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 Review, pages 3 3 1. a). front top side front top side. a) (+) (+) = + (-) (-11) = + c) (-) (+) = -3 d) (-1) (-3) = +7. -1 7. a) Yes. Multiplication is repeated addition. Since the sum of an set of integers is an integer, the product of two integers is also an integer. No. Division of an integer b most other integers gives parts that do not contain a whole number of units. For eample, the quotient of divided b an integer greater than or less than - is not an integer.. $ 9. -1 ºC. 1 L 31. a) - 3. - Chapter 9 3. 1. cm. a) area with bottom:. m area without bottom:.73 m. 3 m. 17. cm 7. clinder A: about 1 1 cm ; clinder B: about 39 cm. a) 1 das 1 das 9. 1 of a cake. 1 of the lifespan of a bison 11. 1 of Earth s surface 3 1. cm 13. a) 1 7 1. winner: $; runner-up: $; third-place: $1 1. km/h 1. Method 1: Since 1 of the flagpole is m long, the remaining must be four times as long, which is m. Method : Since 1 of the flagpole is m long, the length of the whole flagpole is m, which equals m. The length of portion above ground is m - m, which equals m. 17..19 m 3 1. a) 1331 cm 3 about cm 3 19. 7. kg. a) cm 3 9 cm 3 1. cm 3. a) (+) (+3) = +1 (-1) (-) = + c) (-) (+) = -3 d) (-) (+) = - 3. Estimates ma var. a) - 9. 1 and -; -1 and ; and -; - and ; and -; - and 9.1 Analsing Graphs of Linear Relations, pages 337 31. a) The points appear to lie in a straight line. The total height increases b cm for each additional step. Number of Steps Total Height of Steps 1 3 c) total height on step : cm. a) The points appear to lie in a straight line. The number of students increases b si for each additional teacher. The pattern starts with one teacher and increases to four teachers. Number of Teachers Maimum Number of Students 1 1 3 1 c) maimum number of students:. a) The quantities of banana chips range from g to g. The graph is linear because the points appear to lie in a straight line. Quantit (g) Cost ( ) 1 1 c) Yes, it is possible to bu amounts of banana chips that are not eactl multiples of g. 7. a) Yes, the points appear to lie in a straight line, so the graph shows a linear relation. The number of cubes varies from one to three. For ever increase of one cube, the height increases b cm. Answers MHR 1
Number of Cubes Height (cm) c) No, it is not possible to 1 include a point for c =.. The number of cubes must be whole numbers. 3. a) 1 1 3 3 1 c) The points appear to lie in a straight line. For ever increase of one in the -value, there is an increase of two in the -value. d) value of when = 9: 1 9. a) Hours Worked Gross Pa ($) hourl rate of pa: $1 1 1 c) Yes, it is reasonable to include a point for h = 3.. An emploee could work 3 for three and a half hours. 7. a) Yes, it should be possible to purchase two flowers. There should be one point between the two points. 11. a) coordinates of point W: (, ) The number represents the amount of mone invested in dollars. The number represents the amount of interest earned b the $ investment after two ears, in dollars. c) The points lie in a straight line. For ever increase in $ invested there is an increase in $1 in the interest earned. d) simple interest earned on $1 after one ear: $9 1. a) Side Length, s (cm) 1 3 31 Perimeter, P (cm) 1 1 3 11 1 The points lie on a line. For ever increase of 1 cm in the side length of the square, there is an increase of cm in its perimeter. c) Yes, it is possible to have other points between those shown on the graph. It is possible to have squares with side lengths that are not whole numbers. Eample: A square might have a side length of 1.7 cm. d) Yes, the graph represents a linear relationship because the points lie in a straight line. 13. a) Quantit (g) Cost ( ) The points appear to lie in a straight line. The cost ranges 7 from 7 to. 1 c) estimated cost of g of dried apricots:. d) actual cost of g of dried apricots: 3. e) The difference in values was 3 - = 3. 1. a) Boes of Almonds Profit ($) 1 3 The points appear to lie in a straight line. There is an increase in profit of $1 for ever two boes of almonds sold. The profits range from $1 to $. c) profit on the sale of two boes of almonds: $1 d) value of P when the value b is : $1 This is the same value as in part c), since both questions refer to the same point on the graph. 1. a) The number refers to the number of minutes that Tom tped; refers to the number of words that he tped in the two minutes. The tping speed for point A is words per minute. c) Yes, it is a linear relation because the points appear to lie in a straight line. d) Answer ma var. Eample: No. Fatigue, error correcting, or distractions can affect tping speed. 1. a) Time (h) Test Score (%) 1 7 3 9 Yes, the graph is a linear relation. The points appear to lie in a straight line. c) No, the rate cannot continue to increase at this same rate with more and more studing. Alana s test scores will reach % after five hours of studing. It is not possible for her success rate to improve beond %. 17. a) Susie s wages: red points Time (h) Total Pa for Mario ($) Total Pa for Susie ($) 1 3 3 7 c) The two sets of points will meet at the point (1, 1). 1. a) Mark: red points Kendal will run out of mone in 1 das. c) das 9. Patterns in a Table of Values, pages 3 31. d. t 1 1 1 3 7 a. a) a 1 1 1 3 7 1 1 1 1 9 3 w difference in value for consecutive -values: 1; difference in value for consecutive a-values: c) The value of a is equal to four times the value of. d) a = MHR Answers
7. a) d difference in value for consecutive n-values: 1; 3 difference in value for consecutive d-values: 1 c) The value of d is si 1 times the value of n. d) d = n 1 3 7n. a) The relationship is linear because d 1 the difference between consecutive 1 values of each variable is constant. 1 The graph confirms that the relationship is linear. 1 3 n The relationship ma be linear because the difference between three of the consecutive 1 1 values of each variable is constant. The graph confirms that the relationship is linear. 1 3 9. a) The relationship is not linear. The difference between successive q-values is the same but the difference between successive p-values is not the same. The relationship is linear. The difference between successive -values is the same and the difference between successive -values is the same.. a) Time, t (min) 1 3 Number of Words, w 9 1 7 Yes, the relation is linear because the consecutive values for each variable have the same difference. c) w = 9t where w is the number of words and t is the time in minutes. d) words. 11. a) Increase in Mass Over kg, m (kg) Dosage, d (mg) 1 7 3 9 1 7 1 1 9 1 1 Yes. Consecutive values of m increase each time b 1, and consecutive values of d increase each time b. c) m + d) (17) + =. The dosage is mg. e) Yes. The value of kg represents a child with a mass of kg. 1. a) The following five combinations of quarters and dimes each equal $.: quarters and dimes, quarters and dimes, 1 quarters and dimes, 1 quarters and dimes, and quarters and dimes. Number of Quarters, q Number of Dimes, d c) d 1 1 $. in Quarters and Dimes 1 1 q 13. a) Depth (m) Pressure (atm) 1 3 Pressure (atm) p 7 3 1 Depth of Water and Atmospheric Pressure 7d Depth (m) Yes, the relation is linear because the points appear to lie in a straight line. d) largest possible number of dimes: ( quarters); largest possible number of quarters: ( dimes) Label the horizontal ais d for the depth and label the vertical ais p for pressure. c) Divers tend to become dizz at depths greater than m. 1. a) Figure Number Number of Small Squares 1 7 3 13 1 19 s = 3n + 1 where n is the figure number and s is the number of squares. c) Figure : 1 squares d) squares 1. a) Number of Squares, n 1 3 Perimeter, P (cm) P Perimeter of 1 Squares 1 3 n Number of Squares Perimeter (cm) c) The perimeter increases b cm for each additional small square that is added to the pattern. d) P = n + e) Perimeter of squares: cm Answers MHR 3
1. a) Height (m) 1 7 Temperature (ºC) 19 1 17 1 1 1 Temperature ( C) 19 1 17 1 1 t Height and Temperature 1 7 9 Height (m) h c) Yes, the relationship is linear. There is a common difference between the consecutive values for both variables. d) Height climbed if the temperature is 13 C: m 17. a) There is a common difference between the consecutive values for both variables. The prediction is that the graph will be linear. Distance (m) d Distance Travelled b Skdiver 1 1 t Time (s) Yes, the prediction was correct. c) The parachutist descends about m per second after the parachute opens. 1. a) Number of People, n Rental Cost, C ($) Rental Cost ($) C Rental Cost of Banquet Hall n Number of People c) C = n 19. a) Number of People, n Rental Cost ($) Rental Cost, C ($) 1 C Rental Cost of Banquet Hall n Number of People The points on the graph are moved up an equal distance from each of the points on the graph in #1. c) C = n + ; The variable n represents the number of people and the variable C represents the cost of renting the banquet hall.. a) Number of Additional Das 1 3 Rental Cost ($) 7 1 1 1 1 C = 3n + c) $39; A better option would be to bu the snowboard equipment for $. 9.3 Linear Relationships, pages 37 39. a) Time, t (min) 1 3 Cost, C ( ) 1 1 3 C Cost of Long Distance Phone Plan Total Cost ( ) 3 1 1 1 3 t Time (min) 3 1 1 3 d Number of Dogs c) No. An part minutes will be rounded up to the nearest minute.. a) Number of Dogs, d 1 3 Wage, W ($) 1 W Wages Earned for Dog Walking Wage ($) 7. a) = 7 = -3 c) = d) =. a) = = - c) = 3 d) = 9. a) - - 1 1 - -7 - -3-1 c) - - -1 c) No, it is not reasonable to have points between the ones on the graph. The number of dogs walked will be a whole number. 1 MHR Answers
d) - 9 7 3. a) Answers ma var. Eample: c) -1-1 3-1 - -1 1 3-1 9 1 3-3 3-7 d) -1 1 3 3 11. a) = = 1. a) (, ) = -1 c) = -3 13. a) Yes, it is reasonable to assume that there are points between the values given. Without an restrictions in the question, numbers with decimal values can be evaluated in linear relations. 1. a) Since the -values are consecutive integers, consecutive -values will have the same difference in the linear relation. The difference for this linear relation is two. -3 - -1 1 1. a) Mass of Purchase (g) Cost ( ) Answers ma var. Eample: The most logical value is g because the common 1 difference between consecutive values of mass is g. c) C Total Cost ( ) 1 m Mass of Purchase (g) 1. a) $1 $1 c) $ 17. a) Number of Pairs of Gloves, g 1 3 Total Cost, C ($) 7 1 17 7 3 Total Cost ($) C g Pairs of Gloves 1. Amount Spent ($) Points Received 1 3 1 1 c) Yes, the points appear to lie in a straight line on the graph. d) No. The values for g must be whole numbers because the represent the number of pairs of gloves. e) This number could represent the cost of shipping or administrative charges. c) $ 19. a) The difference between consecutive masses is 11 g ecept for the metal with a volume of 1 cm 3, which has a mass of 1 g in the given table. The correct mass is 13 g. m c) A straight line could 1 be drawn through the first four points and 1 etended to show that the correct mass associated with a volume of 1 cm 3 is 13 g. Mass (g) 1 V Volume (cm 3 ). a) $.; $7. Distance Travelled, d (m) 1 Tai Cost, C ( ) Answers MHR
c) Tai Cost ( ) C d) Yes, the relation is linear. The increase in cost for each m travelled after the first segment is constant. 1 d Distance (m) 1. a) The value of d is The -value is four more than the value of t. less than the -value. d t. a) - -1 1 3 11-1 1 3 7 9 Yes, the relation is linear. The difference between consecutive -values and the consecutive -values is constant. Chapter Review, pages 31 1. epression. linear relation 3. formula. equation. variable. table of values 7. a) Time (h) Pa ($) 1 9 1 3 7 3 Yes, the graph represents a linear relation. The points on the graph lie in a straight line and rate of pa is $9 for each hour worked. c) Yes, it is possible that Klaus works for part of an hour and is paid a portion of his hourl salar.. a) The graph shows the amount of mone earned at a grade car wash based on the number of cars washed. For ever car that is washed $ is collected. The points appear to lie in a straight line. c) cost of one car wash: $ d) Number of Cars Income ($) e) $1 1 3 9. a) The points lie in a straight line. The -values range between and. The -values range between and. 1 3 11 1 17 c) = when = d) = 17 when =. a) B The difference in consecutive A-values is one. The difference in consecutive 1 B-values is four. c) In words: 1 For ever increase of one unit in the A-value there is a corresponding increase of four units in the B-value. As an epression: B = A + 1 A 11. a) Table 1: the m-variable increases b one unit; Table : the p-variable increases b two units; Table 3: the d-variable increases b one unit Table 1: the n-variable increases b two units; Table : the q-variable decreases b four units; Table 3: the C-variable increases alternatel b 3 units then b units. c) Table 1 Table n n m Table 3 n 1 m m 1. a) Number of Copies, n 1 3 Total Cost, C ($) 3 Yes, this is a linear relation for one or more copies. The consecutive values for both variables for one or more copies have a common difference. c) For one or more copies: C = n + 1 where C is the cost in dollars and n is the number of colour copies. d) $13 13. a) The variable t represents the time the cclist travels in hours. The variable d represents the distance the cclist travels in kilometres. 1 represents the constant speed of 1 km/h travelled b the cclist. MHR Answers
c) Time (h) Distance (km) 1 1 3 7 d) d 9 7 1 t Time (h) e) Yes, it is reasonable to have points between the ones in the graph. The cclist can travel for times that are not whole numbers of hours. f) 1 km 1. Equation A: = 7 - -1-1 -7 1 7 1 1 Distance (km) 1 = -9 when = -7 Equation B: = 3 - - - -1 - - 1 1 = -3 when = -7 Equation C: = - + 3-7 -1 3 1 1-1 Distance Travelled b a Cclist = 17, when = -7 1. a) Both graphs are linear relations and both graphs cross the -ais at (, 1). The points on the graph lie on straight lines that slant in different directions. The graph of = + 1 increases from left to right and the graph of = - + 1 decreases from left to right. Chapter.1 Modelling and Solving One-Step Equations: a = b, = b, pages 37 379 a. a) 3t = - - w = - c) = - d) - c =. a) - = m 3 -n = - c) -f = -1 d) p = -9 7. a) j = - n = - c) k = -1 d) =. a) r = - p = c) t = - d) d = - 9. a) k = - t = -1. a) b = - = 9 11. a) -3 - c) -9 d) 1. a) - c) d) -1 13. a) s = -3 j = 13 c) j = - d) t = 1. a) f = -7 q = -9 c) h = 1 d) k = - 1. a) - 3 c) -1 d) 17 1. a) 11-1 c) d) -3 17. a) t = -3 h = -1 c) s = - d) = 7 1. a) = - k = c) b = - d) r = 1 19. a) Yes. Yes. c) Yes. d) No.. a) No. No. c) No. d) Yes. 1. a) m = - m = -1 C. a) 13n = 31; n is the number of litres. L 3. a) p = ; p is the height of the pgm owl in centimetres. 17 cm. a) m = 1 m = 1 cm. Let be the percent of right-handed bos. 1 7 = 11 = 77 Therefore, 77% of bos are right-handed.. a) $1 $7 7. 1h = ; h = cm. 9 min 9. a) 99 m in fresh water; m in salt water Sandra. Modelling and Solving Two-Step Equations: a + b = c, pages 3 37 3. a) = 1 g =. a) h = z =. a) = 3 t =-7. a) d = 3 z = 7. a) Add to both sides of the equation. Subtract 3 from both sides of the equation. c) Add to both sides of the equation. d) Add 1 to both sides of the equation.. a) Divide both sides of the equation b. Divide both sides of the equation b -3. c) Divide both sides of the equation b. d) Divide both sides of the equation b -9. Answers MHR 7
9. a) r = m = 1 c) g = d) f = 1.7. a) k = -7 n = - c) = -3 d) n =. 11. a) No. No. c) Yes. d) No. 1. a) 3s represents triple his current savings. B subtracting from 3s, Matt will have the amount he needs: $7. savings: $ c) Answers ma var. Eample: Algebra tiles could be used to determine Matt s savings. 13. 3 etras 1. a) s + = 1 Percent of students who choose skiing: 3% 1. m - = 99; Jennifer has $17. in her account now. 1. w - 3 = 9; width of the classroom: m 17. a) The value of represents the number of metres that the eagle drops ever second. 11. s 1. m 19. 3 m. There are three possible values for m: 7,, and 9. 1. 3.7 km/h.3 Modelling and Solving Two-Step Equations: a + b = c, pages 39 393. a) = 1 b = -1. a) z = 1 d = -3. a) g = -1 n = - 7. a) f = n =. a) Subtract 1 from both sides of the equation. Add to both sides of the equation. c) Subtract from both sides of the equation. d) Subtract 11 from both sides of the equation. 9. a) Multipl both sides of the equation b -. Multipl both sides of the equation b 13. c) Multipl both sides of the equation b 1. d) Multipl both sides of the equation b 3.. a) m = c = 3 c) b = - d) n = 1 11. a) j = -3 r = c) = -1 d) n = 19 1. a) No. Yes. c) No. d) Yes. 13. a) Brian s age: ears old Answers ma var. Eample: Natasha is not getting enough sleep according to the formula. She needs.7 h of sleep. 1. a - = ; Cost of an adult ticket: $1 1. a) - C 9 m 1. m - 1 = ; 1% of students prefer math. 17. a) Calories 31 is greater than the recommended amount of Calories, which is 7. c) = 7. Modelling and Solving Two-Step Equations: a( + = c, pages 39 399. a) = s =. a) = = -7. a) t = j = 7. a) p = 1 n =. a) r = -9 m = c) g = - d) f = -7 9. a) k = - n = c) = 3 d) w = -11. a) No. No. c) Yes. d) No. 11. a) 3(s + 7) = 13 Length of each side of old fence: cm 1. a) 17 7 kj - C 13. a) ( + ) = 9 Maimum dimensions of the square picture: cm b cm 1. Rental time: h 1. Parking time: 3 h 1. a) Andrew s current speed: 1 km/h 9 km/h c) Answers ma var. Eample: Andrew would not be able to get to his grandfather s apartment in two hours if he was riding his biccle through a cit with several traffic lights and several steep hills. It would also depend on the tpes of roads and the terrain that he would have to biccle over, and on his athletic abilit. Chapter Review, pages 1 1. variable. equation 3. opposite operations. numerical coefficient. distributive propert. constant 7. linear equation. a) = -3 n = - c) d = d) = -1 9. a) = r = -3 c) z = - d) t = -3. a) p = -1 n = -33 c) = 3 d) a = 1 11. Answers ma var. Eample: Two equations which would result in an answer of five are -3p = -1 and =. 1. a) 3c + = ; c = 1 - + 7 = -1; = 13. a) Yes. Yes. c) Yes. d) No. 1. a) t = - j = - c) p = d) n = 11. 1. a) d - 3 = Zoë has seven DVDs. 1. a) v = - j = - 17. a) Subtract 13 from both sides of the equation. Then multipl both sides of the equation b -3. Add 7 to both sides of the equation. Then multipl both sides of the equation b 1. c) Subtract from both sides of the equation. Then multipl both sides of the equation b -. d) Add 1 to both sides of the equation. Then multipl both sides of the equation b -. 1. a) v = 1 d = 1 c) = - d) n = 3 19. b - 11 = 3 71; British Columbia had 1 soccer plaers in.. a) r = - w = - 1. a) q = 9 g = -11 c) k = -1 d) = 1. ( + ) = 37; Without the border, the quilt is 7 cm b 7 cm. 3. The sides of the original octagon were 9 cm long. MHR Answers