1. Indices-algebra

2. You have already completed the bridging booklet chapter 5 Rearranging
Reminder
You have already completed the bridging booklet
chapter 5 Rearranging
chapter 7 Indices
If you need support with any of the following you MUST see your teacher
Calculating using the basic rules of indices
Calculating or rearranging with negative or fraction powers
The basic methods for rearranging equations

3. Starter: work these out then check with a calculator
Algebra manipulation
KUS objectives
BAT manipulate expressions using the rules of indices
Starter: work these out then check with a calculator
𝟐 𝟑 𝟐
𝟏 𝟒 −𝟏
𝟏 𝟒 𝟏/𝟐
𝟏𝟔 𝟒𝟗 𝟏/𝟐
𝟏𝟔 𝟑/𝟒
𝟖 −𝟏/𝟑
𝟖𝟏 −𝟑/𝟒
𝟑𝟔 𝟗 −𝟏/𝟐
𝟗 𝟒 −𝟓/𝟐

4. Write in index notation 𝑥 = 3 𝑥 = 2 𝑥 =
WB7 fractional indices
Write in index notation
𝑥 = 𝑥 = 𝑥 =
9𝑥 = 𝑥 = 𝑥 1/2 =
3 8𝑥 = 𝑥 1/3 = 𝑥 5 =
3 𝑥 2 = 𝑥 9 1/2 = 𝑥 /4 =
𝑥 1/2
𝑥 1/3
2𝑥 1/2
3𝑥 1/2
7𝑥 1/2
3𝑥 1/2
2𝑥 1/3
5𝑥 1/3
𝑥 5/2
𝑥 2/3
1 3 𝑥 1/2
1 3 𝑥 1/2

5. Write in index notation 1 𝑥 = 1 𝑥 2 = 1 2𝑥 3 =
WB8 negative indices
Write in index notation
1 𝑥 = 𝑥 2 = 𝑥 3 =
3 𝑥 = 𝑥 = 𝑥 =
3 𝑥 = 𝑥 −3 = 𝑥 −1/2 =
3 𝑥 −2 = 𝑥 2 −1 = 𝑥 −2 =
𝑥 −1
𝑥 −2
½ 𝑥 −3
3𝑥 −1
𝑥 −1/2
½ 𝑥 −1/2
𝑥 1/3
1 8 𝑥 −3
1 3 𝑥 −1/2
𝑥 −2/3
2 𝑥 −1
𝑥 2

6. Practice
Pair up and do these questions
More Practice
2C indices algebra match
2D ever wondered why…?

7. Challenge work in pairs
Choose four integers between -5 and 5 inclusive,
called a, b, c, d
Write the expressions 𝑥 𝑎 𝑏 and 𝑥 𝑐 𝑑
Add your neighbours expressions; multiply them; simplify as far as possible

8. = 𝟗−𝟔 𝒙 +𝒙 𝒙 Write a) 4 𝑥 2 −6𝑥+2 𝑥 2 b) 3− 𝑥 2 𝑥
WB 9
Write a) 4 𝑥 2 −6𝑥+2 𝑥 b) − 𝑥 𝑥
as a polynomial in the form 𝑎 𝑥 𝑚 + 𝑏𝑥 𝑝 +…+ 𝑛𝑥 𝑤
= 𝟒 𝒙 𝟐 𝒙 𝟐 − 𝟔𝒙 𝒙 𝟐 + 𝟐 𝒙 𝟐
= 𝟗−𝟔 𝒙 +𝒙 𝒙
= 𝟒 − 𝟔 𝒙 + 𝟐 𝒙 𝟐
= 𝟗 𝒙 − 𝟔 + 𝒙 𝒙
= 𝟒 − 𝟔 𝒙 −𝟏 +𝟐 𝒙 −𝟐
= 𝟗 𝒙 −𝟏/𝟐 + 𝒙 𝟏/𝟐 −𝟔

9. = 𝟔 𝒙 𝟐 × 𝟐 𝟑 𝒙 −𝟏 𝟐 = 𝟒 𝒙 𝟐 𝟐𝒙 + 𝟏𝟎𝒙 𝟐𝒙 + 𝟔 𝟐𝒙 =𝟒 𝒙 𝟑 𝟐 =𝟐𝒙+𝟓+𝟑 𝒙 −𝟏
WB 10
Rearrange and simplify a) 𝟔 𝒙 𝟐 × 𝟐 𝟑 𝒙 b) 𝟒 𝒙 𝟐 +𝟏𝟎𝒙+𝟔 𝟐𝒙 c) 𝟑 𝒙+ 𝒙
= 𝟔 𝒙 𝟐 × 𝟐 𝟑 𝒙 −𝟏 𝟐
= 𝟒 𝒙 𝟐 𝟐𝒙 + 𝟏𝟎𝒙 𝟐𝒙 + 𝟔 𝟐𝒙 a) b)
=𝟒 𝒙 𝟑 𝟐
=𝟐𝒙+𝟓+𝟑 𝒙 −𝟏
c) does not simplify much
= 𝟑 𝒙+ 𝒙 𝟏/𝟐

10. Write a) 𝑥 2 −2𝑥 4−𝑥 𝑥 3 b) 4 𝑥 3 −9 𝑥 +15 3𝑥
WB 11
Write a) 𝑥 2 −2𝑥 4−𝑥 𝑥 b) 4 𝑥 3 −9 𝑥 +15 3𝑥
as a polynomial in the form 𝑎 𝑥 𝑚 + 𝑏𝑥 𝑝 +…+ 𝑛𝑥 𝑤

11. Practice
Pair up and do these questions

12. One thing to improve is –
KUS objectives
BAT manipulate expressions using rules of indices
self-assess
One thing learned is –
One thing to improve is –

13. END