<p>PATTERNS AND ALGEBRA NAME……………………….</p><p>1 Write the next 3 terms in these sequences. (a) 4 , 9 , 14 , ___, ____, _____ (b) 1 , 8 , 15, ___, ____, _____ (c) 200 , 193 , 186, ___, ____, _____</p><p>2 How many sticks does it take to make the fifth shape in the sequence? (a) </p><p>Answer:</p><p>(b) Consider this to be the framework of a 3 dimensional cube. Answer:</p><p>3 At a party, the kids were given prizes of lollies for each game they played. Here is a picture of how many lollies Anna's mum had given out after each game. After 1 game After 2 games After 3 games </p><p>If this pattern continues, how many lollies had Anna's mum given out after 5 games? Answer:</p><p>4 If Anna's dad had promised to bring home bags of lollies containing 12 in each bag, how many bags would he need to bring home to have enough for 20 games? Answer:</p><p>5 (a) Dots are placed at the corners of the shapes. Complete the table Numberof Shapes 1 2 3 4 Number of Dots</p><p>(b) Number of Shapes 1 2 3 4 Number of Dots</p><p>1 6. How many sticks does it take to make the fifth shape in the sequence? (a) </p><p>Answer:</p><p>(b) </p><p>Answer:</p><p>7 At a party, the kids were given prizes of lollies for each game they played. Here is a picture of how many lollies Jim's mum had given out after each game. After 1 game After 2 games After 3 games </p><p>If this pattern continues, how many lollies had Jim's mum given out after 5 games?</p><p>Answer:</p><p>8. Write the next 3 terms in these sequences. (a) 8 , 15 , 22 ……………………………</p><p>(b) 4 , 9 , 16 …………………………………….</p><p>(c) 100 , 95 , 90………………………………..</p><p>9 How many sticks does it take to make the tenth shape in the sequence? (a) </p><p>Answer:</p><p>(b) </p><p>Answer:</p><p>2 10 At a party, the kids were given prizes of lollies for each game they played. Here is a picture of how many lollies Trudy's mum had given out after each game. After 1 game After 2 games After 3 games </p><p>If this pattern continues, how many lollies had Trudy's mum given out after 8 games?</p><p>Answer:</p><p>11. (a) For the given rule, complete the table of values. Rule: y = x+12 x = 1 2 3 4 5 6 y = (b) For the given rule, complete the table of values. Rule: y = 3x x = 5 6 7 8 9 10 y = (c) For the given rule, complete the table of values. Rule: y = 25 – 2x x = 1 2 3 4 5 6 y = (d) For the given rule, complete the table of values. Rule: y =3x + 7 x = 0 1 2 3 4 y = 12 (a) Find the rule connecting P and Q.</p><p>P 2 6 8 11 Q 7 11 13 16</p><p>RULE: Q= (b) Find the rule connecting A and B.</p><p>A 2 4 6 8 B 12 22 32 42</p><p>RULE : B=</p><p>13. Simplify the following (a) 5a  2a (b) 2x  4y  3x  5y (c) 5d  3d  d</p><p>3 (d) 10b  7b (e) 5p  4 p (f) 4m  4m</p><p>(g) 20h 15h  4b 13b (h) 6m  6n  3m  n (i) 32m 12m</p><p>(j) 10x  3  8  2x (k) 7m 10m (l) 12k 15k</p><p>(m) a  a  a  a  a (n) 4x  2x 2  3x  x 2 (o) 4a  2ab  3b  7ab</p><p>14. Study the following Examples</p><p>Write each product in index form</p><p>(a) a  a  a  a (b) 6 v  v  v (c) m  m  7  n  n  n</p><p>(d) a  a  b  b  b (e) 3 c  c  d  d (f) f  f  f  f  f  f</p><p>(g) 4 b  b  b  w w (h) a  a (i) a  a  b  b  c  c  c</p><p>4</p>