Patterns and Algebra Workbook 8, Part 1

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1 Patterns and Algebra Workbook 8, Part 1 Worksheet PA8-1 page 9 1. a) ; 1; 16 b) +6; +6 0; 6; c) +; + 19; ; 9 d) 1; 1; 1. a) ; 8; ; b) ; ; 69; 6 c) 6; 1; 6 d) 8; 8; 8 ; 6; 9. a) +1; +; +; +; +9 b) ; ; ; ; 1 6 c) +; +6; +1; +; d) 0; 1; ; e) ; 89; 1. Add the previous two terms. +; +; +; +6; +; +8; +9 +; +; +9; +1; +0; +; 8; +; 11; +; 1 Worksheet PA8- page 9 1. a) +; ; +; b) +; ; +9; + c) +; +1; +; +9 d) +; +; 1; + e) 9; ; 6; -8 f) +9; +; +; 8. a) A; B b) B; A c) B: A d) A; B BONUS C; B; A C; A; D; B. a) 8; 16 b) 00; 800 c) 8; d) 000; a) 0; b) 1; 6 c) d) 6. a) Start at and multiply by b) Start at and add c) Start at 1 and subtract d) Start at 81 and divide by e) Start at and multiply by f) Start at and divide by g) Start at and divide by h) Start at and multiply by 0. a) Increasing b) Repeating c) Decreasing d) Increasing e) Repeating f) Decreasing Worksheet PA8- page 9 1. a) ; b) Start at and add c) Start at 1 and add. a) 1; 6; 1 b) 1; 18; c) 1; ;. a) $90 b) 11 th week $ $1 $10 $ $90. 0 cm. $8 6. a) 1; ; 6 ; ; 9 ; 9; 1 b) 1 c) 1. a) 11 kl b) 900 km kl 8. a) 06; 18; 1 b) 19 Worksheet PA8- page 9 1. A number in a square is the sum of the two numbers above it.. a) 1 b) c) d) ; 1 8 e) f) 1; 9 1; 16 0 g) 0; 6 ; 9 h) 6; 9 6; 1 1. b) 8 c) The sum of each row is times the sum of the previous. d) 18. a) b) 9 INVESTIGATION 1 A. 1 B. C. 6 D. E. 1; ; 6; ; 1; 1 F. Worksheet PA8- page a) 8 b) 1 c) 8 d) =. a) s b) n + c) 1 r d) a e) b f) + 6w. a) h b) g c) f + 6. a) h; h b) t; t c) ;. a) h + b) t + 8 c) w a) ; ; b) ; ; 6 c) ; ; 8 d) ; + ; 9 e) ; 8 ; 6 f) ; 1 + ; 1 9. a) 11 b) 11 c) d). a) 18 b) 1 c) 1 d) 11 a) 1 b) c)

2 e) 1 f).8 1. a) 1 b) 1 c) 1 1. a) They are the same. b) The name of our variable does not matter. Worksheet PA8-6 page 1 1. a) b) 0 c) 6 d) e) 1 8 f) g) h) i) 1 j) k) 11 l) 1. a).0 b).8 c) 1. d) 9.8 e) 8. f) 9. g) 0. h).. a) 1h; g b) 0.8 = was substituted into the same epression.. a) $ b) $0 c) 6 + 1; $0. a) 8 b) 1 c) 1 e) 9 f) g) 9 0 h) 6. f; h BONUS Renaming the variables gives the same epression.. a) n b) w c) n + d d) a + b e) a + b + c + d cents 9. m + p + r. a) 1s + 1p + 0d b) $1 c) $1.60 d) Company A Worksheet PA8- page 1. a) 6; 9; 1; 1; 18; 1; ; ; 0; ; 6 1; ; ; ; 1; 16; 19; ; ; 8; 1 b) i) ii) iii) iv) 1. a) ; 6; ; 8; 9; ; 11 9; ; 11; 1; 1; 1; 1; 16 b) i) 8 ii) 0 iii) iv) 16. a) 6; less than; greater than b) 19; equal to; equal to c) ; greater than; less than d) 9; less than; greater than. a) b) c) 6 d) 16. b) t = 8 c) = 8; Order of addition does not matter d) = 8; Location with respect to equality sign does not matter = 1; 8t + = 1; 1 = + 8; 1 = 8w + ; r 8 + = 1; 1 = + 8t; + 8r = 1; 8z + = 1. a) b) d) e) f) g) h) 8. a, f 9. BONUS = ; y = EXTRA Infinitely many. Choose odd. y = 0; y = + 1; y 1 = 0. a) ; ; ; b) They are the same; Adding 1 to each side; doesn t change the solution. c) a) e) 11. Yes; = 1 = 1 1. a) i) ii) iii) iv) b) They are the same; Mutliplying every term by the same nonzero constant does not change the answer. 1. Yes; ( 1) = 11 1 = 1. 1; 19; ; ; 0 Worksheet PA8-8 page 6 1. a) b) c) d). a) b) c) d) +. a) b) c) d) e) f) +. a) Subtract b) Divide by c) Multiply by d) Add. ; 0; 1; ; ;0; 1 Yes 6. 1; ; ; 16 Subtract ; 11 Multiply by ; 1 Add 1; Divide by ; Yes. Subtract from your answer, then divide by. 8. a) b) + c)

3 d) e) f) 9 g) 8 h) 9 + BONUS y + 9. a) Multiply by b) Multiply by c) Add to it d) Subtract from e) Divide by f) Divide it into 6 g) Subtract it from Bonus Add to. a) b) c) d) + e) f) 1 g) h) i) m ; m ; + m 1. a) 1 b) 1 c) d) e) 6 f) 18 g) h) 1 i) 9 j) 6 k) 19 l) 9 m) 6 n) Worksheet PA8-9 page 8 1. b) = 8 + = 8 + = 8 = 8 8 = 8 = ; ; ; Yes c) = = + = + = 0 = 0 = ; 0; ; Yes. b) 1 1= 1= 1+ 1= + 1 = 11 = 11 = ; 11; ; Yes c) + + = + = + = = 8 = 8 = 0 0; 8; ; Yes. a) b) c) 1 d) 1 e) 11 f) g) 6 h). a) b) m c) p d) p. a) h b) $1 c) h 6. a) b) $0 c). a) b b) c Worksheet PA8- page a) ; b) ; c) ;. a) 8 b) c) 8 d) 9. a) = b) = c) = d) =. a) 0 b) 0 c) 0 d) 0 e) f) g) h). a) + = b) + = c) + 1 1= d) = 8 e) + = f) + 9 = 9 g) = h) + + = i) + = j) + 1 = 1 k) + = l) + + = m) = 6. a) ; b) ; c) 6; a) b) c) d) 8. a) 6 = 0; = b) = 1; = c) = ; = Worksheet PA8-11 page 11. a) + 6 b) + c) + d) + 1 e) + 8 f) + 16 g) + 1 h) + 1 i) + 8 j) a) b) 6 d) 1 e) 1 f) b g) 6

4 h) i) 1 j) ; 0 k) ; 1 l) a; ab. b) + = 1 = = c) + = = = BONUS = = 0 =. a) + = 9 b) + 1 = c) + 1 = 9 6. a) + = 8; = 6 b) + 1 = 9; = 8. a) = 6; = b) = 6; = c) = 8; = d) = 1; = 8. a) + = 8; = 6; = b) + 1 = 9; = 8; = Worksheet PA8-1 page a) circle rd figure b) circle th figure c) circel nd figure d) circle 1 st figure. a) circle nd figure b) circle nd and th figures c) circle rd word d) circle 1 st and nd phrases. It is not a vehicle.. a) No. Because J is an eample of a correct pairing. b) 1R; J16; C8. a) F; E1 b) T c) T d) F; r1 e) T f) F; r1 g) T h) T i) F; E1 j) T 6. False. It takes only one countereample to disprove a statement.. a) C; B b) A; F c) D; E 8. a) people; boys; There are people who are girls b) fruits; bananas; Apples are fruits c) animals that live in the water; fish; Whales are not fish. d) starts with a capital letter; form a sentence; Any sentence fragment 9. a) False; All cars are vehicles wth wheels; True b) False; All red fruits are apples; False c) False; All soccer players are girls; False d) True; All shapes are circles; False e) True; Toonies are all Canadian coins worth $; True Worksheet PA8-1 page a) Multiply by. Then add. b) Add. Then multiply by. c) Subtract. Then multiply by. d) Multiply by. Then subtract. e) Divide by. Then add 1. f) Add 1. Then divide by. g) Add. Then multiply by. Then subtract. h) Add. Then multiply by. Then divide by. i) Add. Then multiply by. Then subtract. j) Multiply by. Then add. Then subtract. k) Add. Then multiply by. Then subtract.. a) ( + ) b) + c) ( ) d) e) + f) ( + ) g) ( + ) h) ( + ) i) + j) +. h. i. a) ( + 6) b) (0 + 6) = ; = 6 c) The divides 6, not just. 6. a) ; b) 8; ; 16; ; 1; ; 1 c) ; d) Yes. = 0 8. b) 0 = 6 + = 6 + = 9 c) ( + 1) = = 9 1 = 8 9. b) = 0+ 1 = = = 9 c) + = 18 + = 18 = 16 = 16 = 8. Yes. Working backwards is equivalent to changing the equations to ones without brackets. Worksheet PA8-1 page a) No b) Yes; No; = c) ( + 6) + 6. a) Incorrect; + 6 ( + 6) b) Incorrect; forgot to divide 1 by. c) Correct d) Incorrect; when subtracting 6, it must be to both sides. e) Incorrect; didn t multiply by f) Correct g) Incorrect; 0 h) Correct Worksheet PA8-1 page more than a number: + a number divide by : less than a number: the product of a number and : a number decreased by : divided into a

5 number: a number reduced by : a number times : twice as many as a number: a number increased by : +. a) + b) c) d) 8 e) f) + g) h) 6 i) j) ( + ) k) ( ) l) ( ). a) + = ; = 8 b) = 19; = c) = 0; = 6 d) = ; = 8 e) 6= ; = f) = 0; = 8 g) = ; = 0 h) + = 1; = 9 i) = 8 ; = 18 j) = 0 ; = k) ( + ) = 1; 1 11 = = l) = 1+ ; 19 =. a) 9 b) e) + f) + g) +. a) + + 6= 1 b) i) + 1; + ii) + iii) 1, 16, , 1, 16 d) Yes. b) Yes 8. a) i) 1 ii) iii) b) w = A l; w = 9 9. a) i) ii) iii) + iv) + 1 b) i) = ii) = iii) = 9 iv) = 8. D= m; = m ; m+ m+ m = 8; m= 0; m= years old. BONUS 8 years old.