a a + a + a + a... b 3b + 2b... c c + 2c + 3c... d 4d + 2d + d + 3d... e 5e 3e... f 3f f... g 7g + 3g 8g... h 2hk + 8hk 3hk...

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1 2 7.1 Collecting like terms 1 Simplify a a + a + a + a... b 3b + 2b... c c + 2c + 3c... d 4d + 2d + d + 3d... e 5e 3e... f 3f f... g 7g + 3g 8g... h 2hk + 8hk 3hk... i 3m 2 + m 2... j 9n 2 2n 2 n Simplify a 4p + 2p + 5q + q... b 3r + 4r + 7s 2s... c t + u + t + 3u... d 9v + 3w 5v 2w... e x + 4y + 3x 2y... f 3a 9b a + 5b... g 2c 3d + 8c 5d... h e + 3f 3e + 2f i 2g h + 4 3g + 7h 5... j 9j + k 2m 5j + 7 3m... 3 The diagram shows a line made from three sections. The length of each section is given in centimetres. 5a 3b a + 7b 4b 2a Write down an expression, in terms of a and b, for the total length of this line A

2 2 7.1 Collecting like terms 4 Melissa, Mason and Zach are judges in a talent competition. D a For the first performer: Melissa gave a score of x points. Mason gave three times as many points as Melissa. Zach gave 10 points fewer than Mason. Write down an expression in terms of x for the total points scored by the first performer. b For the second performer: Melissa gave a score of 2x points. Mason gave a score of 50 points. Zach gave x points more than Mason. Write down an expression in terms of x for the total points scored by the second performer. c Write down an expression in terms of x for the difference in points between the first performer and the second performer. 107B

3 2 7.2 Using substitution 1 Work out the value of each of these expressions when x = 3. a x b 5x... c x d 2x 9... e 7 + x... f 11 5x... g x 2... h 2x Work out the value of each of these expressions when p = 5 and q = 2. a p + q... b p q... c q p... d 2p + 3q... e 5p 4p... f 6 q p... g 3q p... h p 2 + q 2... i 3q 2... j 10 q Work out the value of each of these expressions when x = 4 and y = 3 and z = 1. D a xy... b yz... c 2xyz... d 2xy + 3yz... e 5xy yz... f x 2 + y 2 + z 2... g 4xy 2... h z 3... i 5z j 6x 2 yz

4 2 7.3 Using the index laws 1 Simplify a a a a a... b 3c 6c c... D c 2e 2e... d f 2f 3f... 2 Simplify Add indices when multiplying. C a g 3 g 2... b k 4 k... c m m 3 m 5... d p p p... 3 Simplify Multiply numbers then letters. a 3q 3 2q 5... b s 4 4s 3... c 4u 2 3u 3 2u... d v 8 2v 4 3v Simplify a 2xy 2 3x 2 y... b 4x 5 y 2 x 3 y 2... c mn 3 2m 3 n 5m 2 n 2... d 10x 2 y 3 z 10xy 4 z Simplify Subtract indices when dividing. a a 5 a 2... b b 6 b... 9 c c 3... d e c e A

5 2 7.3 Using the index laws 6 Simplify Divide numbers then letters. C a 12f 5 6f 2... b 30g 8 12g... c h 4 d 8 2 k 5 7h... 2k... 7 Simplify a 24a 3 b 8 8ab 5... b 100pq 3 20pq... c xy 5 3 d c c 5 5 xy... 12c... 8 Simplify Multiply indices when raising one power to another. a (x 3 ) 2... b (y 4 ) 7... c (w 5 ) 4... d (z 2 ) Simplify Remember to deal with numbers as well as letters. a (3p 2 ) 4... b (2q 5 ) 6... c (10x 6 ) 3... d 4... y B

6 2 7.3 Using the index laws 10 Simplify B a (3xy 4 ) 3... b (5e 2 f 4 ) zb d 4 3 zb... c (10p 2 q 6 ) C

7 2 7.4 Fractional and negative powers 1 Simplify B a x 1... b (y 3 ) 1... c z 2... d w Simplify a (a 4 ) 2... b (b 3 ) 5... c (x 3 ) 2... d (y 4 ) Simplify A a (x 5 ) 0... b (3x 7 y) 0... c (2pq 5 ) 1... d (10c 2 d 5 ) x e 3 10 x f a b 5 8 4ab A

8 2 7.4 Fractional and negative powers 4 Simplify A a (x 8 ) b (y 10 ) c (16x 6 ) d (25y 6 ) e (125w 6 x 12 ) f (9x 8 y 7 ) Simplify a (a 2 ) b (c 6 ) c (32x 15 ) d (x 2 y 6 ) B

9 2 7.5 Term-to-term and position-to-term definitions Find a the rule, b the next two terms, and c the 12th term for each of the following number sequences If the rule for a sequence is add 4 and the 5th term is 19, find the a 1st term b 10th term. 115

10 2 7.6 The nth term of an arithmetic sequence Write down a the difference between consecutive terms, and b the zero term for each of the following arithmetic sequences C a... b , a... b a... b... 4 Here are the first five terms of an arithmetic sequence 3, 7, 11, 15, 19 a Write down, in terms of n, an expression for the nth term of this arithmetic sequence. b Use your answer to part a to work out the i 15th term,... ii 75th term Here are the first four terms of an arithmetic sequence 6, 10, 14, 18 a Write down, in terms of n, an expression for the nth term of this arithmetic sequence. b Use your answer to part a to work out the i 12th term,... ii 20th term Here are the first four terms of an arithmetic sequence 124, 118, 112, 106 Explain why the number 7 cannot be a term of this sequence. 117A

11 2 7.6 The nth term of an arithmetic sequence 7 Here are the first five terms of an arithmetic sequence Write down, in terms of n, an expression for the nth term of this sequence. C a Joanna says that 344 is a term in this sequence. Is Joanna right or wrong? You must fully explain your answer. b. 8 Here are the first five terms of two arithmetic sequences Show that the number 315 is a term in both sequences B

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