Worksheet Angles and Construction - Chapter 3

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:

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:

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