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C1: Chapter 1 – Algebraic Manipulation Dr J Frost Last modified: 2 nd September 2013.

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1 C1: Chapter 1 – Algebraic Manipulation Dr J Frost Last modified: 2 nd September 2013

2 Starter Expand the following. ? ? ? ? ?

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

4 ‘Flip Root Power’ method ???

5 More examples ? ? ?

6 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.

7 Exercises Simplify: Evaluate: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

8 Skill 2: Power of a product ? ?

9 Skill 2b: Power of a fraction ? ? ?

10 ‘Flip Root Power’ method ?? ?

11 Exercises Simplify: ? ? ? ? 6 ? ? Evaluate: 12 8 ? ? ? ? ? ?

12 Skill 3: Changing Base ? ? ?

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

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

15 Recap ? ? ? ?

16 ? ? And that’s it! Laws of Surds

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

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

19 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

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

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

22 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

23 ? ? ?

24 ? ?

25 Quickfire DO2S! ? ? ? ? ? ?

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

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

28 Exercises Page 12 – Exercise 1H Odds


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