1.1 Indices

Indices

Class: Senior Five (S.5)
Subject: Mathematics
Term: Term 1
Topic: Indices (Exponents)

🔹 1. Meaning and Notation of Indices

• Definition of an index (exponent)

• Expressing repeated multiplication using indices
  e.g. 2×2×2=232 \times 2 \times 2 = 2^32×2×2=23

🔹 2. Laws of Indices

Learners will explore and apply the basic index laws:

• Product Law: am×an=am+na^m \times a^n = a^{m+n}am×an=am+n

• Quotient Law: aman=am−n\frac{a^m}{a^n} = a^{m-n}anam​=am−n

• Power of a Power: (am)n=amn(a^m)^n = a^{mn}(am)n=amn

• Zero Index: a0=1a^0 = 1a0=1, where a≠0a \neq 0a=0

• Negative Indices: a−n=1ana^{-n} = \frac{1}{a^n}a−n=an1​

• Fractional Indices: a1n=ana^{\frac{1}{n}} = \sqrt[n]{a}an1​=na​

🔹 3. Simplifying Algebraic Expressions with Indices

• Apply index laws to simplify numeric and algebraic expressions

• Combine different laws in one problem

🔹 4. Solving Exponential Equations

• Equations involving indices
  e.g. Solve 3x=273^x = 273x=27

🔹 5. Application of Indices in Real-life Situations

• Exponential growth & decay (e.g. population growth, compound interest)

• Scientific notation and use in technology

🔹 6. Error Checking and Reasoning

• Estimating and validating answers

• Common misconceptions with powers