Algebraic Expressions

March 30, 2021

Scheme of work: Year 12 A-Level: Pure 1: Algebraic Expressions

Prerequisite Knowledge

Know and apply the following rules of indices:
- Multiplication Rule n^a x n^b = n^{a + b}
- Division Rule n^a x n^b = n^{a + b}
- Power Rule (n^a)^b
- Power of Zero
Evaluate expressions with fractional and negative powers
Simplify a surd
Rationalise a denominator in the form 1/√a

Success Criteria

Understand and be able to use the laws of indices for all rational exponents.
Use and manipulate surds, including rationalising the denominator.

Key Concepts

Simplifying surds at the start of a problem often makes future working much simpler.
Students need to:
- evaluate expressions involving numerical and algebraic bases with a fractional and negative power.
- apply the rules of indices to fractional and negative powers.
- know how the complex conjugate is used to rationalise a denominator.

Common Misconceptions

Students often leave surds un-simplified, especially when rationalising a denominator.
1/2x is often written incorrectly written as 2x^-1 rather than (2x)^-1.
Students often struggle to evaluate indices involving both a fractional and negative power. This is especially true when the base involves an algebraic and numerical term.

Algebraic Expressions Resources

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