c) e) ( ) = ( ) ( ) ( ) ( ) 88 MHR Principles of Mathematics 9 Solutions + 7=5 d) ( ) ( ) = 24 b) ( ) ( ) Chapter 3 Get Ready

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1 Chapter Polynomials Chapter Get Ready Chapter Get Ready Question Page 0 a) c) 5+ ( 9) 4 d) 5 ( 4) 5+ ( + 4) e) 4 6 f) 9 ( ) ( 9) g) ( ) + ( ) 4 h) ( 4) ( 8) 4+ ( + 8) Chapter Get Ready Question Page 0 4 a) ( ) + ( ) + 0 ( ) 0 + ( + ) c) 5+ ( 7) + 75 d) ( ) ( ) 4+ + e) ( 9) 6 ( 9) + ( 6) 5 f) ( ) + ( + ) ( ) ( ) ( ) g) h) ( 8) + 9+ ( ) Chapter Get Ready Question Page 0 a) ( 8) 4 ( ) ( ) c) 8 4 d) ( ) ( )( ) ( ) ( ) e) 5 60 f) MHR Principles of Mathematics 9 Solutions

2 Chapter Get Ready Question 4 Page 0 ( ) ( ) a) c) 6 d) ( ) ( ) e) f) Chapter Get Ready Question 5 Page a) c) d) e) f) 4 Chapter Get Ready Question 6 Page 0 a) c) 06. ( 095. ) 057. d) ( )( ) ( ) ( ) e) f) MHR Principles of Mathematics 9 Solutions 89

3 Chapter Section : Build Algebraic Models Using Concrete Materials Chapter Section Question Page 08 There are 4 x -tiles, x-tiles and 5 negative unit tiles. The expression represented is 4x x 5. Answer C. Chapter Section Question Page 08 a) x + x x + 5 c) x + x+ d) x + x MHR Principles of Mathematics 9 Solutions

4 Chapter Section Question Page 08 a) x + x + c) x + x+ 6 d) x + 4x+ 4 Chapter Section Question 4 Page 08 a) 4 km 7 km c) x km d) 4x km Chapter Section Question 5 Page 08 Answers will vary. MHR Principles of Mathematics 9 Solutions 9

5 Chapter Section Question 6 Page 08 a) 4 cm 4 cm 4 cm The volume is 4 64 cm. c) A 4 6 The area of one face is 6 cm. Chapter Section Question 7 Page 09 a) s 6 s 6 A side length of 6 cm gives a volume of 6 cm. A 6 6 The area of one face is 6 cm. Chapter Section Question 8 Page 09 a) s 49 7 s A side length of 7 m would give this area. V 7 4 The volume of the cube is 4 m. 9 MHR Principles of Mathematics 9 Solutions

6 Chapter Section Question 9 Page 09 a) Chapter Section Question 0 Page 09 s 8 s SA 6s 6 4 The total surface area of all six faces is 4 cm. Chapter Section Question Page 09 Answers will vary. You can show that the conjecture works for the first few prime numbers Use your calculator to verify that each of these is a prime number. Tip: you only need to investigate divisors up to the square root of the number. MHR Principles of Mathematics 9 Solutions 9

7 Chapter Section Question Page 09 Start by using for a and the largest number, 6, for b. 6 d + c + e f Then, use your graphing calculator or spreadsheet to investigate all of the other combinations. A sample spreadsheet is shown. Click here to load the spreadsheet. The smallest possible value of the expression if 90 when a, b 6, c 5, d, e 4, and f. Chapter Section Question Page will contribute 40 zeros to the product, and 40 0 will contribute 0 zeros, for a total of 70 zeros. Answer C. 94 MHR Principles of Mathematics 9 Solutions

8 Chapter Section Question 4 Page 09 Answers will vary. You can show that the conjecture works for the first few prime numbers Use your calculator to verify that the first two of these is a prime number. Tip: you only need to investigate divisors up to the square root of the number. Notice that the numbers become very large very quickly. MHR Principles of Mathematics 9 Solutions 95

9 Chapter Section Work With Exponents Chapter Section Question Page Answer B. Chapter Section Question Page 4 5 Answer C. Chapter Section Question Page 4 a) ( 5) ( 5) ( 5) ( 5) c) Chapter Section Question 4 Page 4 a) ( 4) ( 4) ( 4) ( 4) 64 c) Chapter Section Question 5 Page 4 a) 9 79 ( ) c) 6 d) e) f) g) h) ( ) i) MHR Principles of Mathematics 9 Solutions

10 Chapter Section Question 6 Page 4 a) c) + + d) 4 ( ) ( ) ( ) ( ) e) f) ( ) 5 Chapter Section Question 7 Page 5 ( ) a) 6s ( 5) πr π. 4 (.) ( 5. ) c) a + b + d) πr h π e) πr π( 5. ) f) x x ( 6) ( 6) MHR Principles of Mathematics 9 Solutions 97

11 Chapter Section Question 8 Page 5 a) ( ) ( ) ( ) ( ) When the exponent is odd, the power is negative, and when the exponent is even, the power is positive. c) Negative bases will give a positive answer if the exponent is even and a negative answer if the exponent is odd. ( ) ( )( ) ( ) ( )( )( ) Chapter Section Question 9 Page 5 a) The graph is non-linear. It is increasing, as an upward curve. c) After day, or 4 h, the population will be 800. After days, or 48 h, the population will be 800. d) Food poisoning will occur much faster if a large quantity of the bacteria is ingested rather than a smaller quantity because it will take the bacteria longer to multiply to a harmful amount. A faster growth rate of bacteria will cause the food poisoning to begin rapidly while a slower growth rate of bacteria will cause the food poisoning to start at a relatively slower rate MHR Principles of Mathematics 9 Solutions

12 Chapter Section Question 0 Page 6 a) Continue the table: The population of E. coli will overtake the population of Listeria just after 80 min, or h. c) The population of each will be about 7000 when they are equal. MHR Principles of Mathematics 9 Solutions 99

13 Chapter Section Question Page 6 Chapter Section Question Page 6 0 This answer makes sense. The length of a whole note is. A calculator shows that any non-zero base raised to a power of 0 equals. 00 MHR Principles of Mathematics 9 Solutions

14 Chapter Section Question Page 7 a) Let A represent the area of the rectangle. Let w represent the width of the rectangle. Let h represent the height of the rectangle. A w h w ( w) w A w ( 8) 8 The area of a crest with a width of 8 cm is 8 cm. c) 7 w 7 w 6 w 6 w h 6 A crest with an area of 7 cm has a height of cm. MHR Principles of Mathematics 9 Solutions 0

15 Chapter Section Question 4 Page 7 a) The graph is non-linear. It is decreasing, as a downward curve. c) h is 0 57., or about 5.7 half-lives. The amount of U-9 remaining is about 00 or about.69 mg., d) Use the "guess and check" method on your graphing calculator to determine that about half-lives, or 5.8 min, are required for the sample to decay to mg. 0 e) The original amount of U-9 is 00. This makes sense, since any non-zero base raised to the exponent 0 equals. 0 MHR Principles of Mathematics 9 Solutions

16 Chapter Section Question 5 Page 8 a) years is equivalent to about 4. 0 s. 7 c) d) Answers will vary. A sample answer is shown. Very large and very small numbers can be represented using a lot less space. It is also easier to understand scientific notation than trying to count the number of zeros in very large or very small numbers. It also reduces the probability of errors when rewriting these numbers. Chapter Section Question 6 Page 8 a) Construct a table to organize your thinking. A sample table is shown. After days, there are 7 customers. After 5 days, there are 6 customers. Barney's will reach 500 new customers on the ninth day. c) After n days, the number of new customers is given by the expression C n. d) Answers will vary. A sample answer is shown. Assume that the trend continues without any change. MHR Principles of Mathematics 9 Solutions 0

17 Chapter Section Question 7 Page 8 Calculate the powers of, as shown. Note that the last digit follows the pattern, 9, 7,, repeating after every 4th power. Note that There are 08 full cycles, plus 0.5 cycles. 4 The last digit in the expanded form will be 9. Chapter Section Question 8 Page 8 Use the "guess and check" method on your calculator to determine that 79. Answer C. Chapter Section Question 9 Page 8 Start with powers of, then powers of, and so on until the powers exceed 000. The perfect powers less than 000 are: 4, 8, 6,, 64, 8, 56, 5, 9, 7, 8, 4, 79, 5, 5, 65, 6, 6, 49, 4, and MHR Principles of Mathematics 9 Solutions

18 Chapter Section Question 0 Page 8 Investigate values of x and y using a spreadsheet to determine any patterns. Click here to load the spreadsheet. y 0 y or y 5 y or y > x MHR Principles of Mathematics 9 Solutions 05

19 Chapter Section Discover the Exponent Laws Chapter Section Question Page Answer B. Chapter Section Question Page a) ( ) ( ) ( ) c) d) ( ) Chapter Section Question Page Answer D. 06 MHR Principles of Mathematics 9 Solutions

20 Chapter Section Question 4 Page 7 a) 8 8 ( ) ( ) ( ) ( ) ( ) ( 6) ( 6) ( 6) ( 6) 6 c) d) Chapter Section Question 5 Page 7 ( ) Answer A. Chapter Section Question 6 Page 7 a) ( ) ( ) ( ) ( ) 79 6 ( ) ( ) 4 4 c) d) ( 0. ) MHR Principles of Mathematics 9 Solutions 07

21 Chapter Section Question 7 Page a) c) ( ) d) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) MHR Principles of Mathematics 9 Solutions

22 Chapter Section Question 8 Page a) y y y y c) k k k k d) k 0 5 ( ) 4 c 4 c c m m m m + + e) ab ab a b f) 5 ab ( uv ) u ( v ) 8uv 6 8uv + + g) mn mn m n h) mn i) ( ) ( ) ( ) ab a b a 6 ab b hk hk h k hk MHR Principles of Mathematics 9 Solutions 09

23 Chapter Section Question 9 Page 7 a) km 4km k 4 m km a ( a ) 8 a ( a ) a a 5 6 a a a a c) ( ) ( ) ( ) ( ) x x x ( x ) x x x x 9x 9x d) d w 6dw 4d w dw 8dw 4d w 5 7 4dw 4 4d w + + d dw w ( ( ) ( ) ( ) ( ) ( ) e) f g 8fg 4f g f) 6f g 6 f g 5 7 f g 4 6 f g f g f g f fg g a ab a b ab 9a b a b 4 9ab ab 4 9a b 9a g) + + 5cd 4cd 0c d cd c d ( ) ( ) 5 0cd 4c d 0cd 4 4cd 5c d 5cd MHR Principles of Mathematics 9 Solutions

24 h) ( ) ( ) ( ) ( ) ( ) ( ) ( ) xy 4x y 4 x y x y x y x y 08 x y x y 4x y 6 08 x y x y 4 4 4x y x y 4 4 4x y xy 4 4 4x y 7x 7xy y i) ( ) 0gh gh 0 g h g h + + 5gh 6gh 0g h + + 0g h 0gh 4 0gh 0gh 4g 4g 4 h MHR Principles of Mathematics 9 Solutions

25 Chapter Section Question 0 Page 8 a) 5xy x y 5 ( xy) ( xy) ( )( ) ( ) ( ) ( ( )( ) ) ( ) xy x y 0x y x y 0xy 4x y 5 5 x xy y 5 5 xy ( )( ) 5 c) Answers will vary. A sample answer is shown. Substituting values into a simplified expression is much easier than substituting into the original expression. The disadvantage is that it is easy to make a mistake when simplifying the expression. Chapter Section Question Page 8 V The volume of the crawl space is m. MHR Principles of Mathematics 9 Solutions

26 Chapter Section Question Page 8 a) The probability of tossing 6 heads in a row is. The probability of tossing heads in a row is Chapter Section Question Page 8 a) The probability of rolling a 6 with a standard number cube is 6. The probability of rolling four 6s in a row is 4, or c) The perfect squares on a number cube are and 4. The probability of rolling a perfect square with a number cube is, or 6. d) The probability of rolling eight perfect squares in a row is 8, or 656. e) MHR Principles of Mathematics 9 Solutions

27 Chapter Section Question 4 Page 8 Solutions for the Achievement Checks are shown in the Teacher's Resource. Chapter Section Question 5 Page a) c) ( ) ( ) d) ( ) ( ) Chapter Section Question 6 Page 9 a) Answers will vary. A possible prediction is 0.5. The prediction was correct. ( 0 5 ) ( 0 6 ) ( 0 5 ) ( ) Chapter Section Question 7 Page 9 a) Answers will vary. A possible prediction is ( 0 8 ) ( 6 0 ) ( ) ( 6 0 ) 5 0 Note that the calculator uses an E rather than a 0 for Scientific Notation. Chapter Section Question 8 Page 9 a) ( ) Answers will vary. A sample answer is shown. 5 You must apply the power to both the number and the power of 0, using the exponent rules. ( ) MHR Principles of Mathematics 9 Solutions

28 Chapter Section Question 9 Page 9 The exponents of a must add to 9, and the exponents of b must add to 0. Chapter Section Question 0 Page 9 x x x x x From least to greatest, the values are x,x,x, x, and. x MHR Principles of Mathematics 9 Solutions 5

29 Chapter Section 4 Communicate With Algebra Chapter Section 4 Question Page 4 a) The coefficient is, and the variable is y. The coefficient is, and the variable is x. c) The coefficient is, and the variable is mn. d) The coefficient is, and the variable is x. e) The coefficient is, and the variable is w. f) The coefficient is 0.4, and the variable is gh. Chapter Section 4 Question Page 4 There are terms in 7x xy 4y + +. It is a trinomial. Answer C. Chapter Section 4 Question Page 4 a) There is one term. x is a monomial. There are terms. 6y y is a trinomial. c) There are terms. a b is a binomial. d) There are terms. u uv+ v is a trinomial. e) There are terms. k k is a binomial. f) There are 4 terms. m + 0. n 0. + mn is a four-term polynomial. Chapter Section 4 Question 4 Page 4 The highest exponent is. The degree of the expression is. Answer B. 6 MHR Principles of Mathematics 9 Solutions

30 Chapter Section 4 Question 5 Page 4 a) The degree of the term is. The degree of the term is. c) The degree of the term is 0. d) The degree of the term is 6. e) The degree of the term is 5. f) The degree of the term is. Chapter Section 4 Question 6 Page 5 a) The degree of the polynomial is. The degree of the polynomial is. c) The degree of the polynomial is. d) The degree of the polynomial is 7. e) The degree of the polynomial is 6. Chapter Section 4 Question 7 Page 5 A contestant's total points is represented by the expression 500c 00i. Answer B. Chapter Section 4 Question 8 Page 5 a) The total points is described by w + t. Answer D. Answer C is technically correct, but is considered improper form. C shows a coefficient of and D does not, but t t. MHR Principles of Mathematics 9 Solutions 7

31 Chapter Section 4 Question 9 Page 5 a) x ( ) y c) a + b d) ( ) m n Chapter Section 4 Question 0 Page 5 a) Answers will vary. A possible variable is s. 07. s c) 0. 7s 0. 7( 5. 99) 9. 6 The school receives $9.6. d) 07. s 07. ( ) The school will receive $575.7 for this fund raiser. 8 MHR Principles of Mathematics 9 Solutions

32 Chapter Section 4 Question Page 6 a) 5s + 7a c) 5s+ 7a Meredith will receive a bonus of $0. Chapter Section 4 Question Page 6 a) 5g + 8r+ 5b c) 5g+ 8r+ 5b The area will earn $ Chapter Section 4 Question Page 6 a) c w c w Chapter Section 4 Question 4 Page 6 Answers will vary. MHR Principles of Mathematics 9 Solutions 9

33 Chapter Section 4 Question 5 Page 6 Answers will vary. A sample answer is shown. Hello Manuel, A term is made up of a coefficient (a number) and a variable (e.g., a, x, j), but there are no mathematical operations (addition, subtraction) involved. A polynomial is a set of terms being added or subtracted (e.g., 7x + 5y). Jill Chapter Section 4 Question 6 Page 7 a) height w height 5 0 A crest that is 5 cm wide will be 0 cm high. c) 5 w 5 w 5. w A crest that is 5 cm high will be.5 cm wide. Chapter Section 4 Question 7 Page 7 Solutions for the Achievement Checks are shown in the Teacher's Resource. 0 MHR Principles of Mathematics 9 Solutions

34 Chapter Section 4 Question 8 Page 7 a) Answers will vary. Choose s for the swim, c for the cycle, and r for the run. s c r c) The total time is modelled by the trinomial d) s c r Alberto's total time will be.85 h. e) Answers will vary. A sample answer is shown. It is a reasonable time considering all the things he has to complete in only.85 h. MHR Principles of Mathematics 9 Solutions

35 Chapter Section 4 Question 9 Page 8 a) Answers will vary. A possible prediction is that it is faster to walk. w t Ashleigh will take 7.5 s to walk around the border. c) Let the diagonal distance that Ashleigh must swim be represented by s. s s s s s s t Ashleigh will take 6.9 s to swim the diagonal. d) It is faster to walk by , or 9.4 s. MHR Principles of Mathematics 9 Solutions

36 Chapter Section 4 Question 0 Page 8 a) Answers will vary. One possible prediction is that it will be faster to walk half the length, and then swim. s s s s s 6 s w t The time taken for Path # is.5 s. It is fastest to walk all of the way. c) Walking all the way takes 7.5 s and it is the fastest way. Find the time for all three ways and compare the times. MHR Principles of Mathematics 9 Solutions

37 Chapter Section 4 Question Page 9 a) Let an x-tile represent 0.v, and show one of them. Let a y-tile represent 00s, and show three of them. c) Let a unit tile represent $00. The model is shown. d) C ( ) + 00( 50) It costs $ to insure a 50-seat plane valued at $ Chapter Section 4 Question Page 9 m + 5 m 5 m 8 n 7 n + 7 n 8 m+ n Answer C. Chapter Section 4 Question Page 9 Since the value of the expression is even, one of the prime numbers must be. Let a. Divide by repeatedly to show that Divide 567 repeatedly by to show that You may conclude that x + y + z , or 0. Answer B. 4 MHR Principles of Mathematics 9 Solutions

38 Chapter Section 4 Question 4 Page 9 m 4 m m This expression is true for all values of m. MHR Principles of Mathematics 9 Solutions 5

39 Chapter Section 5 Collect Like Terms Chapter Section 5 Question Page 5 x + xy + contains no like terms. Answer B. Chapter Section 5 Question Page 5 a) x and 5x are like terms. y and z are unlike terms. c) x and x are like terms. d) 4 a a nd a are unlike terms. e) ab and a are unlike terms. f) 5 x y and xy are unlike terms. g) uv and vu are like terms. h) 9 p q Chapter Section 5 Question Page 5 and 4q p are like terms. Chapter Section 5 Question 4 Page 5 Answers will vary. Sample answers are shown. a) m, 9m 4x, 6x c) 9y, 7y d) ab, ab Chapter Section 5 Question 5 Page 5 a) x + 6x 9x These are not like terms. The expression cannot be simplified. c) 5h+ 8h+ h 5h d) 7u+ 4u+ u u 6 MHR Principles of Mathematics 9 Solutions

40 Chapter Section 5 Question 6 Page 5 a) 4k k k 8n n 7n c) z 7z 4z d) These are not like terms. The expression cannot be simplified. Chapter Section 5 Question 7 Page 5 a) x + 5+ x+ x+ x+ 5+ 5x y+ 8+ y y+ y + 8y k + m+ 4m+ 6k k + 6k + m+ 4m 7u+ v+ v+ u 7u+ u+ v+ v c) d) 8k + 7m 8u+ v 8n+ 5 n 8n n+ 5 e) f) 5n + 4p + 7q q p 4p p+ 7q q p+ 4q Chapter Section 5 Question 8 Page 5 a) x 8 4x+ x 4x 8+ x 5 y 9 7 6y y 6y 9 7 5y 6 c) x + 7x+ 4x + x x + 4x + 7x+ x 6x + 8x d) 7m+ 6m m+ m 6m + m + 7m m 7m + 5m e) k 5+ 8 k + 4k k k 4k k + 4 f) u+ u 5+ u+ u u + u u+ u+ 5 u 6 Chapter Section 5 Question 9 Page 5 a) a ab 6+ 4b ab b a a a ab + 5ab b + 4b 6+ 7 ab b + 4b + mn + 6m n + m mn + n 4 mn mn + 6m m n + n + 4 5m + n MHR Principles of Mathematics 9 Solutions 7

41 Chapter Section 5 Question 0 Page 5 a) Claudette: 7t + 00 Johanna: 7t + 5 Ming: 7t + 0 Claudette: 7t Claudette makes $40. Johanna: 7t Johanna makes $00. Ming: 7t Ming makes $99. c) 7t t+ 5 d) 7t The students make a total of $89. This is the same as the sum of the answers found in part. 8 MHR Principles of Mathematics 9 Solutions

42 Chapter Section 5 Question Page 5 a) Yannick added the constants to the coefficients of the x-terms. He did not realize that 4 is an unlike term. Answers will vary. A sample answer is shown. You can substitute any value for x into the original expression and into the simplified expression, and show that they do not give the same result. c) x x 9x + 4. Verify by substituting a value for x into the expressions, and show that they give the same result. Chapter Section 5 Question Page 5 a) P w+ w+ w+ w 8w P The perimeter of the field is 400 m. c) 600 8w 600 8w w The width is 00 m, and the length is 00, or 600 m. MHR Principles of Mathematics 9 Solutions 9

43 Chapter Section 5 Question Page 5 a) x+ + 5x+ 4 8x + 5 4y+ y y + c) x+ 5y+ 8 x y+ y MHR Principles of Mathematics 9 Solutions

44 Chapter Section 5 Question 4 Page 5 a) The perimeter measures w+ w+ w+ w6w. The two white bars measure w+ w w. The total length of white trim needed is 6w+ w 7w. For a crest of width 0 cm, the length of trim needed is 7(0), or 70 cm. Chapter Section 5 Question 5 Page 5 a) P x+ x+ x x c x + x x c x P x+ x+ x x + x The perimeter of the isosceles triangle is x + x, which is greater than the perimeter of the equilateral triangle. MHR Principles of Mathematics 9 Solutions

45 Chapter Section 5 Question 6 Page 5 x h + x x h + x 4 x h 4 x h A x x x 4 The area of the isosceles triangle is x, which is greater than the area of the equilateral triangle, which is 4 x. Chapter Section 5 Question 7 Page 5 The coefficient of the first term is increasing by. The coefficient for the 00th term will be + 99, or 0. The coefficient of the second term is increasing by. The coefficient for the 00th term will be + 99, or 99. The exponent of x is increasing by. The exponent for the 00th term will be + 99, or 00. The exponent of y is increasing by. The exponent for the 00th term will be + 99, or 99. The 00th term will be 0x y 99. Answer D. MHR Principles of Mathematics 9 Solutions

46 Chapter Section 5 Question 8 Page 5 Calculate the powers of. The last digit forms the pattern, 4, 8, 6, repeating after a cycle of The exponent 00 occurs after cycles. The last digit in the expanded form will be 6. 4 Answer C. MHR Principles of Mathematics 9 Solutions

47 Chapter Section 6 Add and Subtract Polynomials Chapter Section 6 Question Page 57 ( ) ( ) x 7 + x+ 8 x 7+ x+ 8 x+ x x + Answer C. Chapter Section 6 Question Page 57 a) ( ) ( ) x x+ 5 x+ 4+ 7x+ 5 c) ( ) ( ) x+ 7x x + 9 4m + m 8 4m + m 8 4m+ m 8 7m 9 ( ) ( ) y y y y d) ( ) ( ) y+ 6y+ + 7y d + d 6 5 d + d 6 d + d d e) ( ) ( ) ( ) 4k + 5+ k + 5k + 4k + 5+ k + 5k + f) ( ) ( ) ( ) 4k + k + 5k k + 5 6r + r+ + 6r 6r + r+ 6r 6r+ r 6r + r Chapter Section 6 Question Page 57 ( x 5) ( x 4) ( x 5) + ( x+ 4) x 5 x+ 4 x x 5+ 4 x Answer A. 4 MHR Principles of Mathematics 9 Solutions

48 Chapter Section 6 Question 4 Page 57 a) ( x+ ) ( x+ 6) ( x+ ) + ( x 6) x+ x 6 x x+ 6 x c) ( 6m+ 4) ( m+ ) ( 6m+ 4) + ( m ) 6m+ 4 m 6m m+ 4 4m + e) ( 9 6w) ( 6w 8) ( 9 6w) + ( 6w+ 8) 9 6w+ 6w+ 8 6w+ 6w ( 8s+ 5) ( s+ 5) ( 8s+ 5) + ( s 5) 8s+ 5 s 5 8s s s d) ( 4v 9) ( 8 v) ( 4v 9) + ( 8+ v) 4v 9 8+ v 4v+ v 9 8 7v 7 f) ( 5h+ 9) ( 5h+ 6) ( 5h+ 9) + ( 5h 6) 5h+ 9+ 5h 6 5h+ 5h h + MHR Principles of Mathematics 9 Solutions 5

49 Chapter Section 6 Question 5 Page 57 a) ( ) ( ) 7x 9 + x 4 7x 9+ x 4 7x+ x 9 4 8x ( ) ( ) y+ 8 + y 5 y+ 8 y 5 y y+ 8 5 y + c) ( 8c 6) ( c+ 7) ( 8c 6) + ( c 7) d) ( k + ) ( k ) ( k+ ) + ( k + ) e) ( ) ( ) 8c 6 c 7 k + k + 8c c 6 7 k k + + 7c k + 4 p 8p+ + 9p + 4p p 8p+ + 9p + 4p p + 9p 8p+ 4p+ p 4 p f) ( 5xy + 6x 7y) ( xy 6x+ 7y) ( 5xy + 6x 7y) + ( xy + 6x 7y) 5xy + 6x 7y xy + 6x 7y 5xy xy + 6x + 6x 7y 7y xy + x 4y g) ( 4x ) + ( x+ 8) ( x 5) ( 4x ) + ( x+ 8) + ( x+ 5) 4x + x+ 8 x+ 5 4x+ x x x + 0 h) ( ) ( ) ( ) ( uv v v + u + 4uv 9u uv v ) + ( v u ) + ( 4uv 9u) uv v v u + 4uv 9u uv + 4uv u 9u v v 6uv u 4v 6 MHR Principles of Mathematics 9 Solutions

50 Chapter Section 6 Question 6 Page 58 a) n + 0. n n n 00 copies: (00) 8560 If their CD sells 00 copies, the group is paid $8560. Gold status: (50 000) If their CD sells copies, the group is paid $ Diamond status: ( ) If their CD sells copies, the group is paid $ c) Frederick makes the most money at each level in the table in part. d) Answers will vary. Sample answers are shown. Fixed rate: If there are few sales, the musician still makes some money. However, if there are lots of sales, the musician does not profit as much as they would with other methods of payment. Royalty: The more sales that are made, the more money the musician makes. The musician, however, will make no money if there are no sales. Combination: The musician still gets the fixed rate if there are no sales but receives some royalties if there are sales. The downside is that the fixed rate is smaller than if they were just being paid by a fixed rate and the royalties rate is also smaller than if they were just receiving royalties. MHR Principles of Mathematics 9 Solutions 7

51 Chapter Section 6 Question 7 Page 58 a) Total Earnings: b b E ( ) The total earnings for these players are $ MHR Principles of Mathematics 9 Solutions

52 Chapter Section 6 Question 8 Page 59 a) ( x 5) ( x ) x + 7 ( y y ) ( y y ) y + 5y+ c) ( ) ( x + x+ 4y + x + x+ y ) 4x + 4x+ 6y MHR Principles of Mathematics 9 Solutions 9

53 Chapter Section 6 Question 9 Page 59 a) P w+ w+ 5+ w+ w+ 5 6w + 0 c) P The length of coping needed is 46 m. Chapter Section 6 Question 0 Page 59 a) Answers will vary. One possible prediction is that the length of coping will double. P If the width is doubled, 8 m of coping are required. This is not double the amount in question 9. The amount does not double because the extra 5 m added to the width to form the length does not change when the width changes. Chapter Section 6 Question Page 59 The proportions of the pool change when you change the width. The width is w, the length is w + 5, and the perimeter is 6w + 0. If the width is doubled, the length and perimeter are not doubled. Example: for a width of 6 m, the length is (6) + 5, or 7 m, and the perimeter is 46 m. If the width is doubled to m, the length is () + 5, or 9 m, and the perimeter is 8 m. For the smaller pool, the ratio of length to width is 7:6. For the larger pool, it is 9:. These are not the same. 40 MHR Principles of Mathematics 9 Solutions

54 Chapter Section 6 Question Page 59 a) Answers will vary. MHR Principles of Mathematics 9 Solutions 4

55 Chapter Section 7 The Distributive Property Chapter Section 7 Question Page 66 ( x ) + 5 x 5 Answer D. Chapter Section 7 Question Page 66 x+ x+ 6 a) ( ) ( ) x x+ 4 x + 4x x+ + x+ 5 x+ + x+ 0 c) ( ) ( ) 5x + Chapter Section 7 Question Page 66 a) 4( x+ ) 4( x) + 4( ) 4x + 8 c) ( y+ ) ( y) ( ) y ( ) 5( k ) 5 k + ( ) 5( k ) + 5( ) 5k + ( 5) 5k 5 ( ) d) 8 ( d) 8+ ( d) 8 ( ) 8( d ) 6 + 8d ( ( ) ( ) 5 ( t) + 5( ) 0t + ( 5) e) 5t 5t+ f) 0t 5 ) ( ) ( 4y 5) 4y ( 5) 4 ( y) ( 5) + 4y MHR Principles of Mathematics 9 Solutions

56 Chapter Section 7 Question 4 Page 66 a) y( y 4) y( y) + y( 4 ) r( r+ 5) r( r) + r( 5) y 4y r + 5r c) x( x 5) x( x) + x( 5) x 5x d) q( 4q+ 8) q( 4q) + q( 8) 4q + 8q ( ) ( ) ( e) z z+ z z + z f) z + z ) m( m ) m( m) m( Chapter Section 7 Question 5 Page 66 ( ) ( ) ( a) b b 5 b b + b 5 6b 0b ( ) ( ) ( c) 4w w 4w w 4w d) w + 4w m 5m ) v( 8v+ 7) v( 8v) + v( 7) 4v + v ) 6m( m 5) 6m( m) 6m( 5) 6m + 0m ) e) q( 4q+ ) q( 4q) + q( ) 8q + 6q f) d( d ) d( d) d( + ) d 6d Chapter Section 7 Question 6 Page 66 ( ) ( ) ( )( 4n + ( 0) a) n 5 4 n n 0 ) ( p+ 4) 9 p( 9) + 4( 9) 8 p + 6 ( ) ( ) ( ) ( ) 8m + ( 4) c) 7m m d) 8m 4 ( 7+ c)( c) 7( c) + c( c) c+ c e) ( 6w)( ) ( ) + ( 6w)( ) 6+ w f) ( 4k + 7)( k) 4k( k) + 7( k ) k + ( k) k k MHR Principles of Mathematics 9 Solutions 4

57 Chapter Section 7 Question 7 Page 66 a) ( a + 5a+ ) a + 0a+6 ( ) c) 4k k k 4k 4k k d) n 8n+ 5 6n + 4n 5 ( + ) + ( ) e) x 5x x 5x 6 f) ( + )( ) + ( )( ) Chapter Section 7 Question 8 Page 67 a) ( x+ ) + 4( x 5) ( x) + ( ) + 4( x) + 4( 5) x+ 6+ 4x 0 x+ 4x x 4 4( y+ ) + ( y ) 4( y) 4 ( ) + ( y) + ( ) 4y 4+ 4y 6 4y+ 4y c) ( u+ v) ( u v) ( u) + ( v) ( u) ( v) u+ v u+ v u u+ v+ v u+ 5v d) 4( w ) ( w+ 7) 4( w) + 4( ) ( w) 7 ( ) 4w 8 4w 4 4w 4w 8 4 e) ( a+ ( a ( a) ( ( a) ( a b a+ b a a b+ b 5a b f) ( p q) + ( p+ q) ( p) + ( q) + ( p) + ( q ) p q p+ q p p q+ q 0 5h h 7h 5h + 5h + 0h y + y 4y 8y + y 4y 44 MHR Principles of Mathematics 9 Solutions

58 Chapter Section 7 Question 9 Page 67 a) x+ ( x 4) [ x+ x 8] [ x 8] 9x 4 5 ( y ) 5[ y ] 5 [ y 5] 0y 5 ( ) [ k ] 4 ( r 5) + r 4[ r+ 5+ r] 4[ r + 5] c) k + k k d) [ k ] k 6 e) h h h h+ f) [ h + ] 6h + 4 4r + 60 ( ) [ ] ( p + ) p [ p+ 4 p ] 4 [ p] Chapter Section 7 Question 0 Page 67 a) 0h + 50 ( 5. ) 0h A.5 h repair job will cost $ h+ 00 c) ( h ) d) ( 5) 60h p The cost for a.5 h repair job on a holiday costs $50. This makes sense. It is twice the answer from part. Chapter Section 7 Question Page 67 Niko is right. The order of operations always apply and if there is no other way to simplify the expression according to the order of operations, then the expression is in simplified form. Chapter Section 7 Question Page 68 A ( a+ h ah + bh MHR Principles of Mathematics 9 Solutions 45

59 Chapter Section 7 Question Page 68 a) ( x+ x+ ) 5 ( x+ ) ( ) 0x + x x+ 6x + x ( ) c) P ( x) + ( x+ ) 6 ( x+ 9x+ ) 5 ( x + ) 0x + 6 ( ) ( ) ( ) x( x ) A x x x + 8x d) The perimeter has tripled. Triple the old perimeter is (0x + ) or 0x + 6, which is equal to the new perimeter. e) The area has not tripled. Triple the old area is (6x + x) or 8x + 6x, which is not equal to the new area. Chapter Section 7 Question 4 Page 68 The distributive property is true for numerical expressions. Examples will vary. A sample is shown. ( ) 5 4 ( ) MHR Principles of Mathematics 9 Solutions

60 Chapter Section 7 Question 5 Page 68 x + x+ 5 x 6+ x+ 5 a) ( ) ( ) ( ) ( ) 5x + 9 k 4 k + k k k 4 0. p p p p 0. p 0. p +. p 08. p c) ( ) ( ) 4h h+ + h h 4h 8h+ h h 4. p 8. p d) ( ) ( ) e) ( ) ( ) h h 5j j j j 5j 5j j + j j j 07. w w 06. w w + 4. w +. w 06. w 8. w f) ( ) ( ) g) ( ) ( ) ( ) 0. w + 0. w y 4 y + 6 7y y y+ 6 7y 8 4k k k k + 4 k 5 4k k k + 6k 8 k + 5 h) ( ) ( ) ( ) k 6k MHR Principles of Mathematics 9 Solutions 47

61 Chapter Section 7 Question 6 Page a + ( ) + 4 a a) ( a ) ( 4a ) a+ + a a + 6 ( a) ( a) ( ) y + y + x ( x y) ( y x) ( x) c) ( m ) ( 8m ) x+ ( y) + ( y) x x y+ y x 6 ( ) m ( ) + 8 m m 6m+ 4m + 6 ( m) ( m) ( ) v d) ( 4u v) ( 6u 0v) 4 u ( v ) ( 6 u ) u+ v u+ 6v u+ v 5 4 ( u) v u ( v) 48 MHR Principles of Mathematics 9 Solutions

62 Chapter Section 7 Question 7 Page 69 Solutions for the Achievement Checks are shown in the Teacher's Resource. Chapter Section 7 Question 8 Page 69 a) m m ( m+ ) m[ m m 6] m[ m 6] 4m m p p p+ 4 + p p p + 8p+ p p p 8p + 9p 4p ( ) c) + ( x 6) + ( x 5) + 8 [ + x ] + [ x+ 0+ 8] [ x 9] + [ x+ 8] 4x 8 6x+ 54 x + 6 d) ( y 5) 4 ( y+ ) ( 6 y)( ) [ y+ 5] 4[ y+ + y ] 7 [ y] 4[ y+ 5] Chapter Section 7 Question 9 Page 69 x+ x + x+ x + 6x x 6 x + 4x 6 a) ( )( ) ( )( ) Answers will vary. c) Answers will vary. A sample answer is shown. + y 4y 60 8 y Multiply the first term in the first binomial by each term in the second binomial, and then multiply the second term in the first binomial by each term in the second binomial. Simplify the resulting polynomial by collecting like terms. Chapter Section 7 Question 0 Page 69 ( k )( k k ) ( k ) k ( k )( k) ( k )( k + k k k k k k k ) MHR Principles of Mathematics 9 Solutions 49

63 Chapter Section 7 Question Page 69 Use the "guess and check" method on your calculator to determine that x MHR Principles of Mathematics 9 Solutions

64 Chapter Review Chapter Review Question Page 74 a) Each tile represents km, for a total of 4. Each tile represents an unknown distance x, for a total of x.. c) The x-tile represents the unknown distance, plus unit tiles, for a total of x +. d) Each tile represents the unknown amount of paint per coat, for a total of x. Chapter Review Question Page 74 a) V 7 The volume of the cube is 7 cm. c) A 9 The area of one face of the cube is 9 cm. MHR Principles of Mathematics 9 Solutions 5

65 Chapter Review Question Page 74 a) ( ) 4 8 c) d) Chapter Review Question 4 Page 74 a) ( ) ( ) 5 n The amount in the account after 5 years is $.8. ( ) ( ) 0 n The amount in the account after 0 years is $ Chapter Review Question 5 Page 74 r % The annual rate of interest is 6%. 5 MHR Principles of Mathematics 9 Solutions

66 Chapter Review Question 6 Page 74 a) The graph is non-linear. It is a curve, approaching the horizontal axis. c) years is close to about 4.4 g , or about.509 half-lives. Use your graph to interpolate an answer d) Use your graph to extrapolate an answer close to about 5.6 half-lives, or , or about 000 years. MHR Principles of Mathematics 9 Solutions 5

67 Chapter Review Question 7 Page a) c) ( 4) ( 4) ( 4) d) ( 7 ) Chapter Review Question 8 Page 75 a) 5 5+ n n n 4 n n n n n cd c d c d 5 5 cd n 4 c) + + ab a b 6a b ( 4ab ) 4 a ( b ) 4 5 6ab 6ab 4 5 6ab 4 6ab a b 8 ab 8 ab MHR Principles of Mathematics 9 Solutions

68 Chapter Review Question 9 Page 75 a) The coefficient is 5, and the variable part is y. The coefficient is, and the variable part is uv. c) The coefficient is, and the variable part is ab. d) The coefficient is, and the variable part is de f. e) The coefficient is 8, and there is no variable part. Chapter Review Question 0 Page 75 a) x + x 5 has terms. It is a trinomial. 4xy has one term. It is a monomial. c) a+ b c+ has 4 terms. It is a four-term polynomial. d) has term. It is a monomial. e) 6u 7v has terms. It is a binomial. Chapter Review Question Page 75 a) The number of points is given by the expression w+ o+ l, where w represents a win, o represents an overtime win, and l represents an overtime loss. w o l ( 4) ( ) The team earned 6 points. Chapter Review Question Page 75 a) The degree of x is. 4 The degree of 6n is 4. c) The degree of 7 is 0. d) The degree of abc is 4. MHR Principles of Mathematics 9 Solutions 55

69 Chapter Review Question Page 75 a) The degree of y 5 is. The degree of d d is. c) The degree of w 6w + 4 is. d) The degree of x 5x + x is. Chapter Review Question 4 Page 75 a) Like terms are p, and p. Like terms are 5x, 5 x, and x. Chapter Review Question 5 Page 75 a) 4x + 6x+ 5 4x+ 6x + 5 7k + 5m k 6m 7k k + 5m 6m 0x + 6k m c) d) 6a 5a+ a + 5a 4 6a a 5a+ 5a+ 4 a x 4xy+ 5y 6+ x + 4xy x + x 4xy+ 4xy+ 5y 6 6x + 5y 8 56 MHR Principles of Mathematics 9 Solutions

70 Chapter Review Question 6 Page 75 a) ( ) ( ) 4x+ + x 4x+ + x 4x+ x+ 7x + ( ) ( ) 5k + k 5 5k + k 5 5k + k 5 8k 7 c) ( 6u+ ) ( u+ 5) ( 6u+ ) + ( u 5) 6u+ u 5 6u u+ 5 4u 4 d) ( y y) ( y 5y) ( y y) + ( y + 5y) y y y + 5y y y y+ 5y y + y e) ( a 4a ) ( a 4a+ ) ( a 4a ) + ( a + 4a ) a 4a a + 4a a a 4a+ 4a a 4 f) ( v ) ( v ) + ( v 7) ( v ) + ( v+ ) + ( v 7) v v+ + v 7 v v+ v + 7 4v 6 Chapter Review Question 7 Page 75 P x+ x 5+ x+ x 5 x+ x+ x+ x 5 5 0x 0 MHR Principles of Mathematics 9 Solutions 57

71 Chapter Review Question 8 Page 75 a) ( y 7) ( y) + ( 7) y c) m( 5m ) m( 5m) + m( ) 5m m ( x+ ) ( x) ( ) x 6 d) k( k ) k( k) k( ) 8k 4k e) 5( p + p ) 5( p ) 5( p) 5( ) 5p 5p+ 5 f) 4bb ( b+ 5) 4bb ( ) + 4b( + 4b( 4b 8b + 0b Chapter Review Question 9 Page 75 a) ( q 5) + 4( q+ ) ( q) + ( 5) + 4( q) + 4( ) q 0+ q+ 8 q+ q q 5x( x 4) ( x + 8) 5x( x) + 5x( 4) ( x ) ( 8) 5 0x 0x 6x 4 0x 6x 0x 4 4x 0x 4 c) ( m 6) ( 8 6m) ( m) ( 6) 8 ( ) ( 6m ) 6m m 6m+ 6m d) ( d ) + ( d d) d( d + ) ( d) + ( ) + ( d ) + ( d) d( d) d( ) 8d 0+ d 9d d d d d 9d + 8d d 0 d d 0 ) 58 MHR Principles of Mathematics 9 Solutions

72 Chapter Review Question 0 Page 75 a) 4+ ( x 5) [ 4+ x 5] [ x ] 6x 9 ( k + ) + 5k 9 [ k 6+ 5k ] [ + k] 9 9k MHR Principles of Mathematics 9 Solutions 59

73 Chapter Chapter Test Chapter Chapter Test Question Page 76 7 Answer D. Chapter Chapter Test Question Page w w w w 7 w Answer B. Chapter Chapter Test Question Page Answer C. Chapter Chapter Test Question 4 Page 76 ( ) 6 64 Answer D. Chapter Chapter Test Question 5 Page 76 Answer C shows three like terms. Chapter Chapter Test Question 6 Page 76 k k has terms. It is a binomial. Answer B. Chapter Chapter Test Question 7 Page 76 The degree of u vis 4. Answer D. 60 MHR Principles of Mathematics 9 Solutions

74 Chapter Chapter Test Question 8 Page 76 x 5+ x+ x+ x 5+ 5x Answer B. Chapter Chapter Test Question 9 Page 76 ( ) ( ) ( ) m m m m m 6m + m Answer A. Chapter Chapter Test Question 0 Page 76 ( ) ( ) ( ) ( ) + + a) ( ) ( ) Chapter Chapter Test Question Page a) kn kn k n 7 kn 5 5 6p p p p c) ( g h) ( ) ( g ) 7g 6 7gh h h Chapter Chapter Test Question Page 76 a) ( ) ( ) 5x + x+ 7 5x + x+ 7 5x+ x + 7 7x + 4 ( u 4) ( 5u ) ( u 4) + ( 5u+ ) u 4 5u+ u 5u 4+ u MHR Principles of Mathematics 9 Solutions 6

75 Chapter Chapter Test Question Page 76 a) ( y+ 4) + 6( y ) ( y) + ( 4) + 6( y) + 6( ) y+ + 6y y+ 6y+ 9 y 46 ( b ) ( b+ 5) 46 ( 4( ) ( 5 ( ) 4b+ b 5 4b b+ 5 7b + 7 Chapter Chapter Test Question 4 Page 76 a) They are both correct. It is possible for the expressions to be equal. Use the distributive property to expand the right side of James s formula. ( ) P l+ w l+ w P l+ l+ w+ w P l+ w+ l+ w These can both be simplified to Sylvia s formula, which is equivalent to James s formula. c) Answers will vary. A sample answer is shown. They may have applied the paint too thickly, or they may have spilled some of the paint. 6 MHR Principles of Mathematics 9 Solutions

76 Chapter Chapter Test Question 5 Page 77 a) On the first mailing, the will go to people. On the second mailing, the will go to, or 4 people. On the third mailing, the will go to, or 8 people. Continue the pattern to determine that on the seventh mailing the will go to 7, or 8 people. Continue the pattern to determine that on the ninth mailing the will go to 9, or 5 people. c) Use a table to determine how many people have received the . Click here to load the spreadsheet. d) From the table, it would take 8 mailings to reach all of the students. Chapter Chapter Test Question 6 Page 77 a) n n n n n The publisher must pay the authors $6500 if 00 copies are sold, and $0 500 if 5000 copies are sold. MHR Principles of Mathematics 9 Solutions 6

77 Chapter Chapter Test Question 7 Page 77 a) Use a table to find a pattern. Click here to load the spreadsheet. The number of pennies on the n th square is n. On the 64 th square, there are 6 pennies. The total number of pennies up to the n th square is n. The total number of pennies up to the 64 th square is MHR Principles of Mathematics 9 Solutions

78 Chapters to Review Chapters to Review Question Page 78 a) The next three terms are, 6, and. Add consecutive integers (,,, ) to the previous term. The next three terms are 5, 6, and 49. The sequence shows the number of the term squared. For example, term is or 4. c) The next three terms are, 8, and. Subtract 5 from the previous term. d) The next three terms are 0, 4, and 56. Add consecutive even integers, starting from 4 (4, 6, 8, 0, ), to the previous term. Chapters to Review Question Page 78 Strategy: Substitute the given value of 00 for C in equation and solve for A. A. Substitute A in equation and solve for B. B 40. Substitute B 40 in equation. D 6 9 or Substitute D 9 0 into equation 4. and solve for E. E 0. MHR Principles of Mathematics 9 Solutions 65

79 Chapters to Review Question Page 78 Use a table to organize the possible sums. There are 4 different sums possible. Chapters to Review Question 4 Page 78 There are 6 squares. The area of each square is cm. The side length of each square is 5, or 5 cm. Count the number of side lengths in the perimeter to find that the perimeter is 5 0 cm. 66 MHR Principles of Mathematics 9 Solutions

80 Chapters to Review Question 5 Page 78 a) c) d) Chapters to Review Question 6 Page Mean 7 7 The mean high temperature was ºC. MHR Principles of Mathematics 9 Solutions 67

81 Chapters to Review Question 7 Page 78 The next perfect number is 8. Strategy: A prime number cannot be a perfect number. Skip all prime numbers. Factor each number and calculate the sum of the factors. 8: : + 4 0: : : : : : : : : : : : : : Chapters to Review Question 8 Page 78 Answers will vary. A sample answer is shown. Count how many breaths you take in a minute, multiply by the number of minutes in an hour, hours in a day, and days in a year (number of breaths ). Chapters to Review Question 9 Page 78 Five odd numbers cannot add to 50. Every odd number can be represented as the sum of an even number and. Let the odd numbers be represented by a +, b +, c +, d +, and e+. Their sum is a+ + b+ + c+ + d + + e+ a+ b+ c+ d + e+5. The sum of even numbers is an even number, so a+ b+ c+ d + e is an even number. The sum of an even number plus an odd number is an odd number, so a+ b+ c+ d + e+ 5 is an odd number. Thus, five odd numbers cannot have a sum of 50. Since the sum of five odd numbers must be an odd number, the sum of six odd numbers is an odd number plus an odd number, which gives an even number. So, six odd numbers can have a sum of 50. An example is MHR Principles of Mathematics 9 Solutions

82 Chapters to Review Question 0 Page 78 a) Answers will vary. Example: Answers will vary. Example: c) Answers will vary. Example: Chapters to Review Question Page 78 a) Answers will vary. Answers will vary. A sample answer is shown. Conduct a stratified random sample survey by grade of your school. This is primary data. Chapters to Review Question Page 78 a) Answers will vary. A sample answer is shown. Take a simple random sample of 0% of the grade 9 girls. Answers will vary. A sample answer is shown. Take a stratified random sample by grade. Chapters to Review Question Page 78 a) The taller the student, the greater the shoe size. c) There are no outliers. Outliers should not be disregarded unless the data were inaccurate or unrepresentative. MHR Principles of Mathematics 9 Solutions 69

83 Chapters to Review Question 4 Page 79 a) The population is all 50 employees at the store. Answers will vary. The manager can randomly select 0% of the female employees and 0% of the male employees. Chapters to Review Question 5 Page 79 a) c) The greater the number of storeys, the taller the building. d) Answers will vary. A reasonable answer is 60 m. Chapters to Review Question 6 Page 79 Starting at 9:00, Claire ran at, or 6 km/h until 05. 9:0, then stopped for 5 min. She then ran at a speed 8 of, or 8 km/h until 0:5 when she stopped again 05. for 5 min. Claire then ran back home at 7, or 7 km/h. She arrived home at :0. Chapters to Review Question 7 Page 79 a) The side length of the cube is 64, or 8 cm. The volume of the cube is 8, or 5 cm. 70 MHR Principles of Mathematics 9 Solutions

84 Chapters to Review Question 8 Page 79 a) ( ) ( ) ( ) ( c) d) ) Chapters to Review Question 9 Page 79 + a) n n n n d d d d 6 a c) ( ) 4 4 a a 5 5 e) 4 ( ) 4 ( ) kq kq kq k q 5 4kq 4k q 5 4 4kq 4kq 6k 6kq 5 4 q d) + + mn 4mn m n 4 mn Chapters to Review Question 0 Page 79 a) 0c 5i 0c 5i Theo received a total score of 95. MHR Principles of Mathematics 9 Solutions 7

85 Chapters to Review Question Page 79 a) 5m+ 8 m 0 5m m+ 8 0 m x + 6x x 5x x x + 6x 5x x + x 4 c) ( h+ 5) ( h 8) ( h+ 5) + ( h+ 8) h+ 5 h+ 8 h h h + d) ( 4t+ 5w) + ( t w) ( t+ 4w) ( 4t+ 5w) + ( t w) + ( t 4w) 4t+ 5w+ t w t 4w 4t+ t t+ 5w w 4w t w Chapters to Review Question Page 79 a) 5( x+ ) 5( x) + 5( ) 5x + 5 k( k ) k( k) + k( ) k k c) 4 ( y+ ) + ( y 7) 4 ( y) + 4 ( ) + ( y) + ( 7) d) ( a ) ( 4a ) y y y+ 6y+ 8 8y + + a + () + a + ( a) + + ( a) a+ + a 4a ( ) 7 MHR Principles of Mathematics 9 Solutions

86 Chapters to Review Question Page 79 a) 4n 6+ 5n 8+ 4n+ 4n+ 5n+ 4n 6 8+ n n The perimeter is 44 units. MHR Principles of Mathematics 9 Solutions 7