TOPIC SKILLS R A G. Expand Double Brackets Including brackets with 3 terms. Squaring Brackets (x + 8) 2. Amber/Red Go to. Page 8-10.

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1 TOPIC SKILLS R A G Amber/Red Go to Expand Double Brackets Including brackets with 3 terms (x + 2)(x + 3) = x 2 + 2x + 3x + 6 = x 2 + 5x + 6 Page 8-10 (x + 2)(x 6) = x 2 + 2x 6x 12 = x 2 4x 12 (2x 8)(3x 4) = 6x 2 8x 24x + 32 = 6x 2 32x + 32 (2x + 3)(4x 2 + 3x 5) = 8x 3 + 6x 2 10x + 12x 2 + 9x 15 = 8x x 2 x 15 Squaring Brackets (x + 8) 2 = (x + 8)(x + 8) = x x + 64 Page 10 Square the first term, double the product, square the last term Product means multiply the terms in the bracket together Example (x+7) Product = 7x so Double means 14x (2x+5) Product = 10x Double 20x (3x-8) Product = -24x Double -48x Remember to square the number in the first terms as well. Also the sign at the end will always be positive due to the rules of squaring a negative. 1

2 (2x 4) 2 = 4x 2 16x + 16 Surds You must know your perfect square in order to make this topic easier. Page 11 & 12 Simplifying 8 = Perfect Square factor 8 = = = = 16 3 = 16 3 = = = = = 30 2 Adding/ Subtracting 2

3 Can only add/subtract surds if they are matching. Similarly to algebra 2x + 3y + 5x = 7x + 3y = 6 8 If surds do not match you must simplify first, it is sometimes smarter to start with the smallest surd = = = = 26 2 Multiplying Surds If the surds match then the answer is the number underneath the surd. 2 2 = 4 = 2 If they don t match we must combine the surds. Only whole numbers can multiply and surds multiply. We must then look to simplify = = 40 4 =

4 = = = = 24 7 Dividing Similarly to Multiplying combine the surds 48 3 = 48 3 = 16 = 4 Or 48 3 = 16 3 = = 4 Rationalising the Denominator To rationalise the denominator is to get rid of the surd in the denominator = Remember, it is only the surd that makes the denominator irrational

5 = = = * Only whole numbers can simplify * Changing the Subject Page 13 Percentage Profit/Loss Page 14 Example. Susan bought a camera for 450, she later sold it for 200. Calculate the percentage decrease. 5

6 = 250. ( ) 100 = 55.56% Appreciation/Depreciation Page 15 For Depreciation or Loss 100% - 8% = 92% 92% 100 = 0.92 Always start by finding the multiplier. The power is the number of times it repeats, hours, weeks, months, years etc. Line of Best Fit Page 16 & 17 6

7 Probability number of desired outcomes Probability Total number of possible outcomes Probability can be represented by a fraction or decimal but should always be a number between 0 and 1. The closer to one the more likely the outcome (better chance). To compare fractions we must have a common denominator. To compare decimals divide the fractions. Page 18 Example: P(Rolling a 4 or 5)= 2 6 = P(Rolling an odd number) 3 6 = 0.5 Better chance of rolling an odd number as 0.5 is closer to 1. 7

8 Expanding Brackets Exercise

9 Exercise

10 2. Extension: Brackets with three terms. 10

11 Surds Leave out. 11

12 Expand and simplify. 12

13 Changing the Subject 13

14 Percentages Percentage Profit & Loss 14

15 Appreciation/ Depreciation 3. 15

16 Line of Best Fit and Equations 16

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18 Probability 3. Two drama clubs are to send representatives to a show. The representatives are chosen at random. Club A has 27 members and has 5 tickets to use. Club B has 36 members and has 7 tickets to use. In which club does any one person have a better chance of being selected? Justify your answer by calculation. 18