Indices-algebra

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

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

Write in index notation 𝑥 = 3 𝑥 = 2 𝑥 = WB7 fractional indices Write in index notation 𝑥 = 3 𝑥 = 2 𝑥 = 9𝑥 = 49𝑥 = 9𝑥 1/2 = 3 8𝑥 = 125𝑥 1/3 = 𝑥 5 = 3 𝑥 2 = 𝑥 9 1/2 = 𝑥 2 81 1/4 = 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

Write in index notation 1 𝑥 = 1 𝑥 2 = 1 2𝑥 3 = WB8 negative indices Write in index notation 1 𝑥 = 1 𝑥 2 = 1 2𝑥 3 = 3 𝑥 = 1 𝑥 = 1 2 𝑥 = 3 𝑥 = 2𝑥 −3 = 9𝑥 −1/2 = 3 𝑥 −2 = 𝑥 2 −1 = 3 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 1 9 𝑥 2

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

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

= 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 2 b) 3− 𝑥 2 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

= 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

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 3 b) 4 𝑥 3 −9 𝑥 +15 3𝑥 as a polynomial in the form 𝑎 𝑥 𝑚 + 𝑏𝑥 𝑝 +…+ 𝑛𝑥 𝑤

Practice Pair up and do these questions

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 –

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