C1: Chapter 1 – Algebraic Manipulation Dr J Frost
Description: C1: Chapter 1 Algebraic Manipulation Dr J Frost (jfrosttiffin.kingston.sch.uk) Last modified: 2nd September 2013 Expand the following. ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Example 7d on page 9 is wrong: ? Whenever you have fractional
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slide1. C1: Chapter 1 – Algebraic Manipulation Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2nd September 2013<br>
slide2. Expand the following. ? ? ? ? ?<br>
slide3. ? ? ? ? ? ? ? ?<br>
slide4. ? ? ?<br>
slide5. ? ? ?<br>
slide6. 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.<br>
slide7. 1 2 3 4 5 6 7 8 9 Simplify: Evaluate: 10 11 12 13 14 15 16 17 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?<br>
slide8. ? ?<br>
slide9. ? ? ?<br>
slide10. ? ? ?<br>
slide11. 1 2 3 5 Simplify: ? ? ? ? 6 ? ? 7 9 10 11 Evaluate: 12 8 ? ? ? ? ? ?<br>
slide12. ? ? ?<br>
slide13. SKILL 1
Taking out a single factor SKILL 3
Difference of two squares (Use ‘commando method’ or ‘splitting the middle term’ method) ? ? ? ? ? ? ? ? ? ? ?<br>
slide14. Page 7 – Exercise 1E
Evens
Page 9 – Exercise 1F
1g,h,i , 2<br>
slide15. ? ? ? ?<br>
slide16. ? ? And that’s it!<br>
slide17. Using these laws, simplify the following: ? ? ? ? ?<br>
slide18. ? ? ? Work these out with neighbour. Simplify as much as possible.
We’ll feed back in a few minutes. ? ?<br>
slide19. 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. ? ? ? ?<br>
slide20. This sometimes helps us to further manipulate larger expressions. ? ? ?<br>
slide21. Here’s a surd. What could we multiply it by such that it’s no longer an irrational number? ? ?<br>
slide22. 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:
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!
It makes it easier for us to add expressions involving surds.<br>
slide23. ? ? ?<br>
slide24. ? ?<br>
slide25. ? ? ? ? ? ?<br>
slide26. Rationalise the denominator. Think what we need to multiply the fraction by, without changing the value of the fraction. ? ?<br>
slide27. Rationalise the denominator. Think what we need to multiply the fraction by, without changing the value of the fraction. ? ?<br>
slide28. Page 12 – Exercise 1H
Odds<br>
slide2. Expand the following. ? ? ? ? ?<br>
slide3. ? ? ? ? ? ? ? ?<br>
slide4. ? ? ?<br>
slide5. ? ? ?<br>
slide6. 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.<br>
slide7. 1 2 3 4 5 6 7 8 9 Simplify: Evaluate: 10 11 12 13 14 15 16 17 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?<br>
slide8. ? ?<br>
slide9. ? ? ?<br>
slide10. ? ? ?<br>
slide11. 1 2 3 5 Simplify: ? ? ? ? 6 ? ? 7 9 10 11 Evaluate: 12 8 ? ? ? ? ? ?<br>
slide12. ? ? ?<br>
slide13. SKILL 1
Taking out a single factor SKILL 3
Difference of two squares (Use ‘commando method’ or ‘splitting the middle term’ method) ? ? ? ? ? ? ? ? ? ? ?<br>
slide14. Page 7 – Exercise 1E
Evens
Page 9 – Exercise 1F
1g,h,i , 2<br>
slide15. ? ? ? ?<br>
slide16. ? ? And that’s it!<br>
slide17. Using these laws, simplify the following: ? ? ? ? ?<br>
slide18. ? ? ? Work these out with neighbour. Simplify as much as possible.
We’ll feed back in a few minutes. ? ?<br>
slide19. 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. ? ? ? ?<br>
slide20. This sometimes helps us to further manipulate larger expressions. ? ? ?<br>
slide21. Here’s a surd. What could we multiply it by such that it’s no longer an irrational number? ? ?<br>
slide22. 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:
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!
It makes it easier for us to add expressions involving surds.<br>
slide23. ? ? ?<br>
slide24. ? ?<br>
slide25. ? ? ? ? ? ?<br>
slide26. Rationalise the denominator. Think what we need to multiply the fraction by, without changing the value of the fraction. ? ?<br>
slide27. Rationalise the denominator. Think what we need to multiply the fraction by, without changing the value of the fraction. ? ?<br>
slide28. Page 12 – Exercise 1H
Odds<br>