equations, and interpreting exponential relationships in graphical form.

Unit 2 (Exponential Modelling and Applications)
Extend to modelling exponential growth and decay in applied contexts, solve exponential equations both algebraically and graphically, and introduce logarithms as inverse operations to exponentials.

Unit 1: Laws and Properties of Indices

1.1 Index Notation and Definitions
Definition & Terminology: base, exponent, power; positive and negative indices.
Zero Index: any non-zero base raised to the zero power is 1.

1.2 Index Laws
Multiplying Powers: same base rule (a^m * a^n = a^(m+n))
Dividing Powers: quotient rule (a^m / a^n = a^(m−n))
Power of a Power: (a^m)^n = a^(mn)
Combining Laws in Expressions: simplification of algebraic terms with indices

1.3 Negative and Fractional Indices
Negative Indices: reciprocal rules (a^−n = 1/a^n)
Fractional Indices: roots and radicals (a^(1/n) = ⁿ√a)
Simplification Practice: rewriting expressions using positive indices and radicals

1.4 Application to Scientific Notation
Writing Large/Small Numbers: converting between standard and scientific form
Calculations: using index laws with numbers in scientific notation
Modelling Contexts: interpreting scientific data and scaling

Unit 2: Exponentials in Algebra and Modelling

2.1 Exponential Functions and Graphs
Definition: y = a^x where a > 0, a ≠ 1
Key Features: domain and range, asymptotes, y-intercept, increasing/decreasing behavior
Graph Sketching: transformations including shifts and reflections
Technology Integration: plotting exponential graphs with TI-Nspire/Casio

2.2 Solving Exponential Equations
Equating Powers: solving when bases are equal
Graphical Methods: estimating solutions via intersection points
Approximation with Technology: use of CAS to solve non-exact exponential equations

2.3 Exponential Modelling
Growth and Decay Scenarios: population growth, radioactive decay, compound interest
Form of Models: y = A * r^t and variations
Interpretation: identifying initial values, growth/decay rates, and time periods
Modelling Tasks: fitting exponential models to contextual data

2.4 Prelude to Logarithms (Optional Extension)
Inverse of Exponential Function: concept introduction
Graphical Symmetry: reflection over y = x
Basic Logarithmic Interpretation: understanding log_a(x) as solving for exponent