Chapter Representing Patterns, pages MHR Answers

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1 . a) x -, x - b) Example: The processes are similar in that the like terms were combined. The processes are different in that one involved addition and the other involved subtraction.. Yes. Example: The opposite term of x is -x and the opposite term for -x is x.. a) b) -7 + a c) -x + x -. a) Example: Group together the like terms: (p - p) + (q - q) + (-9 + ) = p - q - 7. Another method is to change the order of the terms and line up the polynomials vertically. p + q - 9 -p - q + p - q - 7 b) Example: The first method is preferred because the terms are grouped horizontally. 6. a) p + b) a - 7a t t t t 1 t + t + 8. a) + 1n, where n represents the number of people attending b) Example: Another class decides to spend more on food and refreshments for their party and less on printing, decorations, and awards. Their cost for food is $1/person and $ for the other items. The sum of the costs for both classes is ( + 1n) + ( + 1n) = + 7n. The difference of the costs is ( + 1n) - ( + 1n) = - n. Chapter Representing Patterns, pages a) Example: Every time an octagon is added the number of sides increases by 6. b) Number of Octagons, n Number of Sides, s c) s = 6n + ; s represents number of sides, n represents number of octagons d) e). a) Figure Number, n Number of Circles, c b) Example: Three circles are added for each subsequent figure. c) c = n + ; c represents number of circles, n represents figure number d) e) 6 6. a) Figure Number, n Number of Green Tiles, t b) Example: Four green tiles are added for each subsequent figure. c) t = n + ; t represents number of green tiles, n represents figure number d) e) 7. a) Term, t Value, v b) v = 9t - c) 1 d) 8. a) Each subsequent term has one additional heptagon. Figure 1 Figure Figure Figure Figure Figure 6 b) Figure Number, n Perimeter, P (cm) c) P = n + 7; P represents perimeter in centimetres, n represents figure number d) 67 cm e) 9. a) Term, t Value, v b) v = -t - c) -19 d) 9. a) y = x + 1 b) p = 7r + 17 c) t =.7k - d) w = -.f a) s = t +, s represents number of seats, t represents number of tables b) c) Example: Substitute t = into the equation and solve for s. d) 7 1. a) Number of T-Shirts, n Cost, C ($) b) C = 1n + 1; C represents cost, n represents number of T-shirts. The numerical coefficient is the cost for each additional T-shirt. c) $79 d) a) t = s - ; t represents number of tiles, s represents size of frame b) 6 c) cm by cm 7 MHR Answers

2 1. a) Sighting Number, n Year, y b) 6 c) y = 76n + 168; y represents year, n represents sighting number d) No. By substituting y = 7 into the equation and solving for n, a decimal answer results. Therefore, the comet will not appear in a) 17 b) Substitute y = 678 into the equation y = x + 1, and solve for x. If x is a whole number, then 678 is 1 more than a multiple of. 16. a) l =.(n - 1); l represents length of row, n represents number of trees b) 6 trees will not be evenly spaced because the number of trees has a decimal in the answer. 17. a) Number of Rebounds, n Rebound Heights, h (m) b).9 m c) No, this relation is not linear. The rebound heights do not decrease at a constant rate with each bounce. 6. Interpreting Graphs, pages 6. a) 1 km, interpolation b) 7 h. a) 1 b) a) -. b) a) d Sophie s Cycling Distance t b) 1 km c). h 8. a) 9 m b). min 9. a) approximately 1. b) approximately.6. a) b) 11. a) Temperature (ºC) d Winter Temperature Drop b) -. C c) 1 noon 1. a) C Trail Mix Cost 1 8 t m Mass (g) b) $19 c) g 1. a) It is reasonable to interpolate and extrapolate the graph. The submarine can be underwater for a fraction of a minute, and the graph shows a linear relationship. b). min c) 1 m 1. a) Yes, the graph is linear, and it is reasonable to determine the income from the number of programs as long as the number of programs is a whole number. b) $, interpolation c) 1. a) 1 h b) 1.8 h c). h 16. a) Yes, the graph is linear, and it is reasonable to determine the cost from the number of minutes used. b) $ c) min 17. a) The cost for renting four days is $8. The cost per day is $7. Divide the cost for four days by the number of days. b) 6 days 18. a). s b) 1 m c) The skydiver is accelerating at a constant rate. 19. a) d Vehicle Stopping Distance Stopping Distance (m) 8 Speed (km/h) 8 s b) As the speed increases the stopping distance also increases. c) Example: m, 6 m, 8 m d) Example: km/h, 6 km/h, 8 km/h e) Example: 17 m, 6 m f) The graph is not a straight line because the rate of deceleration of the car is different for different speeds of the car. Answers MHR 71

3 6. Graphing Linear Relations, pages 9. a) p c) Ian s Earnings Pay ($) k m m k 8. a) C = 1.7m b) approximately.9 kg c) Yes, 1 t Time Worked (h) b) The graph represents the equation because his pay increases at a rate of $8. for each hour worked. The rate at which his pay increases is the coefficient in the equation. c) $66; substitute t = 8 into the equation and solve for p, or use the graph to estimate his pay using extrapolation.. a) d Andrea s Driving Distance y t x 1 y x r r s r h d) n =.h z n f a) m b) 11 min c) A = 9t d) 9 m/min 1. a) t = min b) T = C c) C/min 1. a) d Paul s Driving Distance c) z = - s b). h 6. a) C b) B c) A 7. a) x y b) t 8 - because the values exist beyond and between the points. However, a cost or mass value less than zero does not exist. 9. a) h = 6t b) cm c) Yes, because the values exist beyond and between the points. However, a height or time value less than zero does not exist.. a) y = -x b) y =.x a) y =.x - 1 b) x = 1. a) y = x - 1 b) t = 1.r + 1 t b) km c) 1.8 h d) d = 1t e) 1 km/h MathLinks 9 Chapter 6 Answers 7 MHR Answers

4 16. a) Temperature ( C) Temperature ( F) Temperature (ºF) f Temperature Conversion 19. a) d Cycling Distances 8 Janice s Distance Flora s Distance 1 t Time After Leaving School (h) Time, t (h) Janice s Distance, j (km) Flora s Distance, f (km) n/a b) This is where the two lines intersect. c) At : p.m. or after h d) At : p.m. or after. h. a) C 8 Cost of Music Downloads c - Temperature (ºC) Cost of Plan A Cost of Plan B b) 1 F c) This is the point where the graph intersects the y-axis. d) a) Depth, Pressure, Scuba Diving Pressure Change d (m) P (kpa) P d Depth (m) b) kpa is the approximate pressure using interpolation c) 9. m d). kpa is the air pressure at sea level (d = ). 18. a) Girls growth appears to be linear at greater than months of age. b) Girls growth appears to be nonlinear prior to months of age. Pressure (kpa) Number of Downloads, d d Number of Downloads Cost of Plan A, A ($) 1 7 Cost of Plan B, B ($) b) If you purchase fewer than songs per month, Plan B is a better deal. If you purchase more than songs per month, Plan A is a better deal. 1. a) Year, y Interest, I ($) Answers MHR 7

5 b) $ I Interest Earned 11. a) t Teacher and Student Population Interest ($) Number of Teachers y Year c).8 years,.7 years d) approximately 1 years Chapter 6 Review, pages 1. linear relation. extrapolation. constant. linear equation. interpolate 6. a) Figure Number, n Number of Toothpicks, T b) Three toothpicks or one square is added in each figure. c) T = n + 1 d) 1 e) The numerical coefficient of n is, and this is the number of toothpicks added in each figure. 7. a) Time, t (weeks) Savings, s ($) b) s = 1t + 6 c) $81 d) 9.6 or weeks 8. a) Pairs of Shoes Sold, s Earnings, E ($) b) E = s + c) $7; You can extrapolate using a graph, or substitute and solve using the equation. 9. a) $7 b) 8 trees. a) 8 kpa, 7 kpa b) 8 m, m c) Yes, because values of air pressure and altitude both exist beyond and between points on the graph. 8 s Number of Students b) 8 teachers, teachers c) students, 1 students 1. a) Number of Days, d Cost, C ($) 1 8 C Snowboard Rental Costs d Number of Days (d) b) $, $18 c) A snowboard would become cheaper to buy after 1 days. d) Substitute the known value into the equation and solve for the unknown value. 1. d 1 t a) Example: You are driving from Toronto to Ottawa at a speed of km/h. b) Example: d = t c) The numerical coefficient in this equation is. This represents the speed at which the car is travelling per hour. The constant is zero. 7 MHR Answers

6 1. a) Number of Hours, t Cost, C ($) c) 8x b) C Parking Lot Costs t Number of Hours c) $. d) 7 h e) C = 1.7t + d) -8x Chapter Multiplying and Dividing Monomials, pages 6 6. a) 1x. a) (x)(x) = 6x b) (-x)(x) = -6x c) (-x)(-x) = 6x. a) (x)(x) = 9x b) (-x)(-x) = x c) (y)(x) = xy. a) 8x b) -6x b) -8x c) -6x Answers MHR 7

Chapter 9. Chapters 5 8 Review, pages Analysing Graphs of Linear Relations, pages

Chapter 9. Chapters 5 8 Review, pages Analysing Graphs of Linear Relations, pages 1. a) -7 No. Different sets of integers can have the same mean. Eample: {-, -1, 1, -,, -1} and {-, 9, -, 1,, } both have a sum of - and a mean of -7.. a decrease of 31 people per ear 3. 7 s. $7 Chapters