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

- 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

- Multiplication Rule n
- Evaluate expressions with fractional and negative powers
- Simplify a surd
- Rationalise a denominator in the form 1/√a

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

- 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.

- 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.

November 5, 2023

Scheme of work: A-Level Further Mathematics: Further Pure 1: The t – formulae

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A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing