Year 12 Consolidation
Ch 1 Algebraic expressions
Learning Objectives:
- Index laws
- Expanding brackets
- Factorising
- Negative and fractional indices
- Surds
- Rationalisation
,Rapid Recap
Index Laws Negative and Surds
𝑎𝑚 × 𝑎𝑛 = 𝑎 𝑚+𝑛 Fractional 𝑎 × 𝑏 = 𝑎𝑏
𝑎𝑚 ÷ 𝑎𝑛 = 𝑎 𝑚−𝑛 Indices 𝑎 𝑎
𝑎𝑚 𝑛 = 𝑎𝑚𝑛 =
𝑎0 = 1 𝑏 𝑏
𝑎𝑏 𝑛 = 𝑎𝑛 𝑏 𝑛 −𝑚
1
𝑎 = 𝑚
Example 𝑎
1 Example
s 𝑎 𝑚 = 𝑚
𝑎 s
𝑛
𝑎𝑚 = 𝑚
𝑎 𝑛
Example
s
, Quick-Fire Practice
Simplify 2 2
2𝑎5 27 −3
4𝑥 3 𝑦 3 Simplify Evaluate
𝑎2 8
× 3𝑎
Ch 1 Algebraic expressions
Learning Objectives:
- Index laws
- Expanding brackets
- Factorising
- Negative and fractional indices
- Surds
- Rationalisation
,Rapid Recap
Index Laws Negative and Surds
𝑎𝑚 × 𝑎𝑛 = 𝑎 𝑚+𝑛 Fractional 𝑎 × 𝑏 = 𝑎𝑏
𝑎𝑚 ÷ 𝑎𝑛 = 𝑎 𝑚−𝑛 Indices 𝑎 𝑎
𝑎𝑚 𝑛 = 𝑎𝑚𝑛 =
𝑎0 = 1 𝑏 𝑏
𝑎𝑏 𝑛 = 𝑎𝑛 𝑏 𝑛 −𝑚
1
𝑎 = 𝑚
Example 𝑎
1 Example
s 𝑎 𝑚 = 𝑚
𝑎 s
𝑛
𝑎𝑚 = 𝑚
𝑎 𝑛
Example
s
, Quick-Fire Practice
Simplify 2 2
2𝑎5 27 −3
4𝑥 3 𝑦 3 Simplify Evaluate
𝑎2 8
× 3𝑎