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C1: Chapter 1 – Algebraic Manipulation Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2 nd September 2013

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Starter Expand the following. ? ? ? ? ?

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Recap: Basic Laws of Indices ?? ?? ? ? ? ?

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‘Flip Root Power’ method ???

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More examples ? ? ?

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Textbook Fail Example 7d on page 9 is wrong: ? Whenever you have fractional powers where the denominator is even, by DEFINITION, you only consider the positive solution.

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Exercises 1 2 3 4 5 6 7 8 9 Simplify: Evaluate: 10 11 12 13 14 15 16 17 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

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Skill 2: Power of a product ? ?

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Skill 2b: Power of a fraction ? ? ?

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‘Flip Root Power’ method ?? ?

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Exercises 1 2 3 5 Simplify: ? ? ? ? 6 ? ? 7 9 10 11 Evaluate: 12 8 ? ? ? ? ? ?

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Skill 3: Changing Base ? ? ?

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Factorising SKILL 1 Taking out a single factor SKILL 3 Difference of two squares (Use ‘commando method’ or ‘splitting the middle term’ method) ? ? ? ? ? ? ? ? ? ? ?

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Exercises Page 7 – Exercise 1E Evens Page 9 – Exercise 1F 1g,h,i, 2

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Recap ? ? ? ?

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? ? And that’s it! Laws of Surds

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Using these laws, simplify the following: ?? ?? ? Laws of Surds

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? ? ? Work these out with neighbour. Simplify as much as possible. We’ll feed back in a few minutes. ? Expansion involving Surds ?

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It’s convention that the number inside the surd is as small as possible, or the expression as simple as possible. This sometimes helps us to further manipulate larger expressions. ? ? ?? Simplifying Surds

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This sometimes helps us to further manipulate larger expressions. ?? ? Simplifying Surds

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Here’s a surd. What could we multiply it by such that it’s no longer an irrational number? ?? Rationalising Denominators

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In this fraction, the denominator is irrational. ‘Rationalising the denominator’ means making the denominator a rational number. What could we multiply this fraction by to both rationalise the denominator, but leave the value of the fraction unchanged? ?? There’s two reasons why we might want to do this: 1.For aesthetic reasons, it makes more sense to say “half of root 2” rather than “one root two-th of 1”. It’s nice to divide by something whole! 2.It makes it easier for us to add expressions involving surds. Rationalising Denominators

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Quickfire DO2S! ? ? ? ? ? ?

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Rationalise the denominator. Think what we need to multiply the fraction by, without changing the value of the fraction. ? ? Rationalising Denominators

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Rationalise the denominator. Think what we need to multiply the fraction by, without changing the value of the fraction. ? ? Rationalising Denominators

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Exercises Page 12 – Exercise 1H Odds

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Ζ GCSE – Irrational Numbers and Surds Dr Frost Objectives: Appreciate the difference between a rational and irrational number, and how surds can be manipulating.

Ζ GCSE – Irrational Numbers and Surds Dr Frost Objectives: Appreciate the difference between a rational and irrational number, and how surds can be manipulating.

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