Math Makes Sense 9 Preparation and Practise Book p2 1. a) 49, 7 b) 4 2 =16, 16 square units. 16 =4, 4 units c) 82 =64, 64 square units. 64 =8, 8 units d) 112 =121, 121 square units. 121 =11, 11 units p3 1. a) 4 b) 144, 12 c) 5, 52 d) 10, 10 2 =100 1. 7, 7, 49, 49 7 3,3,9, 9 3 4,4,16, 16 4 5,5,25, 25 5 6,6,36, 36 6 7,7,49, 49 7 8,8,64, 64 ,8 9,9,81, 81 ,9 10,10,100, 100 ,10 11,11,121, 121 ,11 12,12,144, 144 ,12 p5 3 x3 9 9 3 3 3 x3 9 9 1. a) = , b) x = = , c) 0.25, 0.25 d) 6.25, 6.25 8 x8 2 2 4 4 64 64 2 x2 1. a) is, 3x3 = 9 is, 7x7 = 49 is b) is, 5x5 = 25 is not, it is not the product of 2 equal factors is not c) is, 8x8 = 64 is, 9x9 = 81 is 3 4 3 x3 4 x4 2. a) = b) = 2 9 2 x2 9 x9 p7 1. b) 2.4, Terminating, Yes c) 0.5, Terminating, Yes d) 1.581 138 830…, Non-repeating, Nonterminating, No 1. a) 1x1 1 1 , , 4 x 4 16 16 b) 2 2 2 x2 4 4 x , , 7 7 7 x7 49 49 c) 0.6,0.6,0.36, 0.36 d) 1.1, 1.1, 1.21, 1.21 2. b) Yes; 5x5 = 25, Yes; 7x7 = 49, Yes c) Yes; 6x6 = 36, Yes; 11x11 = 121, Yes d) No, Yes; 5x5 = 25, No e) Yes; 3x3 = 9, Yes; 10x10 = 100, Yes 7 5 3 7 x7 5 x5 1x1 1 3 x3 3. a) , b) , c) , d) , 10 x10 10 12 x12 12 4 x4 4 20 x20 20 4. a) 2.9 b) 0.26 c) 7.15 d) 2.5 5. a) 1.2, terminates, is b) 5.5, terminates, is c) 2.915 475 947, does not appear to repeat or terminate, is not d) 0.16, terminates, is 2 3 3 3 3 9 9 6. a) units, , x , , square units 5 5 5 5 25 25 2 6 36 6 6 6 36 b) units, , x , , The area is square units 7 49 7 7 7 49 c) 5.4 , 5.4 x 5.4, 29.16, The area is 29.16 square units d) 2.1 , 2.1 x 2.1, 4.41, The area is 4.41 square units 3 3 5 9 3x3 25 5 x5 5 7. a) , , , b) , , , The side length is units 6 100 10 x10 10 10 36 6 x6 6 c) 0.01 , 0.1, The side length is 0.1 units d) 46.24 , 6.8, The side length is 6.8 units 2 2 p.10 1. a) 5 b) 7 c) 7 d) 6 2. a) 2.5 b) 2.6 c) 2.6 d) 2.7 p.11 1. a) 16 , 25 , 16 , 4, 25 , 5, 4, 5 b) 4, 9, 4 , 9 , 4 , 2, 9 , 3, 2, 3 p.12 1. a) 92 , 122 , 81, 144, 225, 225 , 15, 15 b) 10 2 , 242 , 100, 576, 676, 676 , 26, 26 p.13 1. a) 9, 16, 9 , 16 , 3, 4, 16, 9, 4, 3, 3, 4, 4 b) 49, 64, 49 , 64 , 7, 8, 49, 64, 7, 8, 7, 8, 7 p.14 25 25 5 5 9 9 3 3 1. a) 25, 81, , , , b) 9, 16, , , , 81 81 9 9 16 16 4 4 p.15 1. a) 49, 64, 49, 64, (answers may vary) 60.5, 60.5 , 7.8, 60.5 2 b) 11 , 121, 122 , 144, 121, 144, (answers may vary) 129.1, 129.1 , 11.4, 129.1 p16 1. a) 36, 49; 6, 7 b) 9, 16; 3, 4 c) 121, 144; 11, 12 d) 81, 100; 9, 10 2. a) 4, 9; 12,3 b) 16, 49; 4,7 c) 4, 25; 2, 5 d) 9, 64; 3, 8 3. a) 1, 4; 1 , 4 ; 1, 2; 1, 4, 1, 2; 1, 2, 1 b) 36, 49; 36 , 49 ; 6, 7; 49, 36, 7, 6; 6, 7, 7 c) 64, 81; 64 , 81 ; 8, 9; 81, 64, 9, 8; 8, 9, 9 4. a) 9, 16; 9 3 ; 16 4 1 1 ; 9 3 b) 1, 9; c) 36, 36; 36 ,1 36 d) 100, 121; 100 10 ; 121 11 5. a) 1, 4; 1, 4; (answers may vary) 1.5; 1.5 , 1.2; 1.5 b) 64, 81; 64, 81; (answers may vary) 70.3; 70.3 , 8.4; 70.3 c) 2.52 , 6.5, 3.52 , 12.25; 6.25, 12.25; (answers may vary) 11.5, 11.5 , 3.4; 11.5 d) 20 2 , 400, 212 , 441; 400, 441; (answers may vary) 431.1; 431.1 , 20.8; 431.1 6. a) 26.01, 39.69; 65.7; 65.7 ; 8.1; 8.1 b) 7.0, 10.5; 49, 110.25; 159.25; 159.25 ; 12.6; 12.6 p. 19 1. a) 4 4 ; 49 49 b) 8 8 64 , , 11 11 121 c) 0.1, 0.1, 0.01; 0.01 d)1.96; 1.96 2. b) Yes; 3 x 3 = 9; Yes; 5 x 5 = 25; Yes c) Yes; 5 x 5 = 25; No; No 3 3 3 4 4 4 6 6 6 3. a) b) c) 4. a) i), iii), and iv) are checked x ; x ; x ; 7 7 7 5 5 5 11 11 11 b) I used a calculator to find the square root of each decimal. If the square root is a repeating or terminating decimal, the decimal is a perfect square. 5. a) 5 5 2 5 5 25 25 ,( ) , x , , 9 9 9 9 81 81 6. a) 4, 9; 4, b) 81 , 100 9 ; 2, 3; 9, 4, 3, 2; 2, 3, 3 9 9 9 9 , x , 10 10 10 10 b) 64, 81; 64 , 81 ; 8, 9; 64, 81, 8, 9; 8, 9, 8 16 9 25 5 ; b) 25, 49, ; 8. a) 4, 9; 4, 9; (answers may vary) 5.2; 5.2 , 2.3; 5.2 49 7 81 4 b) 36, 49; 36, 49; (answers may vary) 48.2; 48.2 , 6.9; 48.2 9. a) 1.12 , 2.2 2 ; 1.21, 4.84; 6.05; 6.05 ; 2.5; 2.5 b) 1.82 , 2.82 . 3.24, 7.84; 11.08; 11.08 ; 3.3; 3.3 p. 23 1. a) Front & Back: 5, 2; 5, 2, 20 Top & Bottom: 5, 3; 5, 3, 30 Right & Left: 3, 2; 3, 2, 12 Total: 62 b) Front & Back: 12, 12; 12, 12, 288 Top & Bottom: 12, 12; 12, 12, 288; Right & Left: 12, 12; 12, 12, 288 Total: 864 p. 25 1. Front & Back: 3, 6 Top & Bottom: 4, 8 Right & Left: 2, 4 Total: 18 p. 27 1. a) 3,1; 1, 3; 3 b) 40, 70, 3; 104 p.28 2. 6; 6, 6; 6,6, 216; Total: 216; 2, 2; 2, 2, 24; 24; Total: 24; 2, 2; 2, 2, 4; Area of Overlap: 4; SA smaller cube, 2(Area of Overlap), 216, 24, 4, 232, 232 1. Back, 2(4)=8; Bottom, 2(4)=8; Left, 2(3)=6; Total = 22; 22 p. 29 2. a) 3, 6; 4, 8; 2, 4; Total = 18; 18 b) 5,10; 2(3)=6; 2(3)=6; Total = 22; 22 p.30 3. SA of larger prism: 15, 5, 150; 2(20 15) =600; 2(20 5) =200; Total = 950; 950 SA of smaller prism: 5, 10, 100; 2(5 10) =100; 2(10 10) =200; Total = 400; 400 Area of Overlap: 10, 5, 50; 50; SA large prism, SA smaller prism, 2(Area of overlap); 950, 400, 50, 1250; 1250 p. 31 4. SA of cube: 30, 30; 30, 30, 5400; 5400; 5400 SA of rectangular prism: 20, 10, 400; 2(20 10) =400; 2(10 10) =200; 1000; 1000 Area of Overlap: 10, 10, 100; 100 SA of composite object: SA cube, SA prism, 2(Area of overlap); 5400, 1000, 2(100); 6200; 6200 p. 32 5. No SA of warehouse to be painted: 20, 20, 800; 30, 20, 1800; 2600; 2600 SA of loading dock to be painted: 30, 10, 600; 30, 20, 600; 20, 10, 400; 1600; 1600 Area of overlap: 20, 10, 200; 200 SA area of composite object to be painted: 2600, 1600, 2(200), 3800; 3800; 3800; 2.50; 3800, 2.50, 9500 p. 34 1. Triangular = 9, 12; 9, 12, 108; Rectangular = 15, 5; 15, 5, 75; 9, 5; 9, 5, 45; 12, 5; 12, 5, 60; Total = 288; 288 p. 35 1. Top Bottom: 4; 2, 4 2 , 100.53 Curved surface: (4), 6; 2, 4, 6, 150.80; Total =251.33; 251 p. 37 1. a) 6, 12; 6, 12, 72 b) 300,720, 2(72), 876, 876 cm 2 1 2. Triangular: 4, 3; , 3, 4, 12 Rectangular: 5, 3; 5, 3, 15; 4, 3; 4, 3, 12; 3, 3; 3, 3, 9; Total= 48; 48 2 p. 38 SA of cube: 3, 3; 3, 3, 54; Total: 54; 54 Area of Overlap: 3, 3; 3, 3, 9; 9 48, 54, 2(9); 84; 84 p. 39 7. a) 16, 81; 1. a) circle of radius 3; 32 ; 28.27 b) prism, cylinder, Area of overlap; 240,56.5, 2(28.27);239.96; 240 p. 40 2. SA of cube: 6, 6; 6, 6, 216; Total =216 SA of cylinder: 1; 2, 12 , 6.28; (1), 4; 2, 1, 4, 25.13; Total =31.41 2 Area of Overlap: 1 , 3.14 SA composite object: cube, cylinder, Area of Overlap; 216, 31.41, 2(3.14); 241.13; 241 p. 41 1. SA of rectangular prism: 4(24 12), 1152; 2(12 12), 288; Total =1440; 1440 1 2. SA of triangular prism: 2( 3 8) = 24; (8.5 4) = 34; (3 4) = 12; (8 4) = 32; Total = 102; 102 2 Area of overlap: 8, 4, 32; 32 SA of composite object: 1440 + 102 - 2(32); 1478; 1478 p. 42 2. SA of cube: 2, 2, 24; Total = 24; 24 SA of cylinder: 2, 6, 226.19; 2, 6, 4, 150.80; Total = 376.99; 376.99 Area of Overlap: 2, 2, 4; 4 Surface Area of composite object: 24, 376.99, 2(4); 392.99; 393 p. 43 3. SA of smaller cake: 2, 52 , 157.08; 2, 5, 5, 157.08; Total = 314.16; 314.16 SA of larger cake: 2, 10 2 , 628.32; 2, 10, 7, 439.82; Total = 1068.14; 1068.14 Area of Overlap: 52 , 78.54; 78.54 SA of Cake: 314.16, 1068.14, 2(78.54); 1225.22; 1225 p. 44 List all the square root day in a year: 1/1 January 1; 2/4 February 4; 3/9 March 9; 4/16 April 16; 5/25 May 25 List all the square days in a year: 1/1 January 1; 4/2 April 2; 9/3 September 3 List all the square years from 1000 to present 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936 p. 46 3 3 9 9 1. a) , , ; b) 98.01; 98.01 7 7 49 49 2. a) Yes, 5 5 =25; Yes, 9 9=81; Yes b) No; Yes, 2 2 =4; No c) Yes, 7 7 =49; No; No 3. a) 2.3; Terminating; Yes b) 12.5; Terminating; Yes c) 2.529822128; Appears to be nonterminating and non- repeating; No 5 4. a) b) 7.7 9 5. 14.5 is between 9 and 16; so, 14.5 is between 9 and 16 . That is, 14.5 is between 3 and 4. Since 14.5 is closer to 16 than 9, 14.5 is closer to 4 than 3. So, 14.5 is between 3 and 4, and closer to 4. p. 47 1 1 9 3 6. a)1; 16; ; b) 9; 64; ; 64 16 4 8 2 7. a) 4,9; 4, 9; 8.5; 8.5 , 2.9; 8.5 b) 6.5 , 42.25, 7.52 , 56.25; 42.25, 56.25; 47.1; 47.1 , 6.9; 47.1 8. a) 4.2 2 , 7.82 ; 17.64, 60.84; 78.48; 78.84 ; 8.9; 8.9 b) 7.12 , 10.52 ; 50.41, 110.25; 160.66; 160.66 ; 12.7; The length of the hypotenuse is about 12.7cm. p. 48 9. Front Back; 2(6) =12 Top Bottom; 2(3) =6 Right left; 2(3) =6 Total: 24 Surface area: 24 10. Surface area of Cube Front/Back, Top/Bottom. Right/Left; 50, 50, 15000 Total: 15000 Surface Area =15000 cm 2 Surface area of rectangular prism Front/Back, 2(20 10) =400; Top/Bottom, 2(40 10) =800; Right/Left, 2(20 40) =1600; Total: 2800 Surface area: 2800 cm 2 p. 49 10. Area of overlap: 20, 10, 200; Area of overlap: 200 SA cube, SA smaller prism, 2(Area of Overlap); 15000, 2800, 2(200); 17400; Surface Area: 17400 11. Surface area of rectangular prism Front/Back, 2(8 4) =64; Top/Bottom, 2(9 8) =144; Right/Left, 2(4 9) =72; Total: 280; SA: 280 Surface area of triangular prism 1 2( 3 4) =12; 5 5 =25; 4 5 =20; 3 5 =15; Total =72; SA =72 2 Area of Overlap 4 5=20; The area of overlap is 20 cm 2 SA rectangular prism, SA triangular prism, 2(Area of Overlap); 280, 72, 2(20); 312; SA =312 p.50 12. 16, 8; 4, 2 Surface area of smaller cylinder 2 2 2 =25.13; 2 8 12 =150.80; Total: 175.93; Surface area: 175.93 Surface area of larger cylinder 2 82 =402.12; 2 8 12 =603.19; 1005.31; Surface area: 1005.31 Area of overlap: 2 2 =12.57; The area of overlap is about 12.57 175.93, 1005.31 -2(12.57); 1156.10; 1156 p.52 1. a) Positive b) Negative c) Negative d) Positive 2. a) 28 b) -18 c) -90 d) 45 e) 15 f) -10 g) -16 h) -12 p. 53 1. a) -6 b) 16 c) -16 d) 18 p. 55 1. a) 2 6 b) 54 c) (10)3 d) 4 2 e) (7)8 2. a) 84 b) 7 2 , 7 squared c) 36 d) 23 , 2 cubed p. 56 1. Power Repeated multiplication Standard Form 23 2 2 2 8 62 6 6 36 34 3 3 3 3 81 10 4 8 squared 10 10 10 10 8 8 10000 63 7 cubed 7 7 7 343 p. 57 1. a) -1; (-1)(-1)(-1); -1 b) 10; -(10 10 10); -1000 c) -7; (-7)(-7); 49 d) -5; -(-5)(-5)(-5)(-5); -625 Practice 1. a) 7, 7; 87 b) 10, 5, 5; 105 c) -2; -2, 3, 3; (2)3 d) 6, -13; -13, 6, 6; (13)6 2. a) 94 b) 56 c) 112 d) (12)5 p. 58 3. a) 3 3 b) 3 3 3 3 c) 2 2 2 2 2 2 2 d) 10 10 10 10 10 10 10 10 4. a) Positive b) Positive c) Negative d) Negative 5. a) (-3)(-3);9 b) 6 6 6; 216 c) (-10)(-10)(-10); -1000 d) –(4 4 4); -64 6. a) (3)3 ; -27 b) (8)2 ; 64 c) 83 ; -512 d) - (1)7 ; 1 7. a) 43 = (4)(4)(4); 64 b) (-2) 9 is negative, because there is an odd number of negative factors. c) (-9) 2 is positive, because there is an even number of negative factors. d) 3 2 is not equal to 2 3 , because 3 2 =(3)(3) =9, and 2 3 =(2)(2)(2) =8 e) (10) 2 =(-10)(-10) =100 p. 59 1. a) The input starts at 1, and increases by 1 each time. The output starts at 5, and increases by 5 each time. You can also multiply the input by 5 to get the output. b) The input in the last row is 4+1 =5. The output in the last row is 20 + 5=25. p. 60 2. a) The input starts at 10, and decreases by 1 each time. The output starts at 100, and decreases by 10 each time. You can als0 multiply the input by 10 to get the output. b) To extend the table 3 more rows, continue to decrease the input by 1 each time. Decrease the output by 10 each time. Input Output 5 50 4 40 3 30 1. a) 7 1000 b) 9 100 c) 4 100 d) 3 10 p. 61 1. a) 1 b) -1 c) 1 d) 1 p.62 1a) 5 b) -7 c) 10 d) 1 1a) 125, 5 5 , 25 , 5, 5 b) 5 c) 1 p.63 2a) 1 b) 1 c) 1 d) -1 e) 10 f) -8 3a) 10 4 b) 106 c) 107 d) 100 e) 109 f) 101 4a) -1 000 000 b) -1 c) -100 000 000 c) -10 5a) 1012 b) 1000 000 000 000, 1014 c) 100 1 000 000 000 000 1014 6a) 50 000 b) (3 10) (7 1) c) (2 1000) (6 100) (4 10) (9 1) d) (7 1000) (8 1) 400+30+7 2000 600 40 9 7000 8 437 2649 7008 p.64 1a) -7 b) 4 c) -3 d) -8 2a) -10, 10 b) -10, -2, -2 p.65 1a) -8 b) 8 c) -17 d) 17 p.66 1a) -2 b) 2 c) -5 p.68 a) (4)(4) + 3 b) (5)(5) – (2)(2) c) 32 d) (1)2 16 + 3 25 – 4 (3)(3) (-1)(-1) 19 21 9 1 p.69 (32 60 ) 2 21 102 (2 22 ) 2 5 32 82 4 (9 1) 2 21 2 2 5 (3)(3) (8)(8) 4 1. a) b) c) 10 2 21 d) 10 8 5 9 64 4 100 64 100 2 45 16 164 50 (6 4) 32 10 102 4 10 9 10 100 4 1. 10 90 25 75 p.70 (2 1) 2 (2 1) 2 (4 2) 2 ( 4) 2 2 22 1 22 1 4 22 42 2 2 2 2 1 2 2 1 32 4 2 2 4 4 2 82 (4)(4) 2 1. a) b) c) d) 1 2. a) b) c) d) 4 1 4 1 4 4 16 2 16 2 3 3 88 1 1 5 3 16 32 8 9 64 1 3 3 2 2 2 (1) 3 (1) 23 (1)3 3 2 3 3 (2 1) (2 1) (2)(2)(2) (1) (3)(3) (1) 2 (3 1) 3 (2)(2)(2) (1) 3 2 3 3 2 1 8 ( 1) 3. a) b) c) 8 (1)(1)(1) d) 3 4. a) 9 (1) b) 3 (3)(3)(3) 3 3 (1)(1)(1) 8 (1) 8 (1)(1)(1) 9 (1)( 1) 27 9 1 8 (1) 9 1 9 7 9 2 2 3 2 3 ( 2) 2 (2) 52 (5)1 (3)(3) (2) 2 (5)(5) ( 5)1 c) 9 (2) d) 25 (5)1 9 (2)(2) 25 (5) 9 4 (5) 2 (2)0 (2) 5. a) 1 (2) (2) (2)(2)(2) ( 2) 2 b) 8 (2) 8 (2)(2) 2 84 (3 2)0 (3 2)0 c) 1 1 2 d) (3 52 ) 0 1 36 2 2 (2)(3) (4) 70 (6)(6) 60 (6)(6) 3(2 1) 2 (2) 2 (3)(4) (2) 30 (2) (2)(3) (4)(4) 2 70 36 60 36 (2)(2) (3)(4) (2) 1 (2) 3(1) e) (2)(3) 16 f) g) h) 6. $4680 2520 2160 4 12 (2) (2) 3(1) 6 16 4680 16 4 3 10 p.72 1. a) Base: 6 Exponent:2 ; There are 2 factors of 6. b) Base: 4 Exponent: 5; There are 5 factors of 4. c) Base: -3 Exponent: 8; There are 8 factors of (-3). d) Base: 3 Exponent: 8; There are 8 factors of 3. 2. a) 7 6 b) 2 4 c) 51 d) (5)5 3. a) 52 5 5 25 b) 23 2 2 2 8 c) 34 3 3 3 3 81 p.73 73 7 7 7 343 100 10000 1000000 1 4. a) 7 2 7 7 49 b)1 5. a) b) c) d) 6. a)1 b)1 c)12 d)-1 6 2 4 0 10 10 10 10 71 7 7 (1103 ) (3 102 ) (2 101 ) (1100 ) (4 103 ) (2 10 2 ) (3 101) (6 10 0) 4 103 (1 1000) (3 100) (2 10) (1 1) (4 1000) (2 100) (3 10) (6 1) 7. a) 4 1000 b) c) 1000 300 20 1 4000 200 30 6 4000 1321 4236 2 1 0 (8 10 ) (110 ) (9 10 ) (8 100) (110) (9 1) d) 800 10 9 819 p.74 5 2 23 23 (3)3 5 5 23 32 5 8. a) 3 3 5 95 14 (2 3) 3 (2)(2)(2) ( 3)3 5 32 82 4 3 3 b) 25 2 c) 5 d) 8 (3) 9. a) 5 9 b) 64 4 25 (2)(2)(2) 5 5 5 8 (3)(3)(3) 45 16 125 25 8 8 (27) 3 17 19 2 3 (10 2) 2 (7 1) (2 2) 32 42 (49 1) (8 2) (3)(3) (4)(4) 12 2 2 c) d) 10. a)exponents b)Square brackets 50 10 9 16 12 4 5 25 3 3 0 (2) (3) 0 (6 3)3 (2 2) 2 (2)(2)(2) 1 c)Exponents d)Evaluate the 0 exponent 8 1 1 7 p.75 3 3 3 5 5 5 5 5 2 2 2 2 2 2 2 2 3 5 5 5 2 2 2 2 2 3 3 5 5 88888 2 2 2 1. a) b) c) d) 88888 1 1 1 9 25 8 1 2 p.77 25 2 4 52 55 (3) 2 (3)3 105 10 1. a) 2 (5 4) b) 5(25) c) (3) (23) d) 10(51) 57 106 29 p.78 (3)5 (3) 2 3 ( 5)3 (5)(5)( 5) 125 (3)9 (3)5 (5)6 (5)3 84 83 98 92 b) (3)(9 5) c) 8(43) d) 9(8 2) 1. a) (5)(63) (3) 4 (5)3 81 96 p.79 1. a) 4 43 4 2 (3) (3) (3) 4(13) 42 (3)(11) (3) 44 42 (3)0 (3) b) 4(4 2) (3)(01) 42 (3)1 16 3 p.80 76 72 (4)5 (4)3 1.a) 7 (6 2) b) (4) (53) 78 105 105 (2) (2) 3 c) (2) (13) (4)8 7 0 71 (3) 4 (3)5 d) 10(55) e) 7 (0 1) f) (3) (45) (2) 4 1010 71 (3)5 (3) 2 56 5 4 2.a) (3)(5 2) b) 5(6 4) (3)3 52 (3)9 103 105 102 (1)9 (1)5 (1)0 23 2 4 2 5 (6)8 58 47 6 4 6 4 (6) 7 10(35) 102 2(3 4) 25 (1)(95) (1)0 56 44 2 2 3 3 c) 4(7 4) d) 5(86) e) 6 (4 4) f) (6) (87) 3.a) 27 25 b) 2 2 c) 108 102 d) (1) 4 (1)0 3 3 (6)1 60 10(8 2) 43 52 2(7 5) (1)(4 0) (2 2) 3 (2 2) 106 212 (1) 4 3 34 4 3 3(4 4) 30 p.81 99 9 7 9 0 (3)1 (3) 2 2 (9) (9 7) 90 (3)(1 2) 2 4.a) (3)3 2 (27) 2 54 b) 9 2 90 9(2 0) 9 55 5 54 5(54) 5 52 50 c) 5(2 0) d) 51 5 2 81 52 5(11) 25 52 5.a) 43 45 4(35) 48 25 b) 2 2 2 2 not 2 c) (3) (3) (3) (6 2) ( 3) 4 not (3)3 d) 70 7 2 7(0 2) 7 2 not 7 0 e) 62 62 (6)(6) (6)(6) 36 36 72 not 6 4 which equals to 1296. f) 106 10 10(61) 105 not 106 g) 23 52 (2)(2)(2) (5)(5) 8 25 200 not 105 which equals to 100,000 p.82 5 5 (55) 10 25 6 2 3 3 3 1 1 1 1 1 1 4 4 4 2 2 2 2 2 2 2 10 2 10 2 2 5 2 5 2 5 25 3 3 3 1 1 1 1 1 1 1.a) 2 2 2 10 10 b) 2 2 2 2 5 5 5 5 1.a) b) 4 4 4 2 2 2 2 2 2 23 102 2 4 54 3 3 16 3 6 4 2 p. 84 1. a) (93 )4 93 94 912 b) [(2)5 ]3 (2)53 (2)15 c) (54 )2 (542 ) 58 p.85 1. a) 54 7 4 b) 82 22 2. a) (-6) 2 = 36 b) 43 = 64 p. 86 Check 35 13 1. a) 5 b) 2. a) 42 , 16 b) 63 , 216\ 3 4 (10) Practice 50 ( 6) 7 32 (1)3 4 4 3 3 5 5 2 3 1. a) 5 2 b) 12 12 c) 3 (2) d) (4) (5) 2. a) 0 b) c) 2 d) 8 57 5 (2)3 p. 87 3. a) 5 23 = 56 b) (2)35 = (2)15 c) 441 = 4 4 d) 803 = 80 4. a) (-12) 2 =144 b) (12)2 = -144 c) 4 2 = 16 d) 30 1 = 30 5. a) (32 )3 323 = 36 , not 35 b) (3 2)2 52 = 25, not 32 22 which is equal to 13 4 4 2 28 2 22 c) (53 )3 533 = 59 d) ( )8 8 e) (3 2)2 62 = 36 f) ( ) 2 2 = , not 9 6 3 3 3 3 g) [(3)3 ]0 (3)30 = (3)0 , not (3)3 h) [(2) (3)] 4 = 64 , not 64 p. 88 1. 54 ( R) 2. 8 (I) 3. 34 (F) 4. 45 (N) 5. -8 (Y) 6. 0 (S) 7. 56 (P) 8. 1 (E) 9. 100000 (A) 10. 6(G) 11. 4 6 (O) Final Answer: A PERSON FRYING AN EGG p. 90 1. a) Base: 6 Exponent: 2 b) Base: -3 Exponent: 8 2. a) 43 b) (3)5 3. a) (-2) (-2) (-2) (-2) (-2) = -32 b) 10 10 10 10 = 10000 c) 6 2 = 6 6 = 36 d) 53 = 5 5 5 =125 4. a) 1 b) 1 c) 8 d) -1 5. a) 9 10 10 10 = 9 1000 = 9000 p. 91 b) (1100) (3 10) (5 1) = 100 30 5 = 135 c) (2 1000) (4 100) (110) (9 1) = 2000 400 10 9 = 2419 d) (5 10000) (3 100) (7 10) (2 1) = 50000+ 300+ 70+ 2 = 50372 6. a) 3 3+3 = 9 +3 = 12 b) 23 = 2 2 2 = 8 c) 25 52 = 25 25 = 1 d) (64-4) (36-6) = 60+30 = 2 7. a) 5 9 = 45 b) 10 (9+1) = 10 10 = 100 d) (-3) + 1 3 = (-3)+ (-3) = -6 c) (-8) + (-12) = -20 p. 92 8. a) 6(3 7) = 6 10 b) (-4) (23) = (-4) 5 b) 10(53) 102 c) (6)(82) (6) 6 10. a) 534 512 b) (-3) 26 = (3)12 11. a) 32 52 b) 25 52 c) (-2) (5 4) = (-2) 9 d) 10 (7 1) = 10 8 9. a) 5 (7 3) = 54 d) 5(106) 54 e) 8(31) 82 f) (-3) (40) = (-3) 4 c) 824 = 88 d) (-5) 54 = (-5) 20 c) (4)3 (5)3 d) 45 35 e) 12 4 10 4 f) (7)6 (9)6 p. 94 14 28 24 4 , 4, 4, b) 2, 2, , 3, 3, 20 40 30 5 12 3 10 20 2. a) 4, 4, b) 3, 3, , 3, multiply c) , 5, 5 d) , 4 , 4 , 4, divide 20 12 15 24 p. 95 1. a)> b) < c) < d) > 2. a) > b) < p. 96 4 3 1. a) 4 , 4 , , 1 , 1 , , A common denominator is 8. 8 8 9 10 b) 3, 3 , , 2, 2 , , Multiples of 4: 4, 8, 12, Multiples of 6: 6, 12, 18 …Common denominator: 12 12 12 9 10 c) 3, 3 , , 5, 5 , , Multiples of 5= 5, 10, 15 Multiples of 3= 3, 6, 9, 12, 15 15 15 Common Denominator = 15 4 3 9 12 9 10 , ,< , ,< 2. a) , , > b) c) 12 12 15 15 8 8 p. 97 1 1. a) 0.75 b) 2 3 0.6 c) 5 8 0.625 d) 0.5 e) 1 5 , 0.2, 4.2 f) , 1 3 , 3 2 5 1 3 5 1 3 9 11 87 5 1 b) , , 4 3. a) b) c) d) e) 1 or 1 0.3 , 2.3 2. a) , , 2 3 9 3 4 8 5 10 10 100 100 10 2 7 f) 5 10 p. 98 4 1. a) Answers may vary. 1 , -2 b) Answer may vary. 0, 0.3 5 p.99 9 4 1 4 1. a) 2.1, -2, 1.8 , -0.3, 0.7 b) -2, - 1 , - 1 , -1 , 10 5 5 5 p. 100 1. a) 3, 5, 0.6 b) 5 3 = 1.6 c) 3 5= -0.6 d) -3, 5, -0.6 e) -5, 3, 1.6 f) 3 (-5)=-0.6 3 3 3 Parts c, d, and f match. This shows that , , are all equal. 5 5 5 2 1 5 1 2. a) < b) c) From the number line, -5 <-5 3. b) -1.6, -0.7, -0.1, 0.8 3 3 6 6 4 4. Answers may vary a) -2 and –1.9 b) 4.2 and 4.3 c) Two possible numbers are: -2 and -1 5 1. a) 5. -2, -1.7, -1 1 3 3 , , 6. -1.5, -1.3, -0.8, 0.9, 2.4 2 4 2 p. 102 5 1. a) 6 P. 103 b) 1. a) 3 b) 2 5 6 1 2. a) , 1 6 5 5 4 2 or 2 6 3 b) 2. a) 3+2+ 4 5 9 1 , ,1 8 8 8 8 2 3 5 5 + = 5 = 5 7 7 7 7 1 2 1 6 7 7 b) 4+1+ = 5+ = 5+ = 5 9 3 9 9 9 9 p. 104 1. a) -2.2 b) -2 2 3 c) 3 8 p. 105 1. a) 12, 2 5 2 , , 2, 2, 12 12 12 b) 15, 10 9 10 1 9 , ( ) , - , 3, 3, and 5, 5, 15 15 15 15 15 p. 106 5 3 5 6 1 1 6 ) = (-1)+ 3 + ( ) = 2+ =2 Use a denominator of 16. 2, 2, 16 8 16 16 16 16 16 3 1 12 5 17 17 12 5 b) 2+1+ = 2+1+ = 3+ =3 Use a denominator of 20. 4, 4, and 5, 5, 5 4 20 20 20 20 20 20 p. 107 Practice 2 1 10 1. a) -4.5 + (-1.2) = -5.7 b) + 2 = 1 2. a) -3.3 b) -0.2 3. a) i) 10 ii)10.5 iii) b) i) -2 ii) 3 3 11 2 2 10 -2.3 iii) c) i) 2 ii) 2.3 iii) d) i) -10 ii) -10.5 iii) 11 11 11 p. 108 Practice 4. a) 1.2 b) -2.3 c) -6.5 d) -44.6 3 2 5 6 1 9 8 17 ( ) = 5. a) - , b) c) ( ) = 9 9 15 15 24 24 24 15 2 1 4 1 1 1 6. a) (-2 + 6) + (- ) + = (-2+6) + ( ) = 4 + =4 5 2 10 2 10 10 1 1 2 3 5 5 b) (-1) + (-3) + (- ) ( ) = (-1) + (03) + ( ) ( ) = (-4) + = -4 6 4 12 12 12 12 1 1 7 3 12 10 c) (-3) + (-5) + (- ) ( ) = (-3) + (-5) + ( ) ( ) = (-8) + (- ) = -8 3 7 21 21 21 21 p. 109 1. a) (-1)+3+ ( 1 a) 1 3 7 or 4 4 3 11 b) 1 or 8 8 c) 2 5 17 4 31 2 2 8 3 3 23 or d) 3 or 2. a) 1, 5, 7 b) 2, , 6, , c) 5, , 20, , 6 6 9 9 3 3 3 4 4 4 p. 110 1. a) - 4 11 3 , , -1 8 8 8 P. 111 b) 4 2 12 10 22 7 ,( ), ,( ) , ,1 5 3 15 15 15 15 6 31 1 1. a) , 18, 18, , -2 Use 15 as a common denominator 5 15 15 b) 19 7 19 28 19 28 47 7 , , , , , (- ), , -5 8 2 8 8 8 8 8 8 Use 8 as a common denominator p. 112 1. a) -2.3 b) 5.5 c) -6.9 d) 6.9 2. 2.7 – 9.7 2.7 + (-9.7) -7 -2.7 – 9.7 -2.7 + ( -9.7) -12.4 -2.7 – (-9.7) -2.7+ 9.7 7 2.7 – (-9.7) 2.7 + 9.7 12.4 p. 113 3. a) 2.4 c) i) 9 b) -5.1 ii) 9.4 iii) c) 34.6 d) -1.4 4. a) i) 3 9 2 , or1 7 7 d) i) -3 iii) - 30 47 7 ) = ( ), or 2 20 20 20 c) 9 5 14 + = 15 15 15 6. a) 13 4 13 4 13 8 5 = ( ) = ( ) = 6 3 6 3 6 6 6 b) iii) 3 7 b) i) -9 ii) -9.4 9 2 iii) , or 1 7 7 3 7 ii) -3.2 5. a) b) ( ii) 3.2 9 7 36 35 1 ( ) = ( ) = 5 4 20 20 20 3 7 3 7 9 14 23 ( ) = = = 2 4 2 3 6 6 6 7. Subtraction Sentence: 42.35 – 24.50 = 17.85 Jenny still owes the cashier $17.85 p. 114 1. Answers may vary. a) - 1 and -1 6 b) -0.2 and 0.1 2 4 7 2. For least to greatest, read the points from left to right; 1 , , 3 5 10 3. a) - 2 =-0.4 5 1 1 =-1.5 2 5 =-1. 6 3 5 - = -2.5 3. b) -2.5, -1. 6 , -1.5, -0.4 2 p. 115 4. a) 2.3 b) -21.5 5. a) 2 1 ,8 8 b) 3 2 5 = 8 8 8 3 2 5 c) - ( ) =8 8 8 d) 3 2 1 ( ) = 8 8 8 6. a) 22 45 23 ( ) = 33 33 33 1 2 7 8. a) ( ) , (- ), 12 6 12 5 7 20 21 1 b) (-1+3) + ( ) = 2 + ( ) = 2 7. a) 3.4 b) -9.1 6 8 24 24 24 b) 3 c) 11 d) 3.3 1 18 10 54 70 16 =- + =+ = 3 7 3 21 21 21 p. 116 9. a) 1.3+5.4=6.7 The temperature rose by 6.7. b) -4.2-2.7 = -4.2+ (-2.7) = -6.9 The temperature fell by 6.9 c) -4.2 – (-5.4) = -4.2 + 5.4 = 1.2 The temperature rose by 1.2 degrees Celsius. p. 117 2 7 2 2 1. a) b) 2, 2, , 2 c) 4, 4, , 4 d) 6, 6, , 6 3 10 3 3 p. 118 3 1 3 97 93 71 3 1 3 , 2 b) 1. a) CF between 9 and 3 is 3. CF between 7 and 14 is 7. 2 5 10 14 3 142 31 2 1 2 6 3 3 3 9 4 15 2 3 6 12 5 2 1 2 2. a) b) c) 7 4 7 2 14 5 14 1 7 7 5 18 1 3 3 p. 119 3 5 4 19 3 7 2 23 112 5 17 1. a) = b) = c) = 5 5 7 12 12 7 17 1 17 3 4 3 4 1 1 2. a) = b) = = 2 Rewrite 1 and 1 as improper fractions. 5 4 20 2 3 23 2 3 p. 120 1 (3) 3 1. a) =The fractions have different signs, so their product is negative. 5 5 25 p. 121 (9) ( 7) ( 3) ( 7) 21 b) = = The fractions have the same sign, So their product is positive. 1112 11 4 44 A common factor of 9 and 12 is 3. CHECK 5 6 (5) 3 15 1 14 11 ( 7) ( 11) 77 7 , or 1 , or 7 1. a) ( ) b) ( )( ) = = 4 7 27 14 14 5 4 5 2 10 10 p. 122 1. a) The change in value is : 80 (-1.13). The product is negative. To find 80 (-1.13), multiply: 80 (-113). 80 (-113)=-9040. Estimate: 80 (-1.13) is about 80 (-1) = -80. So, 80 (-1.13) = -90.40. The shares changes in value by -$90.40 that day. p. 123 1. a) Negative b) Positive c) the same sign; positive d) different signs; negative 2. a) Yes, since changing the order of the factors does not change the product. b) No, since the product is positive, not negative. c) No, since the product is positive, not negative. d) Yes, since the signs and numerical values match. 2 ( 5) 1 ( 5) 5 ( 4) ( 11) (1) ( 11) 11 3. a) = =b) = = 76 73 5 12 5 3 13 21 p. 124 (4) 1 4 1 17 6 (17) (1) 17 4. a)3, = , or 1 b) ( )( ) 3 1 5 3 6 5 1 5 5 5. a) -128, 1, (-3), -3, -1.28 b) (-303), (-7), 2121, -3, -1, 3, 2.121 6. a) The total change in temperature is: 8 (-2.2). The product is negative. To find 8 (-2.2), multiply 8 -22 = -176. 8 (-2.2) is about 8 (-29 = -16. So, 8 (-2.2) = -17.6. The temperature fell by 17.6 degree Celcius in 8h. p. 125 1 3 1 3 1 3 3 1. a) 12 b) b) = c) 4 2 6 \ 6 5 3 5 5 2 1 p. 126 2 4 2 ( 4) 8 2 7 ( 1) ( 7) 7 1. a) ( ) = =b) ( ) ( ) = = 5 3 5 3 15 9 4 9 2 18 p. 127 1. Divide integers: (-75) 5 = -15. (-7.5) 5 is about (-5) 5=-1. So, (-7.5) 5 = -1.5 Practice 1. a) Positive b) Different signs the quotient is negative. c) Different signs; the quotient is negative. d) Same sign; the quotient is positive. p. 128 2 5 2. a) Yes, since the reciprocal of is . To divide, you can multiply by the reciprocal. 5 2 b) No, since the quotient is positive, not negative. c) No, since changing the order of the factors changes the quotient. d) Yes, since the sign and numerical value of the quotient are the same. 2 6 (2) 2 4 15 8 (3) ( 1) 3 1 3, a) ( ) = = b) ( ) ( ) = = , or1 3 7 1 7 7 16 5 2 1 2 2 8 3 ( 8) 1 8 2 2 7 (2) ( 7) 14 4. a) (- ) = = , or 2 b) (- ) ( ) = = 9 1 3 1 3 3 5 3 5 3 15 5. a) The quotient is negative;(-294) 7=-42; (-3) 1 =-3; -4.2 b) The quotient is positive; (-552) (-8)=69; (-6) (-1)=6; 6.9 p. 130 1. a)3.8 + (-4) = -0.2 b) 4.6-9+3.9 (-1.3) = 4.6 – 9 + 3 = -4.4 + (-3) = -7.4 p. 131 3 (1) (1) 3 1 9 2 7 1. a) = = = 4 3 2 4 6 12 12 12 1 1 3 ( 1) 5 3 5 3 5 9 14 ( ) = ( ) ( ) = ( ) ( ) = ( ) b) - ) ( ) 6 5 2 6 1 2 6 2 6 6 6 1 Divide first. Multiply by the reciprocal of . Add. Use a common denominator of 6. 5 p. 132 1. 32+9 (-12.5) 5 = 32+(-112.5) 5 = 32+ (-22.5) = 9.5 -12.5 digrees Celsius is equivalent to 9.5 degrees Fahrenheit. Multiply First. Then divide. Then add. P. 133 1. a) Add. b) Multiply c) Multiply d) Divide 2. a) (-3.6) 1.8 +(-0.3) = -2 + (-0.3) = -2.3 1 3 1 1 2 1 2 1 8 3 5 b) ( ) = ( ) = = - =4 8 4 1 3 4 3 4 12 12 12 3. a) 10 (-2.5) = -4 b) (-4.2) + (-10.2) = -14.4 c) 2.3-3.6 2 = 2.3-7.2 =-4.9 d) 7.5 [-0.7-0.9] = 7.5 (-1.6) = -12 p.134 1 (1)(8) 1 2 3 2 1 1 (1) 82 ( ) = = 1 = ( ) = 5 4 15 5 15 15 15 15 5 4 15 7 3 1 (7) 3 1 21 2 19 3 = = or 2 5. b) ( ) = 4 2 4 4 2 4 8 8 8 8 1 3 1 11 5 1 5 2 15 13 1 = = c) = = - , or 1 9 2 4 3 2 4 6 4 12 12 12 12 5. a) Line 2: 4-(-4.1) = 4+(+4.1) = 8.1 1 2 ( 1) 1 2 1 b) Line 1: = ( ) = 3 3 1 3 3 3 6. Substitute h = 3.5, a = 8, and b = 12 in the formula A=h 2 . A = 3.5 (8+12) 2 = 3.5 20 2 = 70 2 = 35 The trapezoid has area 35 cm 2 . p. 135 1 4 1 1 1 1. -5.8 2. -7.3 3. -3.8 4. 1.58 5. -1.44 6. 7. 8. 9. 10. 2 5 12 20 6 The winning card is Card A. p. 137 11 1. a)i) -16 9 = -1. 7 ii) (-7) 3 = -2. 3 iii) - = (-11) (5) = -2.2 5 16 7 b) Sample Answer. Two rational numbers between and are: -2 and -2.1 9 3 4 7 2. From least to greatest: -3.9, 3 , , 3.3 3. a) 2.7 b) 6.7 c) -10.2 5 2 1 6 7 16 11 5 2 8 6 8 2 2 4. a) ( ) = b) - c) (-1+2)+ ( ) = (-1+2)+(- ) = 1+ = 1 8 8 8 12 12 12 3 9 9 9 9 9 p. 138 7 8 1 3 15 21 75 54 19 ( ) = - , or 1 5. a)- b) ( ) = 12 12 12 5 7 35 35 35 35 31 8 31 16 47 7 c) +(- ) = - ( ) = , or 4 10 5 10 10 10 10 6. a) 5959.1 –(-417.3) = 5959.1 + 417.3 = 6376.4 The difference in elevation is 6376.4m. b) -410.9 –(-417.3) = -410.9 + 417.3 = 6.4 The difference in elevations is 6.4m. c) 8849.7 – 5959.1 = 8849.7 + (-5959.1) = 2890.6 The difference in elevations is 2890.6m. 7. a) Positive b) Negative c) Positive d) Negative p. 139 1 (11) (1) (11) 11 (1) 5 5 2 8. a) = = b) = , or 1 5 10 5 10 1 3 3 3 50 15 4 ( 5) 1 5 1 11 25 (1) (25) 25 1 , or 8 c) - = = , or 1 d) ( ) = 16 3 4 1 4 4 3 11 3 1 3 3 9. a) 141.6 b) 3.78 c) 978.56 d) 60 10. The distance the diver descends is: -0.8 3.5 The product is negative. Multiply the whole numbers: (-8) 35=-280 Estimate: -0.8 3.5 is about (-1) 4=-4. The exact answer is -0.8 3.5 = -2.8 The diver descends 2.8m in 3.5 min. 4. a) p. 140 1 10 1 (2) 2 3 7 ( 1) ( 7) 7 ( ) = =b) ( ) ( ) = = 5 7 1 7 7 5 12 5 4 20 12. a) 1.1- 21.7 = 1.1 + (-21.7) = -20.6 b) -1.8 (-0.3) +[5.1+2.9] = -1.8 (-0.3) +8 = 6+8 =14 ( 5) 1 5 5 5 5 10 5 c) + =- =- = 6 4 12 24 12 24 24 24 3 2 9 3 1 ( 3) 3 3 7 3 4 d) 1 ( ) = 1 = 1 ( ) = ( ) = , or1 4 3 8 4 1 4 4 4 4 4 4 p. 142 1. a) 3(3) + 5 = 9+5 = 14 b) 6+8(3) = 6+24 = 30 2. a) 8(8)-4 = 64-4 = 60 b) 20-2(8) = 20-16 = 4 p. 143 1.b)i) Figure Number Number of Squares 1 2 2 5 3 8 4 11 5 14 ii) Figure Number Number of Dots 1 3 2 6 3 9 4 12 5 15 p. 145 1. +1, +1, +1, +4, +4, +4 a) The number of hits is 4 times the number of swings, plus 1. b) Write an equation to describe the relationship. h=4s=1 c) Use your equation to find h when s = 10 h=4(10)+1 =40+1 =41 p. 146 1. a) P = 50+2b b) P=50+2(20) = 50+40 = 90 Marcel got paid $90. p. 147 1. a) T = 8+6 = 14 b) T=3(6)-2 = 18-2 = 16 c) T=12(6)+9 = 72+9 = 81 d) T = 7(6)+3 = 42+3 = 45 2. b) The expression in part ii: 3f represents the number of dots in terms of the figure number. 3. b) Left side: +1, +1, +1, +1 Right Side: +2. +2. +2. +2 Number of Shaded Tiles, s Number of White Tiles, w 1 8 2 10 3 12 4 14 5 16 c) w=2s+6 d) w=2(25)+6 = 50+6 = 56 When the number of shaded tiles is 25, there are 56 white tiles. 4. a) C = 400+3n b) C = 400+3(200) = 400+600 = 1000 The total cost is $1000. p. 149 11. a) 1. A(-5,-4) B(3,5) C) (2,-5) p. 150 1.b) The points lie on a straight line, so it is a linear relation. p. 152 1.b) The points lie on a straight line, so it is a linear relation. c) A building cannot have part of a floor, so the points should not be joined. p.153 1. X Y=4x-2 -1 -6 0 -2 1 4(1)-2 = 2 2 4(2)-2 = 6 p. 154 1. a) Linear b) Not Linear c) Not Linear d) Linear 2. a) x increases by 1 each time. y decreases by 1 each time. The relation is linear, because a constant change in x produces a constant change in y. b) x increases by 2 each time. y increases by 3 each time. The relation is linear, because a constant change in x produces a constant change in y. c) x increases by 1 each time. y does not increase or decrease by a constant value. The relation is not linear, because the change in y is not constant. p. 155 3. a) i) X Y 2 4 3 6 4 8 5 10 ii) X Y -3 0 -2 1 -1 2 0 3 b) i) when x increases by 1, y increases by 2 ii) When x increases by 1, y increases by 1. c) i) To get from one point to the next, move 1 unit right and 2 units up. ii) To get from one point to the next move 1 unit right and 1 unit up. 4. a) y=4x X Y -1 -4 0 0 1 4 2 8 b) y=-3x X -1 0 1 2 c) y=1-x X 0 1 2 3 p. 156 5. x -1 0 1 2 Y 3 0 -3 -6 Y 1 0 -1 -2 y = 2x-4 -6 -4 2(1) – 4 = 2 – 4 = -2 2(2) – 4 = 4 – 4 = 0 6. a) No, because the fee is for each hour, not for part of an hour b)Yes; the relation is linear because the points lie on a straight line c) 1, 10, 10 p. 157 2x 8 2 x 12 , x = 4 b) 3 – 3 – 2x = -9 – 3, -2x = -12, 1. a) 3, 3, 2x = 8, ,x=6 2 2 2 2 p. 158 1. vertical, x, 1 p. 159 1. b) horizontal line, y, 3 p. 160 1. a) Horizontal line b) Oblique line c) Vertical line d) Oblique line p. 161 1. a) y = 4 b) x = 2 2a) 3 b) -2 c) x = -3 3a) i) Vertical ii) Horizontal b) i) -1 ii) y, -4 p. 162 4. a) i) Vertical line ii) Horizontal line iii) Oblique line b) i) x + 3 – 3 = -1 – 3, x = -4 2 y 10 2y 8 , y = 5; 0, 2y = 8, , y = 4; ii) 1 + y – 1 = 0 – 1, y = -1 c) -2, -2 + 2y + 2 = 8 + 2, 2y = 10, 2 2 2 2 2y 6 , y = 3, 2, 2 + 2y – 2 = 8 – 2, 2y = 6, 2 2 X -2 0 2 y 5 4 3 5. a) y + 3 – 3 = 0 – 3, y = -3, horizontal, y, -3 p. 163 1. a) 9, 13, 17 b) 1, 4 c) 4, 3 d) 4, 3 p. 164 2. Number of Red Buttons, r 2 3 4 5 6 6 Number of Blue Buttons, b 10 13 16 19 22 25 a) 1, 3 b) 3, 4 3b) The points lie on a straight line, so this is a linear relation c) 1, 90 d) 90 units e) 90, 60 p. 165 4. b) 1, 2, 2 units c) 2, 2 5a) Vertical line b) Horizontal line c) Oblique line d) Horizontal line 6. a) y = 3 b) x = -2 c) y = -1 p. 166 1. X Y=x+2 0 Y=0+2=2 1 Y=1+2=3 2 Y=2+2=4 X Y=x-2 0 Y=0-2=-2 1 Y=1-2=-1 2 Y=2-2=0 (0,2), (1,3), and (2,4) do not lie on the graph. (0.-2), (1,-1), and (2,0) lie on the graph. Equation=Y=x-2. p. 168 1. Left side= y=1 Right side = y=2(0) +1 = 0+1 = 1 Substitute x=1 and y=3 Left side: y=3 Right side: 2(1) + 1 = 2 + 1 = 3 Both coordinates satisfy the equation. So, the graph has equation y=2x+1 Practice 1. X Y=x+2 -2 Y=-2+2=0 -1 Y=-1+2=1 0 Y=0+2=2 (-2,0), (-1,1), and (0,2) lie on the graph. 2. X Y=3x X Y=-3x -1 Y=3(-1)=-3 -1 y=-3(-1)=3 0 Y=3(0)=0 0 y=-3(0)=0 1 Y=3(1)=3 1 Y=-3(1)=-3 Y=3x: (-1,-3), (0,0), (1,3); Graph B; Graph B. Y=-3x: (-1,3), (0,0), (1,-3); Graph A; Graph A 3. X Y=x-1 X Y=1-x -1 y=(-1)-1=-2 -1 Y=1-(-1)=2 0 y=0-1 = -1 0 Y=1-(0)=1 1 Y=1-1=0 1 Y=1-1=0 Y=1-x: (-1,2), (0,1), (1,0); Graph A; Graph A Y=x-1: (-1,-2), (0,-1), (1,0); Graph B; Graph B 4. Left side: y=0 Right Side: x-3 = -3-3 = -6 The left side does not equal the ride side. So, y=x-3 does not match Graph A. Left side: y=-3 Right Side: x-3=0-3=-3 The left side equals the right side. Left side y=0 Right Side: x-3=3-3=0 The left side equals the right side. Graph B p. 170 1. a) $14 b)11L p. 171 1. a) About $27 p. 172 1. a) x=5 b) y=-1 2. a) x=3 b) y=-3 3. a) 500m b) 1.5 days c) 1500m d) 4 days p. 173 1. b) c) X Y X Y -4 -4 5 4 0 0 9 0 4 4 13 -4 What do you sea: Sample Answer: A prairie road. p. 175 1. b) Figure Number, n Number of Squares, s 1 1 2 4 3 7 4 10 5 13 c) 1;3 d) s=3n-2 e) s=3(10)-2=30-2=28 There are 28 squares in figure 10. 2. a) 8,9 b) n+4 3. a) y= 2,3,4,5 b) y=1,3,5,7 4. b) The points lie on a straight line, so the graph is linear. c) Hayden only gets a gift on each birthday, not in between, so the points should not be joined. d) 1, 10; 1 unit right, 10 units up 5. a) x=5 b) y=9 c) y=-10 6. a) Vertical line b) Oblique line c) Horizontal line d) Vertical line 7. a) X y=-2x X Y=2x -1 2(-1) = -2 -1 -2(-1)=2 0 2(0)=0 0 -2(0)=0 1 2(1)=2 1 -2(1)=-2 Y=2x: (-1,-2), (0,0), (1,2) Y=-2x: (-1,2), (0,0), (1,-2) The graph passes through the points (-1,-2), (0,0), (1,-2) y=2x 8. For A(-2,0) Left side: -2-0=-2 Right side: 2 The left side does not equal the right side. So, Graph I does not match equation x-y=2 For C(0,-2) Left side: x-y=0-(-2) = 2 Right side: 2 The left side equals the right side. For D(2,0): Left side: x-y=2-0 =2 Right side: 2 The left side equals the right side. Graph ii 9. About 40km. 10. a)i) y=2 ii) y=1 b)i) x=-2 ii) x=4 p. 180 1. a) 3x+1 b) 2x-3 c) -3x+4 d) -2x-2 p. 183 1. The same tiles are used in parts b and c. So, 5-3a 2 -2a and -2c+5-3c 2 represent the same polynomial. p. 184 2. a) 1 term; monomial b) 2 terms; binomial c) 3 terms; trinomial d) 2 terms; binomial e) 1 term; monomial 3. a) 2; 2 b) 4b; 1; 1 c) 4d 2 ; 2; 2 d) -4x 0 ; 0 4. a) 2 f 2 f 5 b) 3n 2 2 c) -7p+3 5. Answers may vary. For example, the tiles in question 4 part b can represent the polynomial -2+3p 2 . 6. a) 3, 1 b) 4, 5, 9 c) 9, 4, 5 d) 3, 1, 1 Parts b and c use the same algebra tiles. So, 4r 2 5 9 and 9 4 z 2 5 z both represent the same polynomial p. 186 1a) +2 b) -1 c) -3 d) 0 p. 188 1. a) 2x-1 b) 2 x 2 3 x 2 c) x 2 3x 2 p. 189 1. a) 8d+1 5+3=8 and 2+(-1)=1 b) 2a 2 5a 2 3a 7a 7a 2 4a 2+5=7 and -3+7=4 2 2 2 2 c) x 2 x 4 x x 5 3 1x 5 x 2 x 5 x 2 d) 2 x 2 2 x 2 6 x 7 x 7 11 0 x 2 13x 4 13x 4 p. 190 1. a) 2 b) 6 c) -3 d) 7 e) 1 f) -1 2 2 2. a) variable z and exponent 2. -z , 2z , -4z 2 b) variable and exponent 1. 4 x.7 x, x 2 3. a) –x+3 b) 4x-2 c) 2 x 3 4. a) 2; 2c b) 3; 3s c) -2+7=5, -2 x 2 7 x 2 5 x 2 d) 8+(-8)=0; 8 e2 8e2 0 5. a) 5m -2m +7+1 = 3m+8 b) 7c 2 4c 2 6c c = 3c 2 5c c) 11 2 9v v v 2 13 10v v 2 v 2 10v 13 d) 7 f 2 3 f 2 12 f 3 f 2 5 10 f 2 9 f 3 6. a) 3x and 2 are not like terms. They cannot be combined. b) 3s and 3s are like terms. To combine like terms, add the coefficients and leave the cariable alone. Since 5+3=8, 5s+3s=8s c) Correct: x 2 and -x 2 are like terms. Since 1-1=0, x 2 -x 2 =0 p. 192 1, a) 4+5=9 b) 6+(-2)=4 c) (-3)+(-5)=-8 d) 3+(-3)=0 e) 5+(-8)=-3 p. 194 1. a) 4p+5 b) 3x 2 x 2 c) e2 3e 3 p. 195 1. a) 10g-7 7+3 =10 and -8+1=-7 2 2 b) 2a 9a 5a 12a 2a 2 5a 2 9a 12a 3a 2 3a 2(-5)=-3 and -9+12=3 c) c 2 11c 3 4c 2 5 1c 2 4c 2 11c 3 5 3c 2 11c +2 p. 196 1. a) 6x+11 b) 3p 2 +3p+5 c) -7b 2 +7b-11 Practice 1. a) (4x-1)+(-x+3)=3x+2 b) (-x 2 +2x-3)+(3x 2 -2x+5)=2x 2 +2 2. a) 2w+5 b) -2 t 2 4t 3 3. a) 5r-4 2+3=5 and -3+(-1)=-4 b) 7h 2 2h 4h 2 9h 4 = 7h 2 -4h 2 -2h+9h-4=3h 2 +7h-4 c) 2 y 2 6 y 1 2 y 2 6 y 5 2 y 2 2 y 2 6 y 6 y 1 5 4 4. a) 11r+4 b) 4a 2 6a 5 c) 4v 2 2v 6 5. a) (s+2)+(2s+5)+(2s+3) = s+2+2s+5+2s+3 = s+2s+2s+2+5+3 = 5s+1p. 198 1. a) 2; 2,8; 8 b) -4; 3+(-4)=-1; -1 c) 5; (-8)+(5) = -3; (-8)-(-5)=-3 d) -4; (-9)+(-4)=-13; (-9)-(4)=-13 p. 200 1. a) (4 p 3) (2 p 1) 2 p 2 b) (5t 1) (2t 3) 7t 2 c) (3e2 2e 4) (4e2 3e 2) e2 e 2 p. 201 (2 5 g 7 g 2 ) (9 g 4 g 2 2) (8 f 3) (7 f 5) 2 5 g 7 g 2 (9 g 4 g 2 2) 8 f 3 (7 f 5) 2 5 g 7 g 2 (9 g 4 g 2 2) 8 f 3 (7 f 5) (4 x 3) (2 x 1) 1) a) b) 2 5 g 7 g 2 9 g 4 g 2 2 1) a) 8 f 37 f 5 2x 2 2 2 5g 9 g 7 g 2 4g 2 8 f 7 f 35 4 g 3g 2 f 8 3 g 2 4 g b) (3x 2 6 x 5) (2 x 2 3x 4) x 3x 1 p. 202 2 3) a) 9 b) -3r c) 2s 2 d) –t 4) a) 2) a) 5r 1 b) v 2 v 1 (4 p 1) ( p 10) (3h 2 5h 4) (h 2 4h 6) 4 p 1 ( p 10) 3h 2 5h 4 (h 2 4h 6) 4 p 1 ( p 10) 3h 2 5h 4 (h 2 4h 6) 4 p 1 p 10 4 p p 1 10 3p 9 b) 3h 2 5h 4 h 2 4h 6 3h 2 h 2 5h 4h 4 6 2h 2 9h 10 (4q 2 3) (3q q 2 3) 4q 2 3 (3q q 2 3) c) 4q 2 3 ( 3q q 2 3) 4q 2 3 3q q 2 3 4q 2 q 2 3q 3 3 (7 x 2 3 x 7) (3 x 2 4) 5) a) 7 x 2 3x 7 3x 2 4 7 x 2 3x 2 3x 7 4 4 x 2 3 x 11 (3a 2 2a 4) (2a 2 3) b) 3a 2 2a 4 2a 2 3 3a 2 2a 2 2a 4 3 a 2 2a 1 5q 2 3q p. 203 1) a) 1 term, monomial b) 2 terms, binomial c) 3 terms, trinomial d) 2 terms, binomial 2) a) 5g – 7 b) 3r 2 4r c) w2 3w 4 3) a) -3x + 4 b) 2 x 2 2 p. 204 4d 2 3d 11 d 2 5d 13 8e 9 5e 4 4) a) 8e 5e 9 4 b) 4d 2 d 2 3d 5d 11 13 5) a) 2v + 3 b) 3u 2 2u 5) a) 4t 7 b) 7 y 2 4 y 11 3e 5 3d 2 2d 2 (3s 4) (4 s 5) (3s 4) (4 s 5) 7) Perimeter = 3s 4 4 s 5 3 s 4 4 s 5 3s 4 s 3 s 4 s 4 5 4 5 14 s 2 p.205 8) a) 6n – 3 b) – v – 7 9) a) (11h 3) (9h 2) (7 j 2 11 j 7) (12 j 2 8 j 3) 11h 3 (9h 2) 7 j 2 11 j 7 (12 j 2 8 j 3) 11h 3 (9h 2) 7 j 2 11 j 7 (12 j 2 8 j 3) 11h 3 9h 2 b) 7 j 2 11 j 7 12 j 2 8 j 3 11h 9h 3 2 7 j 2 12 j 2 11 j 8 j 7 3 2h 5 5 j 2 3 j 4 p.206 1) a) Area length width 6 15 6 (10 5) b) 8 35 8 (30 5) 2) a) 140 7 147 (8 40) (8 3) b) 320 24 344 p.207 1) a) Positive b) Negative c) Negative d) Positive 2) a) 30 b) – 40 c) – 21 d) 48 e) – 60 f) 32 3) a) Positive b) Negative c) Negative d) Positive 4) a) – 7 b) 7 c) 8 d) – 9 e) 9 f) – 6 p.208 1) a) 12p – 9 b) 2 s 2 2 s 6 p.209 (5)(2d 2 ) (5)(3d ) (5)(6) 7(6 y 2 ) 7(8 y ) 7(9) 2 (4)(5e ) (4)(8e) 1) a) 21s 2 27 b) c) 10d 2 15d (30) d) 42 y 2 (56 y ) 63 2 20e 32e 10d 2 15d 30 42 y 2 56 y 63 p. 210 1) a) g2 + 4g b) -2b2 + 3 c) s2-s+2 d) -2t2 + 3t -1 p.211 12 3v 2 v 2 1) a) 12r2, 8, , 2, 3 r2+2, 3r2+2 b) 18v2, -6v, 12, 18, v2, -6, v, 2, 3 v2 (1) v 2 , 4 4e 2 8e 4 2 8 e e 2 e2 (4) e , 2e2 4e , 2 2 2 2 p. 212 5( w 6) (5 w) (5 6) 1) a) m, 4, 4m+16 b) , 5w 30 c) 2) a) 3(3 x 1) 9 x 3 b) 2( x 2 3x 2) 2 x 2 6 x 4 3) a) 18r 12 b) 4b 2 2b 6 4) a) 4t2, 3, -24t2 + 18 b) (8)(3k 2 ) (8)(2k ) (8)(4) , 24k 2 16k (32) . 24k 2 16k 32 5) c) 6) a) h 2 5h b) a 2 3a 2 10 7 7 x 2 7 x 21 7 x2 x (3) , , , 7) a) 10z 2 , 15, , 3, (2) z 2 3 , 2 z 2 3 b) , 7 5 7 7 7 7 (1) x 2 1 x 3 , x 2 x 3 p. 214 1) a) b2 b) -c2 c) f2 d) –g2 2 2) a) 30 r 2 ,30r 2 b) 16 d 2 , 16d 2 c) 4 a (7) a, 4 (7) a a,(28) a2 , 28a d) (5) (9) v v,(45) v 2 , 45v 2 p. 216 1) a) 8, 8 b) -6m2+12m p. 217 1) a) 28, 35, 28, 35 b)-3s2+4s, -3, 4 c) (-9r)(4r)+(-9r)(-5) , -36r2+45r p. 218 12 14c 2 21c 14 c 2 21 c 9 b2 3 b 1) a) , -2, -2 a, -2a b) 9b2, 3b, , , , , 3 b+1 1, 3b+1 c) , , 6 7c 7c 7 c 7 c 3 b 3 b 2 c+(-3) 1, 2c-1 p. 218 - 219 (Practice) 1) a) (2 x)(2 x) 4 x 2 , b) (2 x)( x 3) 2 x 2 6 x 2) a) 2s2 + 8s b) -2t2+3t 3) a) 5r, -1, 20, -4, 20r2 – 4r b) (7s)(-3s) + (7s)(6), -21s2 + 42s c) (-6t)(t) + (-6t)(-3) , -6t2 + 18t 18 y 2 12 y 12v 2 2y 4v 18 y 2 12 y 12 v 2 15w2 28 x 2 2 y 2y 4 v 3w 7 x 2 2 2 18 y 12 y v d) (-8u(-6u)+(-8u)(7), 48u2 – 56u 4) a) 3 b) 15 w c) 28 x 5) a) 2 y 2 y 1 3 w 7 x 3 v 5 w 4 x 9 y 6 1 3v 5w 4x 9y 6 2 2 32 z 24 z 15n 21n 8 z 3n 2 32 z 24 z 15n 2 21n 8 z 8 z 3n 3n 2 2 32 z 24 z 15 n 21 n c) b) 8 z 8 z 3 n 3 n 4 z (3) 1 5 n (7) 1 4z 3 5 7 p. 220 Alphabet soup: 1) 2 x 2 6 x 2) 2 x 2 6 x 3) x 2 4) 7 x 4 5) x 2 3 x 5 6) 4 x 2 12 x 4 7) 6 x 3 8) 6 x 3 9) 0 10) 4 x 3 11) 4 x 3 12) 4 x 2 12 x 4 13) x 2 15) x 2 3 x 5 0) 7 x 4 C, D, P, R, T, O, U = Product p. 222 – 224 7d 8d 4 2 3e2 2e2 8e 11e 1) a) Binomial b) monomial c) trinomial d) binomial 3) a) b) d 2 5e2 3e 13 9 6h 7 h 2 h 2 c) 4 h 2h 2 2h 2 h 4 d) 9k 2 2k 2 15k 4k 8 3 11k 11k 5 2 4) a) 2x 2 and 5x are not like terms. They cannot be combined. 2 x 2 5 x cannot be simplified. b) Correct: 5s and 7s are like terms. To combine like terms, add 7r 11 2r 3 2 the coefficients. Since 5 7 2 , 5s 7s 2s . 5) a) e 6 b) 2 f 3 f 2 6) a) 7r 2r 11 3 5r 14 9 s 5s 16 s 9 s 14 2 6v 5 (13v 3) 2 b) 9 s 16 s 5s 9s 14 7) a) 3t 2 b) u 4u 1 8) a) 6v 5 13v 3 2 2 7 s 2 4 s 14 10 w2 7 (2 w 9 w2 5) b) 10 w2 7 2 w 9 w2 5 10 w 9 w 2 w 7 5 2 2 2 7v 8 9) a) 4(2 x 4) 8 x 16 b) 2(2 x 2 3x 1) 4 x 2 6 x 2 w2 2 w 12 27b 2 9b 36 16a 40 9 8 27b 2 9b 36 16a 40 2 8 8 9 9 9 ( 9)( 2 z ) ( 9)( 4 z ) ( 9)(5) 6(7 y 2 ) 6(1) 16 27 2 9 2 18 z 36 z ( 45) 10) a) b) 11) a) b) a ( 5) b b 4 9 9 8 42 y 2 6 18 z 2 36 z 45 2 2 a 5 (3) b 1 b 4 2a 5 3b 2 b 4 21k 2 7k 21 k 2 4 f (5 f 2) 3e(5e 2) 7 k ( 4 f )(5 f ) ( 4 f )(2) (3e)(5e) (3e)(2) k 12) a) 2c 2 10c b) 3d 2 12d 13) a) b) 14) a) 3 2 2 20 f (8 f ) 1 15e (6)e 3 k 20 f 2 8 f 15e 2 6e 3k 2 2 81m 45m 33n 36n 9 m 3n 2 81m 45m 33n 2 36n 3n 3n 9 m 9 m 2 2 33 n 36 n 81 m 45 m b) c) 3 n 3 n 9 m 9 m 11 n ( 12) 1 9 m 5 1 11n 12 9 m 5 p. 226 9 16 8 ( 5) 4 24 (8) 9 2 ( 5) 17 12 1) a) Multiply b) Divide c) Power d) Divide 2) a) b) 4 (3) c) 11 ( 5) 5 (7) 6 p. 227 6(2 y ) 3(b 2) 1) a) 3b 3(2) b) 6(2) 6( y ) 12 6 y 3b 6 p. 229 n 2 10 n 2 2 10 2 1) n 12 Check :12 2 10 p. 230 – 232 2(t 1) 12 2(t ) 2(1) 12 2t 2 12 1) a) First subtract 4, then divide by – 5 b) First subtract 2, then divide by 5 2) 2t 2 2 12 2 Substitute 2t 14 2t 14 2 2 t7 2(t 1) 2(7 1) t = 7 into the equation. Left side Right side = 12. Since left side = right side, t = 7 is correct. 2(6) 12 s 4 4 12 4 6 c 6 2 6 5 2 v 2 2 z 9 9 10 9 Practice: 1) a) b) c) d) s 8 c 4 7v z 1 n n 3 3 x 15 4 4 3x 3 x 15 n 12 2) a) 4 4(3) Left side = Right side = - 3, n = 12 is correct. b) Left side = 3(5) Right 3 3 4 4 15 n 12 3 x5 5k 6 6 24 6 5k 6 4 x 16 5k 30 5(6) 6 4 x 16 side = 15, x = 5 is correct. 3) 4) 5k 30 Left side Right side = 24, k = 6 is 4 4 30 6 5 5 x4 24 k 6 3 4 y 3 9 3 3 4y 4 y 12 3 4( 3) correct b) 4 y 12 Left side Right side = -9, y = - 3 is correct. 5) a) She divided by 3 3 12 4 4 9 y 3 3 x 6 15 3 x 6 6 15 6 3x 6 3(7) 6 instead of adding 6 first. b) 3 x 21 Left side Right side = 15, Since left = right, x = 7 is 21 6 3 x 21 15 3 3 x7 8 2 w 12 8 2w 8 2 w 8 12 8 8 2(2) correct. 6) a) 4 4 w w 12 b) c) Left side Right side = 12, Since the left 2w 4 8 4 w2 12 side equals the right side, w = 2 is correct. p. 233, p. 235 and p. 236 - 237 4b 2 2b 6 c 5 2c 4 4 m 6 6 2 6 4b 2 2b 2b 6 2b c 5 2c 2c 4 2 c 4 m 8 2b 2 6 3c 5 4 Check: 1) 4m 8 4 4 m 2 Check: 1) 2b 2 2 6 2 2b 4 2b 4 2 2 b2 Check: 1) 3c 5 5 4 5 3c 9 3c 9 3c 3 c3 x 5 4 20 x Check: 1) a) 4 4(5) Left side 4 Right side = 5; Since the left side equals the right side x = 20 is 4 5 x 20 2 7 x 7 5 4 4 4 4 4 4 4 4 2 7 5 correct. b) x 7 5 Left side Right side = ; Since the left side equals the right side, 4 4 x 77 57 5 x 2 4 x = - 2 is correct \ p. 238 – 239 y 4 4 2 y 4 3w 2 2 w 4 2 2 x 3x 2 3 x 3 x 2x 4 6x y 2 y 3w w 6 2 2 x 2 2x 4 2x 6x 2x y y 2 y y 3w w w 6 w 2 2 x 2 2 2 1) 4 4 x 2) a) 2 w 6 b) 2 x 4 c) 2 y 2 4 4x 2y 2 2w 6 2 x 4 4 4 2 2 2 2 2 2 x 1 y 1 w3 x 2 2 j j 8 4 j j 2 8 5 j 2 8 8 5 j 8 d) 10 5 j t 22 42 6 t 2 3) a) 6 Left side t 6 6(2) 6 t 12 t 2 6 12 2 Right side = 4, t=12 is correct 6 22 10 5 j 5 5 4 2 j w 5 5 25 15 5 5 5 w 3 b) 5 Left side 5 (3) Right side = 2, -15 4a)He forgot to write that -3 – 3 is -6 in the w 2 5 5( 3) 5 w 15 4c 3 3 c 3 3 4c c 6 4c c c 6 c second line b) 3c 6 Left side = 4(2) – 3 = 8 – 3 = 5 Right side = 2+3 = 5, 2 3c 6 3 3 c2 p.240 2 x 10 2 x 10 2(5) = 10, so the solution is correct 2 2 x5 b) y – 3 = 15; y – 3 + 3 = 15 + 3; y = 18; 18 – 3 = 15, so the solution is correct m 4c 20 6 x 6(3) 3. a) x + 7 – 7 = -2 – 7; x = -9 b) ; c = 5 c) 4 + 2 = y – 2 + 2; 6 = y d) 6 4 4 m 18 2(3) 2( p ) 4 3q 1 1 17 1 6 2 p 4 3q 18 4. a) 3q 18 3(6) – 1 = 17; the solution is correct b) 6 2 p 6 4 6 2(3 – 5) = -4; so the 2 p 10 3 3 q6 p 5 solution is correct. p.241 1. a) Divide by 3 b) Add 2 c) Add 3 d) Add 4 2a) 6 x 2 2 3x 5 2 3a a 4 6 x 3x 3 3a a a 4 a 5. 6, 2, 3, 5; 6 x 3 x 3 x 3 3 x 3x 3 x 1 h 3 2h 6a) 2a 4 Left side = 3(-2)– 2 = -8, Right side = -2 – 6 = -8; -2 2 a 4 2 2 a 2 h 2h 3 2h 2h b) 3h 3 3h 3 3 3 h 1 5a 6(10) 6 5a 60 Left side = 4 + (-1) = 3; Right side = 1 – 2(-1) = 3; -1 6x c) 5(12) Left side = 6 Right side = 10; 12 10 5a 60 5 5 a 12 p.242 1. a) < b) p.243 1. a) right, is b) Sample answers: 1, 2, 3 p.244 1. a) 0, 1, 4 b) -2, 0, 1 p.245 1. a) True b) False; 3 > -10 c) True d) True 2a) yes b) no c) no d) yes e) yes 3. b) i) 4, 5, 6 ii) 1, 0, -1 iii) -5, -4, 0 4a) s 100 b) n 12 c) p 70 d) n 10 5. i) x < 1 ii) x 0 iii) x > 1 iv) x 2 6a) x 6 b) x < -3 p.247 1. a) -3, -3, 4 – 3, p 1 b) -5 – 2 > 2 + a – 2; -7>a, or a < -7 p.248 3z 1 1 2 z 2 1 4 4x 4 6 5x 4 3z 2 z 3 4 x 2 5 x 1. a) b) 1a) Subtract 1 b) Add 3 c) Add 4 d) Subtract 1 3z 2 z 2 z 3 2 z 4 x 5 x.2 5 x 5 x z 3 x2 p 6 6 2 6 n 4 4 2 4 u 3 3 4 3 2. a) -5, -5, 5 b) 4, +4, 16 3a) b) c) p 8 n2 u 1 2 y 2 2 2 d) i) u 1 ii) n > 2 iii) y > -4 iv) p < -8 y 4 p.249 y 3 3 2 3 42 n22 33 t 33 2b2 52 4. a) i) ii) iii) or n 6 iv) or t 6 y 5 6 n, 6t b3 b) i) -5, -6, -7 ii) 0, 1, 2 iii) 4, 5, 6 iv) 8, 9, 10 c) i) -4 ii) 3 iii) 7 iv) 5 6 a 2 2 5a 1 2 5. a) 4v 6 6 3v 3 6 6 a 5a 1 b) 6 a 5a 5a 1 5a a 1 p.252 4v 3v 3 4v 3v 3v 3 3v v3 1. a) Reverse b) Do not reverse c) Reverse 2 m 8 2a) 2 2 m 4 2m 8 b) 2 2 m4 y (2) ( 2)3 c) 2 y 6 p.253 2 f 5 5(4) 5 2 f 20 1. 1a) i) No ii) Yes iii) Yes iv) No b) i) 8 > -24 ii) -1 < 3 2 f 20 2 2 f 10 3. a) i) Divide by 3 ii) Divide by -4 iii) Divide by -3 iv) Multiply by -2 p.254 3 y 15 4 p 8 q 3x 9 (2) (2)(5) b)i) No ii) Yes iii) Yes iv) Yes c) i) 3 3 ii) 4 4 iii) 3 3 iv) 2 p2 y 5 x3 q 10 5w 11 4 1 8 p 5w 5 2 2 3 2 5 6 6(3) 5 8 3 2r 3 9 3 6 p 5w 4. a) 2r 6 b) 5 c) s 18 d) 8 x 5(8) 5 8 s 18 r 3 p 25 5w 40 5w 40 5 5 w8 p. 257 g 5 5 2 5 f 66 36 1. a) f 3 Check : 3 6 3 3 b) g 3 Check : 3 5 2 3 5h 25 5 5 c) h 5 2 k 6 2 2 d) k 3 Check : 5(5) 25 Check : 2( 3) 6 5 3 4x 2 2 6 2 2 3c 2 7 2 2v 3 3 9 3 4x 8 3c 9 2v 6 2) a) 4 x 8 4 4 x2 4x 2 Left Side: 4(2) 2 6 Right Side = 6 2 is correct (2)(2) (2)( w) 20 4 2 w 20 4 2 w 4 20 4 d) 2 w 16 2 w 16 2 2 w8 2(2 w) b) 3c 9 3 3 c3 2 3c Left side: 2 3(3) c) 2v 6 2 2 v 3 2v 3 Left side: 2(3) 3 7 9 Right Side = -7 Right Side = -9 3 is correct -3 is correct 2a 3 3a 2 3 x x 3 2a 3a 3 3a 2 3a 3 x 3 x 3 3 5a 3 2 x x 6 3) a) 5a 3 3 2 3 b) x x x 6 x 5a 5 2 x 6 5a 5 2 x 6 5 5 2 2 x 3 a 1 Left Side: 2(2 8) 20 Right Side = -20 8 is correct 9 2w w w 6 w 9 3w 6 9 3w 9 6 9 4) a) 3w 15 3w 15 3 3 w5 e6e 6ee 3n 1 n 3 n n m 2 3m 3m 4 3m 2e 6 6 2n 1 3 2m 2 4 2e 6 6 6 6 2n 1 1 3 1 2m 2 2 4 2 b) 2e 12 c) 2n 2 d) 2e 12 2n 2 3 2 2 2 n 1 e6 2x 4 4 24 3 2(3) s 4 2x 6 6 76 3 2 2 2 6 3 42 2 s 2x 1 5) a) 2 , 7 b) 3 6) a) 0,1,2 3(2) , 2 3 s 7 2 2 2(1) 2 x 6 2 2 3 2 x 6 s2 2 2 x 3 2m 6 2m 6 2 2 m 3 b) 0, -1, -2 c) -1,0,1 d) 5,4,3 4 j 1 1 2 j 3 1 7) a 0 b) s > 2 8) a) d 66 46 d 10 2 f 1 1 3 1 4j 2j4 2 f 4 4j 2j 2j 42j b) 2 f 4 2 2 f 2 9) a) 2 j 4 2j 4 2 2 j2 k 22 2k 2 k 4k k k 4k k b) 2k 4 2k 4 2 2 k2 10) a) Do not reverse b) Reverse c) Reverse d) Do not reverse 3b 4 4 5 4 c 3b 9 2 x 4 v 2 z 4 2 (2)(4) d) 2 2(4) 12) a) 11) a) 2 b) c) 2 2 2 2 3b 9 2 x 2 v 8 z 2 c 8 3 3 b3 5 m 3 3 m 3 x 2 2 1 2 n 2 2 2n 2 2 8 m m 2 n 2n 4 x 8 m m m m 1 b) n 2n 2n 4 2n c) 8 2m d) 2 n 4 x 8 2m (2) (2)(1) 2 n4 2 2 x2 4 m p. 262 1) a) 100, 100cm, 700cm b) 0.1 cm, 21(0.1)cm, 2.1 cm 2) a) 0.01, 0.01m, 3.46m b) 0.001m, 1800(0.001m) , 1.8m 3)a) 10, 10mm, 65mm b) 1000mm, 3.8(1000mm), 3800mm p. 263 33mm 4.5cm 1) a) 3.3, 33, , 5.5, 5.5 b) 4.5cm, 1.5cm, , 3, 3 6mm 1.5cm p. 265 (Check) a) 15 cm, 15 cm, 60 cm, 10 cm, 10 cm, 40 cm, 40 cm by 60 cm 13 13 4 3.25 , 15cm, 3.25 10cm, 32.5, 32.5cm by 48.75cm b) 4 Practice 27 mm 15mm 1. a) 2.7cm, 27mm; , 3; 3 b) 1.5cm, 15mm; , 2.5; 2.5 9mm 6mm p.266 4.5cm 2. 3cm, 4.5cm; ; 1.5; 1.5 3cm 7 7 4 =1.75; 4cm;1.75 4cm, 7cm; 7cm 4 4. 3cm, 4cm, 5cm; 2.75; 2.75 3cm=8.25cm; 2.75 4cm=11cm; 2.75 5cm=13.75cm The side lengths of the enlargement are 8.25cm, 11cm, and 13.75cm. p. 267 1.6cm 1. a) Length=3.2cm; Length=1.6cm; =0.5;0.5 3.2cm p. 268 1.5cm b) 6cm; 1.5cm; ; 0.25; 0.25 6cm Check 1. 0.05; 104cm; 0.05 104cm=5.2cm; 89cm;0.05 89cm=4.45cm; 5.2cm by 4.45cm 1 2. =0.02; 10m; 0.02 10m=0.2m; 0.2m=0.2(100cm)=20cm; 50 5m;0.02 5=0.1m;0.1m=0.1(100cm)=10cm; 20cm by 10cm Practice 0.5cm 1.2cm 1.a) 2.5cm;0.5cm; ;0.2;0.2 b) 4.8cm; 1.2cm; ;0.25;0.25 2.5cm 4.8cm 3 0.15 ; 36cm; 0.15 36cm, 5.4cm 2. 20 3 3. a) 170cm; 0.04 170cm=6.8cm b) =0.06; 4m; 0.06 4m, 0.24m; 0.24m=0.24 100cm=24cm 50 1 4. 3cm, 4cm,5cm; 0.25 ; 0.25 3cm=0.75cm; 0.25 4cm=1cm; 0.25 5cm=1.25cm 4 The side lengths of the reduction are 0.75cm,1cm, and 1.25cm. p. 271 1. a) Polygon b) Non-polygon c) Non-polygon d) Polygon e) Non-Polygon f) Polygon p. 273 LengthofAB 5.0cm LengthofBC 2.5cm 1. 90 ; equal; AB, EF, BC, FG; 0.625 ; 0.5 LengthofEF 8.0cm LengthofFG 5.0cm Are not; Are not; Are not 2. E 135 ; F 45 ; P G 135 ; Q H 45 ; are LengthofMN 2.25cm LengthofNp 1.5cm MN, EF, NP, FG; 0.75 ; 0.75 ; are; are; are LengthofEF 3.0cm LengthofFG 2.0cm p. 275 3.6cm 1.5 ; 1.5; DE=1.8cm; 1.5; 1.5 1.8cm=2.7cm; 2.7cm 1. CD=2.4cm and HJ=3.6cm; 2.4cm Lengt hom Re duction 1.8cm 2. Reduction; WX = 1.8cm and ST =3cm; 0.6 ; 0.6; UV=2cm; 0.6; Lengthonoriginal 3cm 0.6 2cm=12.cm; 1.2cm. p. 276 1, E =100 ; F 100 ; C G 60 ; D H 100 ; are LengthofAB 2cm LengthofBC 3cm EF; FG; 1.25 ; 1.25 ; are; are; are LenfthofEF 1.6cm LengthofFG 2.4cm LengthofAB 4.5m LengthofBC 3.2m 2. 90 ; equal; 1.6 ; 1.6 ; are; are; are/ lengthofEF 3m LengthofFG 2m 3. a) 4cm; 4cm, 10cm; 10cm b) LengthofAb 4.8m LengthofBC 3.2m 0.8 ; 1.28 ; are not; are not; are not LengthofJK 6m LengthofKL 2.5m is similar; is not similar; is not similar 2.1cm 1.5 ; 1.5; 4.5cm; 1.5; 1.5 3.4cm=5.1cm; 5.1cm 3. LM=1.4cm and ST=2.1cm; 1.4cm p. 278 1. a) 50 -60 =70 b) 180 -65 -65 =50 2. 70 =110 ; 110 , 55 p. 280 1. a) 36 -68 =76 ; P 76 ; Q 68 ; R 36 ; are; are; PQR LengthofEF 2.8cm LengthofDE 3.2cm b) EF, DE, FD; JK, KL, LJ; 2; 2; LengthofJK 1.4cm LengthofKl 1.6cm LengthofFJ 5.4cm 2 ; the same, are smiliar; D and L; E and K; F and J; LKJ LengthofLJ 2.7cm p. 282 2cm 0.2 ; 0.2; 20cm; 0.2; 1. X , V , W ;XVW; XVW , FGH ; FH=10cm and XW=2cm; 10cm 0.2 20cm=4cm; 4cm. p. 283 1. a) 110 -40 =30 ; U 30 ; T 40 ; S 110 ; are; are; UTS LengthofJK 3.3cm LengthofKL 4.8cm b) JK, KL, LJ; QR, SQ, RS; 1.5 ; 1.5 ; LengthofQR 2.2cm LengthofSQ 3.2cm LengthofLJ 5.7cm 1.5 ; the same; are similar; J and R; K and Q; L and S; RQS LengthofRS 3.8cm LengthofQR 6cm LengthofRP 8cm 2. QR, RP, PQ; CD, DC, BC; 3; 2; LengthofCD 2cm LengthofDB 4cm LengthofPQ 12cm 2.4 ; different, are not similar. LengthofBC 5cm 2cm 0.4 ; 0.4; FG; FG, 4cm; 0.4; 3. G, H F ; GHF; CDE , GHF ; DE=2cm and GF=5cm; 5cm 0.4 4cm=1.6cm; 1.6cm 3.6m 1.8 ; 3m, 1.8; 1.8 3m=5.4m; 5.4m 4. equal; XYZ; enlargement; ZX=3.6m and CA=2m; 2m 5. 1.8, 3.0; A, D, E ; ADE; ADE , ABC ; AD=1.8cm and AB=3.0cm 1.8cm 0.6 ;0.6;DE and BC; BC, 4.0cm; 0.6; 0.6 4.0cm=2.4cm; 2.4cm 3.0cm p. 286 15mm 2.5 ; 2.5 1. 1.5, 15; 6mm 2. 7cm; 7cm, 22.4cm; 5cm; 3.2,5cm,16cm; 16cm by 22.4cm 2.7cm 0.75 ;0.75 3. 3.6cm; 2.7cm; 3.6cm p. 287 4. 0.14; 100cm; 0.14, 100cm, 14cm; 14cm 5. Reduction; DE=4.0cm and HJ=2.0cm; Lengthon Re duction 2.0cm 0.5 ; 0.5; CD; CD,3.2cm; 0.5; Lengthonoriginal 4.0cm 0.5 3.2cm=1.6cm; 1.6cm p. 288 6. KL, MK, LM; QN, PQ, NP; LengthofKl 3.6cm LengthofMK 4.0cm 0.8 ; 0.8 ; LengthofQN 4.5cm LengthofPQ 5.0cm LengthofLM 6.8cm 0.8 ; the same, are similar; K, Q; L, N; M, P; QNP LengthofNP 8.5cm 6.0m 2.4 ; 2.4; RT; RT, 2.0m, 2.4; 2.4 2.0m=4.8m 7. equal; VUW; VUW; RST; ST=2.5m; UW=6.0m; 2.5m 4.8m p. 289 1. a) 1 b) 4 c) 2 d) 0 p. 290 1. a) Yes b) No p. 291 1. a) Yes; Yes; Yes b) Yes; Yes; No p. 293 1. left; vertical; is not; below; horizontal; is p. 294 1. Point E reflects onto itself; Point F’ is 2 squares right of line of reflection; 1 square left of line of reflection; Point G’ is 1 square right of line of reflection; on the line of reflection; Point H reflects onto itself. p. 295 2. a) Hexagon 1: above; horizontal; is Hexagon 2: above, right; diagonal; is not Hexagon 3: right; vertical; is 3. a) Point Image A(0,5) B(2,5) B(2,5) B(2,5) C(3,3) C’(3,7) D(2,1) D’(2,9) b) Point Image E(3,5) E(3,5) F(5,5) F’(1,5) G(5,4) G’(1,4) H(4,3) H’(2,3) J(6,1) J’(0,1) K(3,1) K(3,1) c) Point Image P(1,3) P(1,3) Q(3,3) Q’(1,1) R(3,1) R(3,1) p. 297 1. a) 180 b) 90 counterclockwise p. 299 1. a) 4; 4 p. 300 1. a) 2; 2; b) 3; 3 360 ; 180 ; 180 2 b) 3; 3; 360 ; 120 ; 120 3 p. 302 1. a) 4; 4 b) 5; 5 2. a) 4; 4; 90 ; 90 b) 5; 5; 72 ; 72 3. I have to rotate a tracing of the shape a complete turn before it matches the shape again. So, the shape does not have rotational symmetry. p.303 4. 10; 10 p. 304 1. a) 3 squares left and 1 square down b) 3 squares right and 2 squares up p. 306 1. a) Yes; horizontal; Yes; No; off; Yes; Yes b) Yes; No; No; No; off; No; No p. 307 1. Point Image W(6,5) W’(6,3) X(5,4) X”(5,2) Y(3,4) Y’(3,2) Z(2,5) Z’(2,3) The shape has 2 lines of symmetry. The shape has rotational symmetry. p. 308 2. Point Image P(1,5) P’(5,5) Q(3,5) Q(3,5) R(3,1) R(3,1) S(2,1) S’(4,1) T(2,4) T’(2,4) U(1,4) U’(5,4) The shape has 1 line of symmetry. No, there isn’t a point about which you can turn the tracing. No, the shape doesn’t have rotational symmetry. p. 309 - 310 1. Polygons A and B and polygons A and D; Polygons A and B and polygons A and D 2. Rectangle F; Rectangle H; Rectangles E and F and rectangles G and H. 3. a) No, the triangles don’t face opposite ways. No, the triangles aren’t related by a reflection. Yes, the triangles touch. So, try a point of rotation ON the triangles. Vertex M; After triangle LMN is rotated 90 o counterclockwise about M. Yes, the triangles are related by a rotation. b) Yes, the triangles face opposite ways. One triangle is above the other, so try a HORIZONTAL line of reflection. Yes, the triangles are related by reflection. No, the triangles don’t touch. So, try a point of rotation OFF the triangles. No, the triangles don’t match. No, the triangles aren’t related by a rotation. 4. Point Image P(1,5) P’(5,1) Q(2,5) Q’(4,1) R(3,4) S(3,2) S(3,2) R(3,4) T(1,2) T’(5,4) There is no line on which I can place a Mira so one polygon matches the other. So, the shape does not have line symmetry. Yes, the shape has rotational symmetry. p. 311 Yes, the logo has rotational symmetry of order 2 about its centre, (6,5). The logo has 2 lines of symmetry: - The horizontal line through 5 on the y –axis and the vertical line through 6 on the x-axis p. 313 1. 3.5; 6cm; 3.5 6cm 21cm ; 4cm; 3.5 4cm 14cm ; 14cm by 21cm. 2. Original=5.0cm; Reduction= 1.5cm 0.3 ; The scale factor is 0.3 3. Matching angles: A E 120 ; B F 60 ; 1.5cm; 5.0cm C G 120 ; D H 60 ; All matching angles are equal; Matching sides: AB and EF, and BC lengthAB 2.2cm LengthBC 1.4cm and FG; 0.4 ; 0.4 ; The scale factors ARE equal so, the LengthEF 5.5cm LengthFG 3.5cm parallelograms ARE similar. p. 314 lengthBC 4cm lengthCA 6cm lengthAB 7cm 4. BC, CA, AB; GE, EF, FG; 1.6 ; 1.5 ; 1.4 ; All lengthGE 2.5cm lengthEF 4cm lengthFG 5cm scale factors are DIFFERENT, so the triangles ARE NOT SIMILAR. 5. JKL is a reduction of EFG ; 12cm 0.8 ; The scale factor is 0.8; Length of EF=20cm; Scale factor =0.8; EG=15cm and JL = 12cm; 15cm Length of JK = 0.8 20cm 16cm so JK has a length of 16cm. p. 315 7. Point Image P(3,5) P(3,5) Q(4,5) Q’(2,5) R(4,4) R’(2,4) S(5,4) S’(1,4) T(5,2) T’(1,2) U(3,2) U(3,2) 8. The shape and its image match 4 times. So the shape has rotational symmetry of order 4. Angle of rotation 360 90 symmetry is: 360 4 p. 316 10. Yes, the polygons face opposite ways. Yes, the polygons are related by a reflection. No, the polygons don’t touch. Try a point of rotation OFF the polygons. Yes, the polygons are related by a rotation. 11. b) The shape has 2 lines of symmetry and rotational symmetry. p. 318 x 2 5.0 2 3.0 2 1. a) x 180 50 60 70 b) x 5.0 2 3.0 2 x is about 5.8cm x 5.8 p. 319 OBC 90 1. x 180 90 65 25 p. 320 OST 90 OT 2 OS 2 ST 2 162 r 2 122 1. 256 r 2 144 r 2 256 144 OS is about 10.6cm long. r 2 112 r 112 r 10.6 p. 321 1. a) OE, OF, OJ b) CD, HG c) E, F d) OEC, OED, OFG, OFH 2. a) OBP = 90 b) PQO OTM 90 OTW 90 = 90 ; PRO = 90 3. a) b) x 180 90 25 65 x 180 90 35 55 p. 322 OCT 90 OPQ 90 12 2 x 2 102 x 2 152 152 2 2 2 x 4 6 144 x 2 100 x 2 225 225 2 x 16 36 4. a) x 2 144 100 OC is about 6.6 km. b) 2 OQ is about 7.2 cm c) x 2 450 OP is about x 52 x 2 44 x 450 x 52 x 21.2 x 44 x 7.2 x 6.6 21.2 cm p. 324 OC AB OC AB 1. x 90 2. x 90 Since OA=OB, AOB is isosceles and y 180 90 40 50 y 180 90 55 35 OAB OBA so z =55 p. 326 Check 132 52 a 2 169 25 a 2 1. a 2 169 25 a 144 2 So, a = 12 cm; EG=FG so b = 12cm a 144 a 12 Practice 1. a) Radii: OA, OB, OC, OD; Chords: AB, AC, BD, CD; Diameters: AC, BD b) Radii: ON, OP, OQ, OR, OS; Chords: NS, PQ, RS; Diameters: NS, PQ p. 327 2. a) AC = CB = 4cm so a = 4cm b) MN = 2 PN = 2 3cm = 6cm so a = 6cm 1 1 c) OL KL 18cm 9cm so a = 9 cm d) OS = OT = 1.5cm so a = 1.5cm 2 2 p. 328 OPQ OQP x 90 3. a) b) OP = OQ OPQ is isosceles. so, x 35 y 180 45 90 45 y 180 35 35 110 OB 2 OD 2 DB 2 152 12 2 DB 2 4. 225 144 DB 2 DB 2 225 144 So, DB = 9cm; CD = DB = 0cm by chord properties. So chord BC has a length of DB 2 81 DB 81 OA2 AN 2 ON 2 17 2 152 ON 2 289 225 ON 2 1 1 2 9cm 18cm 5. AN AB 30cm 15cm ; ON 2 289 225 So, On is 8 cm 2 2 ON 2 64 ON 64 ON 8 p. 329 p 90 OAB 90 1. a) OGM b) OME and ONE 2. a) q 180 75 90 b) s 180 21 90 q 15 s 69 p. 330 a 2 20 2 252 a 2 400 625 3. a) OPQ 90 OQ is the hypotenuse of triangle OPQ a 2 1025 b) OBC 90 OB is a leg of a 1025 so, a 20 b 15 2 2 32.0cm 2 400 b 2 225 triangle OBC b 2 400 225 b 2 175 MN 2 ML 4. a) OX = OY; OXY is isosceles so b 35 b) MN 2 6cm MN 12cm so, d 12cm b 175 so, x 13.2cm p. 331 x 90 OBA OAB 5. OA = OB, so triangle OAB is isosceles. y 180 65 90 25 so, z 25 OQ 2 QP 2 OP 2 102 82 OP 2 100 64 OP 2 1 1 6. QP QR 16cm 8cm ; OP 2 100 64 2 2 OP 2 36 The length of OP is 6cm. OP 36 OP 6 p. 334 1 ACB AOB ADB ACB 2 1. a) x 2 25 50 b) c) 2. a) 1 x 28 x 62 31 2 QOP 2 QSP x 2 30 60 QTP QSP y 30 1 ACB AOB 2 1 b) x 70 35 2 ADB ACB y 35 p. 336 – 337 1. a) COB b) AOD, ACD c) DAC d) DAC 2. a) Central: AOB , Inscribed: ACB b) Central: 1 TSR TOR DEG DFG 2 QOR , Inscribed: QPR 3. a) x 2 28 56 b) c) d) x 90 1 x 72 x 84 42 2 4. a) x 34 y 34 b) x 2 15 30 y 15 ACB 90 AOB 2 ACB 5. x 180 90 25 65 6. OA=OB so triangle x 2 50 100 y 2 65 130 y z y y 180 100 OAB is isosceles. In triangle OAB 2 y 80 80 2 y 40, z 40 y p. 340 OHG 90 152 x 2 132 1. a) x 90 y 180 90 20 70 b) 225 x 2 169 ONM 90 x 180 90 75 15 2. a) x 2 225 169 b) x 2 56 x 2 144 16 x 2 160 x 12.6cm 7.5cm p. 341 x 90 y 180 25 90 3. 4. x 90 OM=ON so triangle OMN is isosceles. y 180 115 y 65 1 1 XY XZ 12cm 6cm 2 2 2 2 OX OY XY 2 x 2 12 2 4 2 x 160 x 56 x OST 90 ONP OMP y 27 z 180 27 90 z 63 OX 2 22 62 5. OX 2 4 36 OX 2 40 OX 40 OX p. 342 6. a) 6.3 x 2 14 x 28 x y 90 b) x 43 c) x 90 7. a) w w 180 90 2w 90 ACD is isocsceles; 90 2 w 45 w x 25 y 35 b) x 2 35 70 y 35 8. z 180 25 90 z 180 115 z 65 ; p. 344 35 2 2 20 40 3 3 5 15 17 35% b) 40% c) 15% 2. a) 0.17 1. a) 100 5 5 20 100 20 20 5 100 100 13 3 27 25 25 25 1 13 50 0.26 c) 3 8 0.375 3. a) 27% b) b) 25% 50 8 100 100 100 25 4 70 70 10 7 c) 70% 100 100 10 10 p. 345 1. a) The outcomes are: red, green, purple, yellow. The favourable outcome is GREEN. There are 2 green 2 1 , or marbles. Theoretical probability = Number of green marbles total number of marbles. 20 10 0.1, or10% b) The favourable outcomes are: green, purple, and yellow. Number of favourable outcomes: 2 + 5+ 4 = 11 There are 11 favorable outcomes. Theoretical probability = number of favourable outcomes total number 11 of marbles. 20 0.55, or 55% p.346 11 43 7 1. a) = 0.44, or 44% b) blue or green, , 0.28, or 28% 25 25 25 p. 347 1. a) Felix made his prediction based on the results of a survey or experiment. Explain your thinking: Felix’s prediction is based on the results of a survey (experiment) conducted at school. So, his decision is based on experimental probability. b) Natalie made her prediction based on theoretical probability. Explain your thinking: natalie’s decision Is based on the theoretical probability of rolling double ones 1 since this probability is very small, , Natalie predicts she will lose the game. 36 p. 349 1. a) No; Yes; No; People listen to their dentist’s suggestions, The cost of the toothpaste does not matter, both toothpastes are readily available for purchase. b) Great; a few; less; most 2. a) Salima is not injured; the opposing team has the same ability as the last 5 teams b) higher, injured, lower, the opposing team commits a lot of fouls. p. 350 1. a) Josh made his decision based on theoretical probability. Explain your thinking: Josh knows that 50% of the marbles in the bag are red. He found this probability without conducting an experiment or a survey. So, Josh based his decision on theoretical probability. b) The manufacturer made the decision based on the results of an experiment. Explain your thinking: The manufacturer based its decision on the results of the experiment done by the quality control officer. So, the decision is based on experimental probability. c) Desi made his decision based on personal thoughts or feelings. Explain your thinking: Desi’s decision is based on his feelings. He chooses the grean envelelope because green is his favourite colour. So, Desi’s decision is based on subjective judgement. p. 351 2. a) Lin will prepare for the tes like she did for the other tests, the test will have the same level of difficulty as the others. b) all tunnels on the road have the same height as the first tunnel. c) all team members are healthy, the opposing team is less able than the Tigers. 3. a)i) the same students always buy a drink, the student’s drink preference does not change. The amount of water sold does not depend on the outside temperature. ii) students vary the drinks they buy, the outside temperature decreases; more students buy a drink on any given day, the outside temperature increases b)i) there are fewer cars on the road, the weather is ideal for driving, there will be no accidents or road closures. ii) If there are more cars on the road, or if the weather is bad, or if there is an accident or construction on his route, Marcel may be late for work. p. 352 1. a) Yes, is, What is your favourite type of TV program: Comedy_____Drama______News_____Sports____Other_____? b) No, is not, not needed c) Yes, is, what is your favourite dessert: Pie____Cheesecake____Ice Cream____Fruits_____Other____? p. 354 1. a) No, No, Yes, Explain your thinking: Easter is not celebrated by all cultures and not everybody eats chocolate. So, the survey does not apply to every student. How would you avoid the problems: I would add 2 opening questions. “Do you celebrate Easter? Do you eat chocolate Easter bunnies?” If a student does not answer yes to both questions, the third question need not be answered. b) No, Yes, No, Explain your thinking: The timing of the survey question could be a problem. Most people use sunscreen in the summer. They may not remember much about their sunscreen in January. How would you avoid the problem? I would ask the question in the summer when most people are using sunscreen regularly. p. 355 1. Yes, Yes, No; Explain: The theatre will have to pay for 2 stamps and 2 envelopes for each survey. This may be beyong what a local theatre can afford. The time that it will take to print, Mail, and collect the surveys may be too long. 2. Yes, Yes, No; explain: the survey is too long. Most people won’t have time to spend 30 min on a survey. The timing is wrong. Most people will still be unhappy with the government for raising the taxes. p.356 1. a) Yes, No, No; Explain your thinking: The use of language is a problem. The question is biased. The question is worded in such a way that you are to believe that it is cruel no9t to walk a dog daily. This wording will influence a person’s answer. b) No, No, Yes; Explain your thinking: The survey is insensitive to those students who don’t eat meat, either because they are vegetarians or for religious reasons. Also, some students may not buy lunch in the cafeteria. c) No, Yes; Explain your thinking: The tutor is asking the students to share personal information. Many students, especially those struggling in French, might feel uncomfortable or embarrassed sharing their marks. p. 357 2. a) I would ask a better question: How often do you think a dog should be walked: Less than once a day____More than twice a day___Not at all_____? b) I would add 2 opening questions. “Do you sometimes buy lunch in the cafeteria? Do you eat meat?” If a student does not answer yes to both questions, the survey need not be completed. c) I would suggest the tutor survey the teachers to find out which students might need her help. This way the students will not feel uncomfortable. 3. a) Yes, No, No; Explain: It will take a lot of time and money to survey 10000 people by phone. And the survey is too long. Most people will not have 25 min to complete the survey. b) Yes, No, No; Explain: The timing of the survey could be problematic. Since the school’s volleyball team just won the championship, there is probably a lot of interest and excitement in the wschool for volleyball. This may influence a student’s answer. 4. a) I would insert a notice in each subsciber’s monthly bill asking them to complete a short on-line survey on customer satisfaction.l b) I would poll the students at the beginning of the school year, before sports have started and before any championships have been won. p. 358 1. a) The population is those people who eat at the restaurant regularluy. They will have tried many different entrees. b) The population is all teachers in the school. c) The population is those people in Vancouver who drive a vehicle regularly. p. 359 1. yes, yes, sample 2. no, no, census 3. yes, yes, sample p. 360 1. All residents of British Columbia, no, a sample, no. no 2. All people boarding planes at the Edmonton International Airport, yes, a census 3. All customers of the café, No, a sample, yes, One in 5, or 20% of the customer were surveyed and the sample probably include all types of customers. So, the conclusions would probably be valid. p. 361 1. a) The population is all apartments in the building. b) The population is all teenagers who live in Grande Prairie. c) The population is all thermostats manufactured by the company. 2. a) A sample was used because it would take too logn and cost too much to survey every household in Canada. b) A sample was used because if every item of clothin was washed, there would be no clothing left to sell. p. 362 3. a) A census was used because the information is important and it is used to make important decisions on matters such as healthy care, education, and transportation. b) a census was used because the number of curren Grade 9 students is not too large, and the information will be used to determine the number of classes that will be needed to accommodate all interested students. 4. a) No, No, census b) yes, Yes, sample 5. a) No, No b) Neil looks at 1 of every 4 vehicles, or 235% of the vehicles. The sample probably includes all types of vehicles. So, the conclusions would probably be valid. p. 363 1. Peyton made his decision based on his personal thoughts of feelings. Explain your thinking: Peyton’s decision is based on his feelings. He chose the 17th of the month because 17 is his lucky number. So, peyton’s decision is based on subjective judgement. 2. a) the outside temperature is about the same as it was last week, the caretaker does not adjust the temperature in side the classroom, Lord is as healthy as she was last week b) the caretake turns on the air conditioner because it is hot outside, Lord is not feeling well; the caretaker turns up the heat, the outside temperature increases and the air condition is not turned on. p. 364 3. a) Yes, Yes, Explain your thinking: The timing of the survey could be a problem. Back to school shopping is usually done in August and September. And Victoria Day is in May. Also, customers are being asked to share personal information. They may not feel comfortable telling stranger hos much money they spend. b) The survey could be conducted in late September after families have done their back to school shopoping. The survey could be anonymous with the possible choicese given in rangers. 4. all residents of West Vancouver, yes. Yes. Sample 5. The coach did not survey the goalies or the forwards. These players may use a different type of stick. So, I don’t think the conclusions would be valid. It wouild not take very long to survey all the palyers. I think a census should have been used. p.366 1. a) no, no, yes convenience sampling b) yes, no, systematic sampling c) no, yes, no, self-selected sampling p. 367 1. yes, no, no, yes, yes, Method B 2. Yes, yes, yes, no, no, Method A p. 368 1. Self-selected sampling, no, Why? Only people who go to pet stores will respond. Each member of the population does not have an equal chance of being surveyed. People who go to pet stores have pets or are animal lovers. The opinions of those people who do not have pets are equally important. 2. Systematic sampling, no, no, no p. 369 1. a) The population is divided into groups. Every member in one group is surveyed. So, the method is cluster sampling. b) Each member of the population has an equal chance of being selected. So, the method is simple random sampling. c) Only shoppers in the mall who walk by the researcher are selected. These are the shoppers who are convenient. So, the method is convenience sampling. 2. a) The librarian divided the school population into groups but she surveyed the wrong group. The books students would like to read are not necessarily what the English teachers recommend. The students should be surveyed. b) Only residents of Regina who listen to that radiop station will complete the survey. The listeners must also have access to the internet. This sample will not represent all Canadians. 3. a) no, no, yes, no, Method B b) The residents of the apartment building, no, yes, Method B 4. a) Cluster sampling, no, Why? Students on the honor roll probably have better study habits than many of the other students in the school. The sample will not be representativeo f all students in the school. b) Systematic sampling, yes, Why? One of every 4 people or 25% of the people who order toast are surveyed. The sample probably included people of different ages, genders, and ethnic background. So, the sample is probably representative of the patrons of the restaurant. p. 371 Step 1: CBC Radio, The Vibe 98.5FM, The eagle 100.9, AM 770; Other__None__ Write a question: What is your favourite radio station: CBC radio___ The Vibe 98.5 FM _____The Eagle 100.9____AM770______None_____? Yes, no, yes Step 2: All the students in the school, yes, a sample, no, no, yes, yes, method B Step 3: I will get permission to hand out the survey at the beginning of homeroom. It won‘t take long for students to complete the survey, so the teacher could collect them at the end of class. Step 4: The Vibe 98.5FM, It has the most tally marks, The favourite tradio station is represented by the tallest bar. p. 376 1. Craig made his prediction based on the results of a survey or experiment. Explain your thinking: Craig’s prediction is based on past experience. Craig has seen his hamster run on the wheel at 3:00pm on each of the last four days. So, the prediction is based on experimental probability. 2. The voters are still satisfied with the mayor’s performance; the other candidates have the same popularity as the candidates in the other elections. 3. a) No, Yes, No, Explain your thinking: Course-selection forms are handed out in February. Students will nto know in September if they will need help in Febraruy. b) The survey should be done in Febraruy, when students have received the forms. 4. a) no, Yes, no, The students are being asked to share personal information. This may make the students uncomfortable. b) The company could enclose an anonymous survey with each pay cheque that could be dropped into a box when completed. 5. a) yes, yes, sample b) yes, yes, yes, census 6. no, no 7. a) The population is divided into groups. Some members from each group are selected. So, the method is stratified random sampling. b) Only people who walk in front of the researcher are selected. These are the people who are convenient. So, the method is convenience sampling. 8. Every 5th person was surveyed. This is systematic sampling. People entering a Ford dealership are more likely to drive American-made cars. Most people who drive imports would not go to a Ford dealership. The sample is not representativeo f the population. So, the conclusions would not be valid. 9. yes, Families with young children, yes, no, yes, yes, Method B.