PATTERNS AND ALGEBRA NAME……………………….
1 Write the next 3 terms in these sequences. (a) 4 , 9 , 14 , ___, ____, _____ (b) 1 , 8 , 15, ___, ____, _____ (c) 200 , 193 , 186, ___, ____, _____
2 How many sticks does it take to make the fifth shape in the sequence? (a)
Answer:
(b) Consider this to be the framework of a 3 dimensional cube. Answer:
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
If this pattern continues, how many lollies had Anna's mum given out after 5 games? Answer:
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:
5 (a) Dots are placed at the corners of the shapes. Complete the table Numberof Shapes 1 2 3 4 Number of Dots
(b) Number of Shapes 1 2 3 4 Number of Dots
1 6. How many sticks does it take to make the fifth shape in the sequence? (a)
Answer:
(b)
Answer:
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
If this pattern continues, how many lollies had Jim's mum given out after 5 games?
Answer:
8. Write the next 3 terms in these sequences. (a) 8 , 15 , 22 ……………………………
(b) 4 , 9 , 16 …………………………………….
(c) 100 , 95 , 90………………………………..
9 How many sticks does it take to make the tenth shape in the sequence? (a)
Answer:
(b)
Answer:
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
If this pattern continues, how many lollies had Trudy's mum given out after 8 games?
Answer:
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 2 6 8 11 Q 7 11 13 16
RULE: Q= (b) Find the rule connecting A and B.
A 2 4 6 8 B 12 22 32 42
RULE : B=
13. Simplify the following (a) 5a 2a (b) 2x 4y 3x 5y (c) 5d 3d d
3 (d) 10b 7b (e) 5p 4 p (f) 4m 4m
(g) 20h 15h 4b 13b (h) 6m 6n 3m n (i) 32m 12m
(j) 10x 3 8 2x (k) 7m 10m (l) 12k 15k
(m) a a a a a (n) 4x 2x 2 3x x 2 (o) 4a 2ab 3b 7ab
14. Study the following Examples
Write each product in index form
(a) a a a a (b) 6 v v v (c) m m 7 n n n
(d) a a b b b (e) 3 c c d d (f) f f f f f f
(g) 4 b b b w w (h) a a (i) a a b b c c c
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