ANSWERS TO WARM-UPS AND PROBLEMS
Chapter 1 Basic Concepts and Properties
Worksheet 1 (1.1)
Warm-ups
1.(a) a + b (b) c/d or c  d (c) xy, xy, (x)(y), x(y), or (x)y 2.(a) {x, y, z}
(b) {the months of the year beginning with the letter M} (c) {xx is an even counting
number} (d)  (e) yes 3.(a) Reals, rationals (b) Reals, rationals, integers, nonpositive
integers, negative integers (c) no 4.(a) x + y (b) 15 (c) x = a 5.(a) 12, 6, 11, 6, [5] (b) 6, 3,
6, [9] (c) 20, 12, 5, 2, 4, 2, [2]
Problems
1. c - x 2. 5z, 5z, (5)(z), 5(z), or (5)z 3. {a, b, c} 4. {xx is a counting number divisible by
3} 5. yes 6. no 7. yes 8. Reals, rationals 9. y = x 10. x = y 11. 13 12. 6 13. 13 14. 2
Worksheet 2 (1.2)
Warm-ups
1.(a) 12 (b) -x (c) < 2.(a) 16 (b) 20 (c) 0 (d) -9 3.(a) 18 (b) 5, 13, [-18] (c) 15, 3, [12]
(d) 30, 17, [-13] (e) -14 (f) 0 4.(a) -5 (b) -9 (c) 3 (d) -19 (e) 4, 12, 17, [14] 5.(a) 10, 3,
[30] (b) 5, 7, [-35] (c) 0 6.(a) 20, 5, [4] (b) 42, 3, [-14] (c) 15, 5, [-3]
(d) 0 7.(a) 15, -12, -17, -12, [-5] (b) -11, -22, +66, [71]
Problems
1. 25 2. -5 3. > 4. -31 5. 10 6. 5 7. 8 8. -13 9. 1½ 10. -24 11. 0 12. 43 13. -16.6 14. -7
15. -8 16. -3 17. -6 18. -30 19. 180 20. -5/12 21. 0 22. -48 23. -3 24. 6 25. 0 26. -.7 27.
26 28. -34
Worksheet 3 (1.3)
Warm-ups
1.(a) Distributive Property (b) Multiplication Property of Zero (c) Multiplicative Inverse
Property (d) Commutative Property of Multiplication (e) Associative Property of Addition
(f) Identity Property of Addition (g) Multiplication Property of Negative One 2.(a) 32, 18,
50, [750] (b) ½, 20, 10, [320] (c) -3, -8, -22, -33, [-7] 3.(a) 4, 4, 4, [64] (b) _, _, [4/9] (c)
16 (d) 8, 25, [-17] (e) 4, -8, 12, 4, [64]
Problems
1. Associative Property of Multiplication 2. Multiplication Property of Negative One
3. Additive Inverse Property 4. Distributive Property 5. Commutative Property of Addition
6. 15 7. 40 8. -10 9. 27/64 10. 16 11. -25 12. -.468 13. 12 14. 100
Worksheet 4 (1.4)
Warm-ups
1.(a) 8, 5, [13x] (b) -4a, 2, [4a - 1] 2.(a) 3x, 18, 3x, 18, [5x + 8] (b) 12, 5, [a - 17] 3.(a) -2,
3, -10, 18, [-28] (b) -1, 3, -1, 3, -1, -1, 9, 1, 3, -1, -27, 15, -6, [-48] 4.(a) 8, 7, 8, 7, -16, 35, [51]
297
ANSWERS TO WARM-UPS AND PROBLEMS
b) 4x, 12, 11, 15, 11, 15, -22, 15, [-37] 5.(a) x + 6 (b) 10, x, [10x] (c) x  15 or 15x
(d) 8 - x (e) (5)(x) - 9 (f) 5(2 + x) 6.(a) n - 5 (b) n + 1 (c) 45 - x (d) x  10 or 10x
Problems
1. 20a - b 2. x2 + 3x 3. 10y + 36 4. -13x + 16y 5. -25 6. 24 7. 352 8. 58 9. 20
10. 6y or y  6 11. y + 12 12. 2y - 4 13. (y  2) + 5 or 2y + 5 14. 3x + 1
15. 10d + 25q
Chapter 2 Equations and Inequalities
Worksheet 5 (2.1)
Warm-ups
1.(a) 5, 5, 10, 14, 14, True, [yes] 2.(a) -1, -1,_,_, -4, -4, [{-4}] (b) 2, -5x, -5x, 2, 2, 9, -_,
-_, -3, [{-3}] 3.(a) 3n, 7n, -7n, -7n, 4, 4, 16, -¼, -¼, -4, [{-4}], -4, -4, -4, -4, -20, -8, -16,
-12, -16, -16, [True] (b) 6, 3m, -5m, -5m, -2m, 10, 10, 20, -½, -½, -10, [{-10}] 4.(a) n + 11, n
+ 11, 11, -11, -11, 44, ½, ½, 22, 33, [22,33]
Problems
1. no 2. {-3} 3. {5} 4. {2} 5. {12} 6. x + 2x + 1 = 58, There are 39 women.
7. 87 = 3x + 30, The rate was $19 per hour.
Worksheet 6 (2.2)
Warm-ups
1.(a) 12, 12, 12, 12, 12, 12, 6x, 8, [-9 + 6x = 8] (b) 20, 20, 20, 20, 20, 20, 8, 20, -5
2
[8(4x - 1) + 20 = -5(5x + 2)] 2.(a) 12, 12, 12, 12, 12, 6x, 8, 6x, 176 ,   176   ; Ck: 176 , 17
12 , 3 ,
[True] (b) 9, 9, 9, 9, 9, 9, 3, 3, 39, 40, 10, [{10}] 3.(a) x, 2x , 4x , 2x , 4x , 2x, x, x, [12]
x 2x
x 2x
x 2x
(b) , + 40, , + 40 , x , , + 40 , 2x + 360, [90,30,60]
3 9
3 9
3 9
Problems
1. LCD = 9, 4x - 1 = 3(3x + 1) - 9x + 36 2. LCD = 2, 6x - 1 + 1 = -4x - 10
3. 15(3a - 1) + 20(a - 2) = 63 + 12(a - 1), {2} 4. 3(2x - 1) = 18 + 2(5x + 2), - 254 
x + x + 8 + x + 19
 5x 
= 84 ,
5. 40x + 5  = 420 , The rate is $8 per hour. 6.
3
 2
ANSWERS TO WARM-UPS AND PROBLEMS
The scores were 75, 83, and 94.
Worksheet 7 (2.3)
Warm-ups
1.(a) 102 = 100, 100, 100, 100, 100, 100, [200y = 60y + 21] 2.(a) 100, 100, 100, 100,
298
100, 100, 7x, 15200, -8x, -8x, -1x, -16000, -16000, -800, -1, -1, 800, [{800}]; Ck: 800,
800, 56, 64, 216, 216, [True] (b) 100, 100, 100, 100, 100, 12x, 31000, 11x, 23x, -77000,
-77000, -46000, - 231 , - 231 , 2000, [{2000}] 3.(a) .15x, .15x, 1150, 100, 100, 100, 100, 100,
15x, 85x, 1352.94, [$1352.94] (b) 12000 - x, .06x, .08(12000 - x), 12000 - x, 820, 100, 100,
100, 100, 100, 8, 96000, -2x, -14000, 7000, 5000, [$7000,$5000]
Problems
1. 102 = 100, 5x + 8(10000 - x) = 62000 2. 103=1000, 222x = 200 - 220x, {.45}
3. 102 = 100, 6x + 5(8000 - x) = 45000,{5000} 4. x + .065x = 17944,
The price was $16848.83. 5. .07x + .045(x - 1500) = 392.50,
He invested $4000 at 7% and $2500 at 4.5%.
Worksheet 8 (2.4)
Warm-ups
1.(a) .085, [204] (b) -1, -1, 2y, 6y, 3, 3, 7, - 61 , - 61 , - 76  2.(a) 2, 2, 2A,
hb1 , hb2 , - hb1 , - hb1 , hb2 , h1 , h1 , 2A - hb1, 2A - hb1 (b) -4y, -4y, 5y, 3x, 3x, 3x, 5, - 51 , - 51 , 3x +
5, -3x - 5 3.(a) 56, 16, x, 56, 2x, 24, 12, [12 feet] (b) x + 10,
Chart: 3(x + 10), 3x, Diagram: (x + 10), Equation: 3(x + 10), 360, 30, 6x, 330, 55, 65,
[55 mph, 65mph]
Problems
A - 2lh
ac + by - bc
1. 5% 2. x = -5 3. w =
4. x =
2h + 2l
a
5. .15x + .25(200) = .20(x + 200), It will take 200 ml of 15%-salt solution.
6. x + x + 10 + 3x = 180, The angle measures are 34, 44, and 102.
Worksheet 9 (2.5)
Warm-ups
1.(a) -3, -3, -6, 3, -1, True, [yes] 2.(a) 5, 5, >, ½, ½, > (b) -2, -2, 16, -5x, -5x, -4x,
-¼, -¼,  3.(a) <==) >, (-,3) (b) x  8 4.(a) 2x, -6, -6, 8, -½, -½, >, < (==>,
3
(-4,) (b) x, 2, 3, 10, 3x, 3x, 4x, -10, -10, -7, ¼, ¼, - , -  , 7
4
7
4

-4
ANSWERS TO WARM-UPS AND PROBLEMS
Problems
1. no 2. x  2 3. x > -4 4. {xx  -5}, [-5, ) 5. < (==>, (3,) 6. x >-2, < (==>
3
7. x  ,  , 
5
4
-2
5
4
Worksheet 10 (2.6)
Warm-ups
1.(a) -2 < x < 3, < (==) >, (-2, 3) (b) <==] (==>, (-, 0] union (4, ) (c) < (==>,
-2
3
0
4
-2
(-2, ) 2.(a) 5, 5, 3, 3, 2, 6, x < 2, x > 6, <==) (==>, (-, 2) union (6, ) (b) 2, 2, 2, -6,
2
6
9, _, _, _, x, -2  x  3, < [==] >, [-2, 3] 3.(a) x, 5, 5, 5, 450, 352, -352, -352, 98, 98
-2
3
299
Problems
1. 1 < x < 3, < (==) >, (1, 3) 2. <==) (==>, (-, -5) union (1, ) 3. <==) >, (-, 2)
1
3
4. all real numbers,<
-5
1
2
>, (-, ) 5. {x-1/2  x < 3/2}, < [===) >,
-1 3
2 2
[-1/2, 3/2) 6. 1000(.09) + 1000x > 130, The rate must be higher than 4%.
Worksheet 11 (2.7)
Warm-ups
1.(a) -4, 2 - m = -4: -2, -2, -6, -1, -1, [m = 6]; 4, 2 - m = 4: -2, -2, 2, -1, -1, [m = -2], [{-2, 6}]
(b) -11, 11, -1, -1, -1, 10, ½, ½, ½, -6, 5, < [==] > 2.(a) (b) (-, ) (c) -½, [{-½}]
-6
5
Problems
16
16 

or x > 4 ,  -  ,-  union (4,  ) 2. (-, ) 3. 
1. x < 7
7 

Chapter 3 Equations in Two Variables and Their Graphs
Worksheet 12 (3.1)
Warm-ups
1.(a) -2, -2, 4, 0, (4,0),
, (0,-2), y, 0, y 2.(a) -2 (b) 5 (c) (5,-2)
3.(a) origin (b) x, -x, y, -y, y2 - 4, [x-axis] (c) x, -x, x4 - 16, [y-axis] 4.(a) y-axis,
ANSWERS TO WARM-UPS AND PROBLEMS
-4, -4, 2, -2, 2, -2, -3,
(b) origin, -½, -¼, -1,
Problems
1.
7. y-axis symmetry 8.
2. (7,4) 3. (3,-1) 4. (6,-2) 5. x-axis symmetry 6. origin symmetry
9.
300
Worksheet 13 (3.2)
Warm-ups
1.(a) 4, 2, 1,
(b) 3, -3,
2.(a)
Problems
, 2 (b)
1.
, -4
2.
3.
4.
Worksheet 14 (3.3)
Warm-ups
1.(a) 0, True,
(b) dashed, False,
ANSWERS TO WARM-UPS AND PROBLEMS
Problems
1.
dashed line 2.
solid line
Worksheet 15 (3.4)
Warm-ups
1.(a) 5, -3, 1, 4, 8, -3, 64, 9, 73,

73
 2.(a)
0, 4, 5, (-3), -4, 8, -½
301
(b)
-2, (-2), 3, 5, 0, -2, horizontal (c)
4, (-1), 3, 3,
5, 0, vertical 3.(a) 18, 9, [9 inches]
Problems
1. 5 2. m = -2/3
3. m = undefined
4. m = 0,
5. The run is 12 inches.
Worksheet 16 (3.5)
Warm-ups
1.(a) 4, -3/4, -2, 4, -3/4, 2, 4, 4, 3x, 6, [3x + 4y = 10] (b) 4, -2, -7, 3, -7/3, 4, -7/3, -2, 4, 7/3, 2, 12, 2, 12, 14, [7x + 3y = -2] 2.(a) -1/2, 3, -1/2, 3 3.(a) -2x, 2x, 2 4.(a) -2x, (2/3)x,
3, 2/3, -3/2, -3/2, -3, -3/2, 3, 10, 3, 10, 9, [3x + 2y = 1]
Problems
1. 4x - y = 17 2. 2x + y = -3 3. y = (2/5)x - 5 4. y = -_x + 2, slope = -_
5. 2x - y = 10.
ANSWERS TO WARM-UPS AND PROBLEMS
Chapter 4 Polynomials
Worksheet 17 (4.1)
Warm-ups
1.(a) 5 (b) 3 2.(a) 3x2, x, -4, 5, 4, 2, [5x2 - 4x + 2] (b) a, 3a, 6, -2, 6, 1, [6a - 1]
3.(a) 8x2, 2x, 6, 8x2, 2x, 6, -11, 1, 2, [-11x2 - x + 2] (b) 5x, 2, -3, 2, 3, 2, 9, 2,
[9x + 2] 4.(a) 2x + 3, 5x - 4, 4, 6, 10, 8, 14, 2, [14x - 2] (b) 14, 2, 56, 2, 54,
[The perimeter of the rectangle is 54 units.]
Problems
1. 5 2. 1 3. 4y2 - 8y - 3 4. 8b - 7 5. 5x2 + 8x - 6 6. -2x - 9 7. 8x2 - 20
8. P = 52 units
Worksheet 18 (4.2)
302
Warm-ups
1.(a) y12 (b) x6 (c) 55 (d) 212 (e) x10 (f) 16x2 (g) x4 (h) 1 2.(a) 8, [8x3y6] (b) -30, x7, [30x7] (c) -3, x2, y, [-27x6y3] 3.(a) -7, a, b2, [-7ab2] (b) 9, x4, 1, [9x4]
Problems
1. a14 2. 79 3. y24 4. 8y3 5. m5 6. 1 7. -3c5d7 8. -3d9 9. 16x20y8 10. 2x3 11. -4a2b5
Worksheet 19 (4.3)
Warm-ups
1.(a) -10x4y2, 15x2y3, 25x2y, [-10x4y2 + 15x2y3 - 25x2y] 2.(a) 6x, 5x, x, [x2 + x - 30]
(b) 3x2, 6x, 15, x2, x, 15, [x3 + x2 - x + 15] 3.(a) x2 + x - 12 (b) 6x2 - 7x - 20
4.(a) x2 - 10x + 25 (b) 9a2 + 12ab + 4b2 (c) 2x, 7, [4x2 - 49] (d) x, x, 5, x, 5, 5, x3, x2, 5,
x, 25, 125, [x3 - 15x2 + 75x - 125] (e) 2x, 2x, 3, 2x, 3, 3, 8x3, 4x2, 3, 2x, 9, 27,
[8x3 + 36x2 + 54x + 27]
Problems
1. 6y4 - 15y3 + 27y2 2. -3x3y4 + 7x2y5 - 2xy3 3. c2 + 5ac - 3cd - 15ad
4. a3 + a2 - 15a + 18 5. x2 - x - 42 6. 10x2 + 8x - 24 7. 25x2 - 60x + 36 8. 49x2 - 4 9. y3 +
9y2 + 27y + 27 10. 27a3 - 108a2b + 144ab2 - 64b3
Worksheet 20 (4.4)
Warm-ups
1.(a) composite (b) prime 2.(a) 21, 7, [237] (b) 70, 35, 7, [2257] 3.(a) 3x, 1, [5x2(3x 1)] (b) xy, 4, [3xy2(xy + 4)] (c) 5, x, [(a - b)(5 - x)] 4.(a) a, b, a, b, a, b,
[(x + c)(a + b)] (b) y, 2z, y, 2z, 2, a, y, 2z, [(2 + a)(y - 2z)] (c) y, 3, y, 3, y, 3, y, 4, [(y 3)(y - 4)] (d) c, d, c, d, a, b, c, d, [(a + b)(c - d)] 5.(a) y, 8, y, 8, -8, [{0, -8}]
(b) c, 3, c, 3, 0, 3, [{0, 3}] (c) ax, 2c, ax, 2c, 0, a, 2c, 2c/a, [{0, 2c/a}] 6.(a) 20s, 20, 20,
20, [20 units]
Problems
1. composite 2. prime 3. composite 4. 2223 or 2223 5. 555 or 53 6. 2217 or 2217 7.
8a3b(3a - b) 8. 6x(3x2 + 2x - 4) 9. (a - 2)(y + 5) 10. (y + 5)(x2 - 8)
11. (2 - a)(x + 3) 12. (a + b)(x - y) 13. (5 - c)(m + n) 14. {0, 2} 15. {0,3}
16. {0, b/2a} 17. πr2 = 8πr; The radius is 8 units.
ANSWERS TO WARM-UPS AND PROBLEMS
Worksheet 21 (4.5)
Warm-ups
1.(a) x, 6, [(x + 6)(x - 6)] (b) 5a, 7, [(5a + 7)(5a - 7)] (c) a2, 4b2, a2, 4b2, a2, 4b2, a2, 4b2, a,
2b, [(a2 + 4b2)(a + 2b)(a - 2b)] (d) b, b, [(a - 1 + b)(a - 1 - b)] (e) x2, 9, x, 3,
[2(x + 3)(x - 3)] (f) prime polynomial 2.(a) x, 2, x, 2, x, x, 2, 2, [(x - 2)(x2 + 2x + 4)] (b)
3x, 1, 3x, 1, 3x, 3x, 1, 1, [(3x + 1)(9x2 - 3x + 1)] (c) 5y, 4z, 5y, 4z, 5y, 5y, 4z, 4z, [(5y 4z)(25y2 + 20yz + 16z2)] 3.(a) 49, 5x, 7, 5x, 7, 5x, 7, 5x, 7, 5, -7, 5, 7, -7/5, 7/5, [{-7/5,
7/5}] (b) x2, 9, x2, 9, x, 3, x, 3, x, 3, x, 3, -3, 3, [{-3, 3}] (c) x2, 36, x, 6, x, 6, x, 6, x, 6, -6,
6, [{0, -6, 6}] (d) x, 3x, 3, 25, 25, 5, 5, x + 5, x - 5, -5, 5, 5, 15,
[The width is 5 feet and the length is 15 feet.]
Problems
1. (y - 8)(y + 8) 2. (4a + 3)(4a - 3) 3. (x2 + 9)(x + 3)(x - 3) 4. (x + 2 + y)
(x + 2 - y) 5. 3(x + 4)(x - 4) 6. prime polynomial 7. (a - 3)(a2 + 3a + 9)
8. (2x + 5)(4x2 - 10x + 25) 9. (4x - 1)(16x2 + 4x + 1) 10. {-9, 9} 11. {-7/2, 7/2}
303
12. {0, -10, 10} 13. x3 = 4x2; The number is four or zero.
Worksheet 22 (4.6)
Warm-ups
1.(a) 5, 3, [(x + 5)(x + 3)] (b) 4, 5, [(x - 4)(x - 5)] (c) 3, 4, [(x + 3)(x - 4)] (d) 6, 3,
[(x + 6)(x - 3)] 2.(a) +1, -2, [(3x + 1)(x - 2)] (b) +3, -4, [(2x + 3)(3x - 4)] (c) -7, -1, [(5x 7)(2x - 1)] 3.(a) x, 9, [(x - 9)2] (b) 4x, 4x, 3, 3, 4x, 3, [(4x + 3)2]
Problems
1. (x - 5)(x - 2) 2. (x + 8)(x - 3) 3. (y + 6)(y + 7) 4. (a - 7)(a + 2) 5. (4x + 3)(x - 2) 6. (5x
- 2)(x - 4) 7. (6x + 5)(2x - 1) 8. (a + 4)2 9. (2x - 5)2 10. (x + 3)(x2 - 3x + 9) 11. (a - b)(x
+ y) 12. 5x2y(y2 - 2x) 13. (3x - 2)2 14. (9y + 5)(9y - 5)
15. (3b - 4)(2b + 5)
Worksheet 23 (4.7)
Warm-ups
1(a) 3, 1, 3, 1, 3, -1, 3/5, -1/2, [{3/5, -1/2}] (b) 3x, 10, 3x, 10, 5, 2, 5, 2, 5, -2, [{5, -2}] (c)
-12, 4, 3, 4, 3, -4, 3, [{-4, 3}] 2.(a) x, 2, 2x, 2x, 120, 12, 10, 12, 10, -12, 10, 10, 12, [The
two consecutive even whole numbers are 10 and 12.] 3.(a) x2, 4x, 4, 100, 4x, 96, x2, 2x,
48, x2, 2x, 48, 8, 6, 8, 6, -8, 6, 8, [The two legs are 6 inches and 8 inches.]
Problems
1. {5/6, -3/2} 2. {-10, 3} 3. {6, -1} 4. x(x + 2) = 63; The two consecutive odd whole
numbers are 7 and 9 5. x(2x + 5) = 133; The width is 7 inches and the length is 19 inches.
6. x2 + (x + 4)2 = (x + 8)2; The three sides are 12 cm, 16 cm, and 20 cm.
ANSWERS TO WARM-UPS AND PROBLEMS
Chapter 5 Rational Expressions
Worksheet 24 (5.1)
Warm-ups
  x + 2 
 2(m + 3) 
1.(a) 65 (b) - 3z5 (c) m - 3, m - 3, m - 3, 
(d) x + 2, x - 2, x + 2, 5, - 


 m-3 
  5 
Problems
9y
y+3
15 2
 a +6  - a - 6
1. a 2. 2
3.
4. - 
 or
3
2(y + 2)
16bc
y - 3y + 9
 3 
Worksheet 25 (5.2)
Warm-ups
304
1.(a) 141 (b) a + 7, a - 7, a - 7, [5b] (c) a - 3, 3a - 1, a + 3, 3a + 1,
 x 
 3a - 1 
2a + 5, 
2.(a) - 32 (b) 15xy, 24x2y2, x3, y, x2, y4,  3  (c) 2m2 - 7m - 9,

 3a + 1 
2 y 

(m + 1 )2 
-27 + 15m - 2m , 2m - 9, m + 1, 3m - 1, m + 5, 
 (m + 5)(-3 + m)
Problems
6x(x + 5)
(y + b)(x - 3)
1. - 181 2.
3. -4 4. 74 5. 5x 6.
x-5
3(y - 2b)(2x - 1)
2
Worksheet 26 (5.3)
Warm-ups
 2 x3 + 15 
1.(a) 4, x + 2, [2] (b) 20, 48,  481  (c) 10x2, 5, 2x2, 5, 2x2, 15, 2x3, 
2 
 10 x 
 7x - 13 
(d) (2x + 1)(x - 5), x - 5, 2x + 1, x - 5, 2x + 1, 15, 4x, 
 2.(a) 4m, 20, m - 5,
 (x - 5)(2x + 1) 
m - 5, [4] (b) x, x + 3, x, x + 3, x(x + 3), 2x2, 5x + 15, 2x2, 5x + 15,
ANSWERS TO WARM-UPS AND PROBLEMS
 2 x 2 - 5x - 15 
 x(x + 3)  (c) 1, x + 3, 1, x + 3, 1(x + 3), 5x, 2(x + 3), x + 3, 2x, 6,


3(x - 2) 
 3x - 6
 x + 3 or x + 3 
Problems
10n + 21 4(2x - 1)
8  4(2x + 1) 
+
1. 85 2.
3.
,
36
2x - 1
2x - 1  2x - 1 
4x - 12
(x + 1)(x - 3)  x + 5  x + 7
33x - 12
4.
,
5.
6.
+

12
(x + 3)(x - 3) (x + 3)(x - 3)  x + 3 
8 x2
- x + 18
7.
(2x - 1)(x + 3)
Worksheet 27 (5.4)
Warm-ups
 2x + 3 
1.(a) 19, 1, 1, 24, 24, 1, [38] (b) 2x, x, 2x + 3, x - 5, x - 5, x, x, x - 5, 
 x - 5 
 5y - 2x 
(c) xy2, xy2, xy2, xy2, xy2, xy2,  2
 (d) n + 3, n + 3, n + 3, n + 3, n + 3,
 6 y + 3xy 
 6n + 16 
n + 3, 18, 15, 
 5n + 16 
305
Problems
2
7y
3x + 14
(4y + 3)
x
1.
2. 2
3.
12
y (2x + 1) - 5x + 17
Worksheet 28 (5.5)
Warm-ups
8ab 4b 

+  (b) x3 + x2, -3x - 3, [x2 - 3], 0 (c) 2x4 - 10x2,
1.(a) 6a2b3, 8a3b, 12ab, 2 b3 3
a

- 3x + 51 

10x2 - 50, 2 x2 + 10 + 2

x -5 

ANSWERS TO WARM-UPS AND PROBLEMS
Problems
1. 8a2b4 - 4b3 + 3ab 2. x3 - x2 + x - 1 3. 5y - 2 +
11y - 3
2
y -2
Worksheet 29 (5.6)
Warm-ups
1.(a) 0, 0, 12x, 12x, 12x, 12x, 12x, 12x, 16, 9, 7, 107 ,   107   (b) 2, 2, 5(y - 2),
5(y - 2), 5(y - 2), 5(y - 2), 5(y - 2), 5(y - 2), 2y, 4, 2y, 2, [] 2.(a) 2x - 1, 3x + 2, 18x, 12,
22, 11, [{11}] 3.(a) 40 - x, 40 - x, 4, 40 - x, 40 - x, 40 - x, 40 - x, 40 - x, 4, 204, 34, [The
numbers are 34 and 6.]
Problems
1.  2. {3} 3. - 141  4.
x
5
= , [The dimensions are 20 m by 32 m.]
52 - x 8
Worksheet 30 (5.7)
Warm-ups
1.(a) x+3, x-3, -3, 3, -3, 3, (x+3)(x-3), (x+3)(x-3), (x+3)(x-3), (x+3)(x-3), (x+3)(x-3),
(x+3)(x-3), 1, x-3, x+3, x2+6x+9, 4x2-19x-5, 4x+1, x-5, -1/4, 5, [{-1/4, 5}] 2.(a) 4, 6, x,
12x, 12x, 12x, 2x, 6, 6/5, 1 1/5
Problems
1.  2. 2 3. 18 minutes 4. 15 hours
Chapter 6 Exponents and Radicals
Worksheet 31 (6.1)
Warm-ups
 


1.(a) 1 (b) 1 (c) 1 (d) -1 2.(a) a3,  a13  (b) 32, 9,  91  (c) y3, y3, [5y3] 3.(a) -2,  312 = 91  (b) 2,





[4] (c) 2, -1, 25, 2,  252  (d) 4, 3, 16, 27,  16
(e) 2, [49] 4.(a) -4, y4,  y14 
27 
(b) 6, -8,
 x6 
 8
 y 
5  10y 
4
(c) 10, 6, 10, 6, 4, [y ] (d) -5, 1, y, x , 
306

x 
5

8

(e) -4, 6, 8, -12, 8, 12,  49ab1 2  5.(a)

3
2
2 3 3
2 3
2 y -x
11 
32, 21, 9, 2, 2, 9, 11,  18
 (b) x , y , y , x , y - x ,  2 y3
 x



Problems
1
1. 1 2. 1 3. -1 4. 1 5. z15 6. 2b4 7. 125
8. 81 9. 9 10. 498 11. 25 12. 13 13. a13
ANSWERS TO WARM-UPS AND PROBLEMS
15
12
3
14. xy18 15. z13 16. ab-62 17. 9xy8 18. 209 19. aa3+bb2
2
Worksheet 32 (6.2)
Warm-ups
1.(a) 9 (b) 0 (c) -8 (d) 3/7 2.(a) -3 (b) 4/5 (c) 2 3.(a) 12 (b) 4, 2, 2 10


2, 10, 2, 10 2 (d) 9, 2, 3, 2, 32 , 2,
 2
2 
2 , 2 , 2, 2, 
4.(a)

3
2

2

(e) 27, 2, 3, 2, 3 3 2


 3 20 

2 


 21 
6 
(b) 21, 36, 21, 6, 
(c) 20, 8, 20, 2, 
 (c) 25, 2, 5,
(d) 16, [4] 5.(a) 8,
10, 12, 30, s = 15; 15, 15, 15, 15, 15, 7, 5, 3, 1575, 39.7,
[The area of the triangle is 39.7 square units.]
Problems
1. 6 2. 0 3. -10/3 4. 11 5. -3 6. 2 7. -1/3 8. 8 9. 5 3 10. 6 6 11. 43 7 12. 2 3 6 13.
10
8
14.
15.
3 98
7
6
3
16. 5103  71.4 sq.in.
Worksheet 33 (6.3)
Warm-ups


1.(a) 9, 3, 25, 3, 3, 3, 5, 3, - 4 3 (b) 8, 5, 2, 5, 2/5, 5, 1/3, 2/5, 5, 6, -1/15, - 151 3 5  2.(a)

2
3x, 5 x y
5b,
 10ab 
 5b 


 3



2


1

2
2
2
2

3x (b) 6, x , y , 6xy , 2x y, 6xy , 2 x y
3
6x y
(b) 5x, 3x, 5x, 3x, 3x, 3x, 6x, 5x, 9x2, 6x, 15x2,

 3.(a) 10ab, 25b , 10ab,

2

2

2
 6x 

2
 15 x 
(c) 32x, 32x, 9x, 33x3, 9x,
3x,  3 3x9x  4.(a) 5, 6, 2, -10, 6, 8, -12, - 12 y (b) 5, x, 5, x, 5x, 5x, 3x3, 5x, 2x2, 5x, 9x3,

5x, 4x3, 5x, 5 x3 5x
Problems

35
2 2. 6 3 3 3. 2 x3 y 7xy 4. 3 ab3 3 2ab 5.
1. 12
3ac
3a
6.
10xy
4 y3
7.
3 28 x 2
2x
8. - 29 a 9. 0
ANSWERS TO WARM-UPS AND PROBLEMS
Worksheet 34 (6.4)
Warm-ups
1.(a) 16, [4] (b) -6, 15, - 6 15 (c) 35, 12, 35, 4, 3, 35, 2, 3, 70, 3, 70 3 (d) -12, 8, -12,






2, [-24] 2.(a) 12, 4, 3, 2, 3, 10 + 2 3 (b) 6, 20x, 6, 4, 5x, x, 6, 2, 5x, 15x, 12, 5x, 15x,
12





5x - 15x 30 (c) 3, 24, 2, 2, 3, 3, 4, 3, 2, 3, 4, 6, 3, 4 + 6 3 3  (d) 42, 18, 42, 9, 2,
42, 3, 2,


35 + 15 - 42 - 3 2 (e) 18, 4, 15, 10, 4, 10, 4, 18, 2, 15, 10, 48, 2, 10, 36, 15,


10, 12, 5, 10, 12 + 5 10 (f) 9, 6, 6, 4, 3, 2, [1] 3.(a) 8, 9, 16, 8, 3, 16, 8, -
307

13,  -2 -133 - 8 or

2 3 +8 
13 
(b) x, x , 2 x , 2, x, 4, x,




3 x , 2, x,4,  x + 3x - 4x + 2 
Problems
1. 3 5 2. - 30 5 3. 30 21 4. 12 3 3 5. 3 2 - 42 6. 20a 3 + 8 15a
7. 9 - 2 3 18 8. 6 - 22 + 15 - 55 9. 163 10. 5 323+ 6 11. 2x - 11x - 9x + 15
Worksheet 35 (6.5)
Warm-ups
1.(a) 7, 7, 3x + 1, 49, 3, 48, 16; ck: 16, 49, 7, 7, 0; [Solution set = {16}] (b) 3, 3,
x2 - 9, -8, x2 - 1, x + 1, x - 1, x + 1, x - 1, -1, 1; ck: -1, 1, -8, -2 or 1, 1, -8, -2; [Solution Set
= {-1, 1}] (c) 2, 2, a + 3, a2, 6a, 9, a2, 7a, 6, 6, 1, 6, 1, 6, 1; ck: 6, 6, 9, 3, 3, 3 or 1, 1, 4, 2, 2, -2; [Solution Set = {6}] 2.(a) x - 4 , 2, x - 4 , 2, x + 4, x - 4, 4, 4, 4, 4, 1, 1, 2, 1, x 4, 5; ck: 5, 5, 9, 1, 3, 1, 2; [Solution Set = {5}]
Problems
1. {14} 2. {11} 3. {10} 4. {-3}
Worksheet 36 (6.6)
Warm-ups
1.(a) 81, [9] (b) -64, [-4] (c) 16, 81, [2/3] (d) 9, 3, [27] (e) 16, 2, [1/2] (f) 125, 125, 2, 5,






2, 25, [1/25] 2.(a) 3, 2,  3 y 2  (b) 4, 3,  2 4 x3  (c) ab3,



1
1


3
2

 ab  (d) 5, 4, 
3
5

(a + b )4 3.(a) 1,
3, 1, 3, 1, 3, a 3 b 3 (b) 1, 5, 2, 5, 3, 5, x 5 y 5 (c) 3,
ANSWERS TO WARM-UPS AND PROBLEMS

3


5

 
5
4, 2(a - b )4 4.(a) 10, 10, 2, 3, 10, 5, 10 x 4 (b) 3, 3, 8, 3, 3, 5, 3 a 12 (c) 2, 2, 4, 5, 16, 1, 4,







 1 

6
 2 2 
5,  16x4  5.(a) 1, 2, 1, 4, 3, 4, 4, 3, 4, 27,  4 27  (b) 3, 2, 3, 2, 2, 9, -7, 6, 6, 7, 2, 

y5
Problems
2
1. 7 2. -3 3. 1/2 4. 64 5. 1/6 6. 1/16 7. 6 a5 8. 3 x 2 y 9. 5 5 x2 10. 7 (x - y )
4
1
1
1
3
7
5
11. x 5 y 5 12. 2 4 x 4 13. 3(x + y )2 14. 15 y 12 15. 21 16. 125 x 4 17. 10 27 18. 3 25
x1 5
Worksheet 37 (6.7)
Warm-ups
1.(a) 2, [(4.76)(10)2] (b) -5, [(9.645)(10)-5] (c) 2.9, 7, [(2.9)(10)7] (d) 1.36579, -2,
[(1.36579)(10)-2] 2.(a) 934,500 (b) 0.000215 (c) 6000 (d) 0.0002 3.(a) 4.864, 7,
[48,640,000] (b) 3.41, -4, 1.9, -3, 3.41, 1.9, -4, -3, 6.479, -7, [0.0000006479] (c) 7, -2, 3,
9, [3,000,000,000] (d) 2.5, 4, 2.5, 4, 35, 0, 14, 1, 2.5(10)-1, [0.25]
Problems
1. (5.611)(10)3 2. (3.19)(10)-4 3. (5.2)(10)11 4. (8.72)(10)-7 5. (3.51267)(10)0 6.
2,496,780 7. 0.09 8. 0.0031864 9. 70,000 10. 13,413,000,000 11. 0.0000015 12.
50,000,000,000 13. 0.4
308
Chapter 7 Quadratic Equations and Inequalities
Worksheet 38 (7.1)
Warm-ups
1.(a) -2, 5 (b) 0 + (-5i) or 0 - 5i (c) 49, 7, [7i] (d) 45, 3 5 , [ 3i 5 ] 2.(a) -8, 3, -4,
-6, [-4 - 6i] (b) -1, -4, [-1 + 3i] 3.(a) 4 + 3i, 4 + 3i, 8, 20i, 15, [-7 + 26i] (b) 3 - 5i, 3 - 5i, 3
- 5i, 3 - 5i, 9, 25i2, 25, [-16 - 30i] (c) 2 + 7i, 2 + 7i, 4, 14i, 4, 49, [53]
8 10
4.(a) 5 + 4i, 5 + 4i, 5, 4i, 10i, -16, 41, [ - + i ] (b) 7 + 2i, 7 + 2i, 8i, 21i, 13i, 6, 4,
41 41
ANSWERS TO WARM-UPS AND PROBLEMS
34 13
7
i ] (c) -5i, -5i, -35i, -25i2, 25, [ - i ]
53 53
5
Problems
1. a = 2, b = -5 2. 7 + 0i 3. 10i 4. 4i 3 5. -2 + 9i 6. -6 - 3i 7. 10 + 30i
10 15
2 11
2 3
8. 12 - 16i 9. 10 10. - i 11. - i 12. + i
13 13
5 5
5 5
34, [
Worksheet 39 (7.2)
Warm-ups
1.(a) -16, 4i, [{±4i}] (b) 36, 6, 6, -6, 7, -5, [{-5, 7}] (c) -45, 45, 5, 3, 3 ± 3 i 5 ,
33i 5
}] (d) 50, 25, 25, 5, -5, 0, -10, [{0,-10}] 2.(a) x, 625, 1875, 1875, 43,
2
[The length of the parking lot is 43 yards.]
[{
Problems
24i 3
} 4. {-6, 4} 5. x2 + x2 = 202,
3
The length of the square is 14.1m.
1. {±7i} 2. {-2, 6} 3. {
Worksheet 40 (7.3)
Warm-ups
1.(a) 2, 2, 2, 2, 4y, -5, 4, 4, -1, y + 2 (b) 3x, 10, 10, 94 , 94 , 40, x - 32 2.(a) -28, 25, 25, -3, y 25 25
5, -3, 5, 3, [{ 5  i 3 }] (b) 5x, 3, 2, 2, 2, 2, 32 , 16
, 16 , 49,
5 49 7 7
7
x - 4 , 16 , 4 , 4 , - 4 , 3, -½, [{-½, 3}]
Problems
2
2
49
1. (y - 5 ) = - 3 2.  x - 45  = 16
3. x 2 - 143 x + 499 = 53 + 499 ,  x - 73
 5, - 31  4. y2 + 8y + 16 = -25 + 16, (y + 4)2 = -9, {-4 ± 3i}
309
2 = 649 ,
ANSWERS TO WARM-UPS AND PROBLEMS
Worksheet 41 (7.4)
Warm-ups
1.(a) 0, 1, 2, -2, 2, 2, 1, -2, 1, -2, 8, 12, 3, - 1  3 , - 1  3 , [{ - 1  3 }]
- 3  5i  -3  5i 
(b) 2, 6, 17, 2, 6, 17, 6, 6, 2, 17, 2, -6, 36, 136, -100, 10i, -3 ± 5i,
, [  2  ] (c) 6, 2
5, -25, -5, -5, 6, -25, 6, 25, 600, 12, 625, 25, 25, 25, 52 , - 53 , [  52 , - 53 ] 2.(a) 1, 5, -24, 5, 1, 24, 96, 121, [two real solutions] (b) 2y2 - 6y + 17, 2,
-6, 17, -6, 2, 17, 36, -100, [two nonreal complex solutions] 3.(a) 5 + i 3 , 5 - i 3 ,
-10, 1, 5 + i 3 , 5 - i 3 , 28, 1, 25, 3
Problems
1. x =
- (-3)  (-3 )2 - 4(1)(7)
2(1)
 3  i 19 
- (5)  (5 )2 - 4(2)(-3)
,
2.
,  - 3, 21  3.
x
=

2
2(2)


- (-20)  (-20 )2 - 4(4)(25) 5
,  2  4. The discriminant is 2304.
x=
2(4)
There are two real solutions. 5. The discriminant is 0. There is one real solution with
multiplicity of two.
6. Sum: 156 + - 53 = 65 , 65 = 65 Product:  156  - 53 = - 256 , - 256 = - 25
6
7. Sum: ( - 1 + 3 ) + ( - 1 - 3 ) = - 21 , -2 = -2
Product: ( - 1 + 3 ) ( - 1 - 3 ) = - 21 , -2 = -2
Worksheet 42 (7.5)
Warm-ups
1.(a) x + 2, x, x + 2, x2, 4, 2x2, 1248, x2 + 2x - 624, 1, 1, 625, 24, -26, 26, [The two
consecutive even whole numbers are 24 and 26.] (b) 2x + 3, x + 6, 2x + 9, x + 6,
2x + 9, 21x, 54, 21, 21, 2, -765, 2, 6561, 15, 33, [The dimensions are 15m by 33m.]
Problems
1. 35 = x ( 2x - 3) , The polygon has 10 sides. 2. 82 + x2 = (x + 2)2,
The tower is 15 yards high.
ANSWERS TO WARM-UPS AND PROBLEMS
Worksheet 43 (7.6)
Warm-ups
1.(a) 4, -3, <==) (==>,  x | x < - 3 or x > 4,  - , - 3 union  4,   (b) 5, 1,
-3 4
< [==] >,  x | 1  x  5
1
, [ [1, 5] ]
2.(a) 1, -5, < (==) >, [{x  -5 < x < 1}],
5
-5
1
[(-5, 1)] (b) 0, x + 4, x + 4, x, 4, x + 6, -6, -4,<==] (==>, [{x  x  -6 or x > -4 }],
-6 -4
310
[(-, 6]  (4, )]
Problems
1. <==] [==>, {x  x  -4 or x  3}, (-, -4]  [3, ) 2. < (==) >,
-4 3
-5
-1
{y  -5 < y < -1}, (-5, -1) 3. <==] (==>, {x  x  -3 or x > 2}, (-, -3]  (2, )
-3 2
4. < (==) >, {x  < x < 2}, ( , 2)
3
2
3/2
3
2
2
Chapter 8 Conic Sections
Worksheet 44 (8.1)
Warm-ups
1.(a) 3, 6, 3, 6,
2.(a) 3, 12,
3.(a) -½, -2,
4.(a) 1, 1, 4,
5.(a) -1, -1, -7,
Problems
1.
2.
3.
ANSWERS TO WARM-UPS AND PROBLEMS
4.
5.
311
Worksheet 45 (8.2)
Warm-ups
1.(a) 1, 1, 4, (-1, -4), 1 unit, 4
units, -3, -3, 0,
0,
(b) 4, 8, x
- 2, 1, -1,
-1, -7, -7,
2.(a) -2, 3, 4, 2, 3, 4, y2, 6y, 9, 16, 6y, 3, [x2 + y2 + 4x -
6y - 3 = 0] (b) 1, 9, 1, 9, 1, 3, 4, 1, 3, 2, C = (1, -3), radius = 2,
Problems
1. y = (x + 3)2 - 5,
2. y = -2(x + 1)2 + 4,
3. x2 + y2 - 6x + 2y + 1 = 0 4. (x - 4)2 + (y + 2)2 = 52, C = (4, -2), Radius = 5
Worksheet 46 (8.3)
Warm-ups
1.(a) 25, ±5, 5, -5,
2.(a) 9, 4, 9, 16, 3, 16, 0, 4, 4, 7, -1, 0, 4, 2, 2, 0, -4, 0, -4,
ANSWERS TO WARM-UPS AND PROBLEMS
Problems
1.
2.
312
Worksheet 47 (8.4)
Warm-ups
1.(a) ±4, 4, -4, 0, ±3/2, ±5  2.2
2. (a) 4, 1, 36, 25, 2, 225, 0, 15, 15,
17, -13, 0
Problems
1.
2.
Chapter 9
Functions
Worksheet 48 (9.1)
Warm-ups
1.(a) 2, 3, 4, 5, [{2, 3, 4, 5}] (b) 1, [{1}] (c) real, all real numbers (d) real, all real
numbers (e) x - 1, , 1, [{x  x  1}] (f) , 1, [{x  x  1}] 2.(a) 5, 8, 11, 12,
[{5, 8, 11, 12}] (b) -2, -1, 0, 1, 2, [{-2, -1, 0, 1, 2}] (c) real, all real numbers (d) 0, 1, 1,
[{y  y  1}] (e) real, all real numbers (f) 0, 0, [{y  y  0}] 3. In the above list of
relations, warm-up a, c, d, and f are functions. 4.(a) -5, -5, -7, [-7] (b) -4, -4, 17, [17]
(c) _, _, -_, - 32 ,  - 32  5.(a) all real numbers, 0, 0, [{f(x)  f(x)  0}] (b) x2 - 25, -5,
5, 0, 0, [{f(x)  f(x)  0}] (c) x2 - 4, -2, 2, 0, 0, [{f(x)  f(x)  0}]
Problems
1. Domain: {1, 2, 3, 4}, Range: {1} 2. Domain: all real numbers, Range: all real numbers
3. Domain: all real numbers, Range: {y  y  0} 4. Domain: {x  x  3},
ANSWERS TO WARM-UPS AND PROBLEMS
Range: {y  y  0} 5. yes 6. no 7. - 61 8. 21 9. Domain: {x  x  0, x  -3},
Range: {y  y  0}
Worksheet 49 (9.2)
313
Warm-ups
1.(a) 4, 0,
(b)
2.(a) upward, 1, 4, 4, 1, -2, -2,
-2, -1, (-2, -1), -1, -1, 0, (-1, 0), (-3, 0),
(b) downward, -2, 4, 4, -2, 1,
1, 1, 2, (1, 2), -1, -1, -6, (-1, -6), (3, -6),
3.(a) 148 - 2x, x(148 - 2x),
x(148 - 2x), -2, 148, 148, -2, 37, [The maximum area occurs when the width is 37 rods and
the length is 74 rods.] 4.(a) x  4, 4, (4, 0), 1, 2,
Problems
1.
2.
3.
4.
5.
ANSWERS TO WARM-UPS AND PROBLEMS
314
Worksheet 50 (9.3)
Warm-ups
1.(a) vertical, 2, upward,
(b) horizontal, 2, right,
2.(a) 1x , x-axis and y-axis,
3.(a) shrinking,
1
8
,
(b) x , y-axis,
(b) stretching, 2,
4.(a) x, horizontal translation, vertical translation, vertical stretching, upwards, 1, 2,
Problems
1.
2.
3.
5.
6.
7.
4.
Worksheet 51 (9.4)
Warm-ups
1.(a) x - 2, x2 - 4x + 4, [x2 - 4x + 4], -2, -2, [16] (b) x + 5,
1
 1 
,
,
2x + 10  2x + 10 
ANSWERS TO WARM-UPS AND PROBLEMS
315
1 + 10x 


-½,  91  2.(a) x2, x2, [x2 - 2], 0, [-2] (b) 2x1 ,  2x1 + 5 or
, 3,  31
6 

2x


Problems
1. (f  g)(x) = 2x + 7 , (g  f)(x) = 2 x + 2 + 5 , 5, 5 2. (f  g)(x) = x,
(g  f)(x) = x, 5, -3
Worksheet 52 (9.5)
Warm-ups
1. Graph a, b, and c pass the vertical line test and are functions. 2. Graph c also passes the
horizontal line test and is a one-to-one function. 3.(a) 1, 2, 3, [{(3, 1), (5, 2), (7, 3)}]
(b) 2y, 21 x + 3 ,  21 x + 3  (c) 6, ½, -2y + 3, -3x + 3/2, [-3x + 3/2] 4.(a) ½ x + 3, x, [x], 2x 6, x, [x] (b) - 3x + 32 , x, [x], - 31 x + 21 , x, [x] 5.(a) -4, 2, 1,
(b) 0, -½, 32 , 3,
4,
Problems
1. One-to-one function 2. One-to-one function 3. Function, not one-to-one 4. Not a
function 5. {(2, -2), (3, -1), (4, 0), (5, 1)} 6. f -1 (x) = 3 x - 1 7. f -1 (x) = 2x + 1
8. (f  f -1)(x) =


3
-1
-1
x - 1 + 1 , (f  f )(x) = x, (f  f)(x) = 3 ( x + 1) - 1 ,
(2x + 1) - 1
(f -1  f)(x) = x 9. (f  f -1)(x) =
, (f  f -1)(x) = x,
2
 x-1 
(f -1  f)(x) = 2 
 + 1 , (f -1  f)(x) = x
 2 
3
3
Instal Equation Editor and doubleclick here to view equation. 11.
10.
ANSWERS TO WARM-UPS AND PROBLEMS
Worksheet 53 (9.6)
Warm-ups
 22  (b) 227 , 21, 66, [The circumference is 66 cm.] (c) 3, _,
1.(a) 7, 22
7 , 7
[The constant of variation is _.] (d) 8, 2 3 3 , [When y = 8, x  2.9.] 2.(a) 25, 375
(b) 125, 3, [The pressure is 3 pounds.] 3.(a) y, z3 (b) b, c2 4.(a) 10, 2, 25, 4, [200]
Problems
1. The constant of variation is 68 mph. When the distance is 34 miles, it will take 1/2 hour.
316
2. The constant of variation is 2. When x = 64, y = 16. 3. The constant of variation is 20.
k y
When x = 10, y = 1/5. 4. T = kVP 5. x = z 6. The constant of variation is 1/2. When
b = 10 and h = 8, A = 40.
Chapter 10 Systems of Equations
Worksheet 54 (10.1)
Warm-ups
1.(a)
[(2, -1)], consistent 2.(a) 2 - 3x, 6, 9x, 11, 1, 1, -1, [{(1, -1)}]
ck. 1, -1, 1, -1 3.(a) 0.04y, 540, 10,000 - y, 10,000 - y, 600, 0.06y, 60, 3000, 3000, 7000,
[Brian invested $7,000 at 6% and $3,000 at 4%]
Problems
1.
{(4, 1)}, consistent 2. {(-8, 2)} 3. System: x + y = 90,
x = y + 30, The two angles are 30 and 60.
Worksheet 55 (10.2)
Warm-ups
1.(a) 12, 4, 4, 3, 1, [(4, 1)] (b) -65, -5, -5, -15, -6, 3, [(-5,3)] 2.(a) 2x + 7, 4x, 14,
-14, [no solution]
Problems
1. {(2, -3)} 2. {(1, -5)} 3. {(x,y)2x + y = 9}
ANSWERS TO WARM-UPS AND PROBLEMS
Worksheet 56 (10.3)
Warm-ups
1.(a) 15, -3, -3, -9, 1, -3, 1, 6, 1, 7, 2, [(2, -3, 1)] (b) -33, -5z, 3, -30, 5, 5, -28, -4, -4, 5, -8,
0, 0, [(-4, 0, 5)]
Problems
1. {(6, -4, 2)} 2. {(-7, 3, -5)}
Worksheet 57 (10.4)
Warm-ups
1.(a) 3, 3, 6, -1, [(-1, 3)] (b) 1, 1, 2, -2, -2, 1, 3, 5, -2, [(-2, -2, 1)]
Problems
317
1. {(-3, 5)} 2. {(2, -1, 3)}
Worksheet 58 (10.5)
Warm-ups
1.(a) 2, 3, 5, 6, [-1] (b) 5, -4, -18, -20, [2] 2.(a) 3, -6, 10, 18, D = 28; -8, -6, -8, 48,
Dx = -56; -8, 5, 3, -4, -40, 12, Dy = -28; -56, 28, x = -2, -28, 28, y = -1, [(-2, -1)]
(b) 1, -4, -12, 4, D = -8; 9, -1, 9, -4, -1, -4, -36, 4, Dx = -40; 9, -1, -1, 9, -3, 9,
Dy = -12; -40, -8, x = 5; -12, -8, y = 3/2; [(5, 3/2)]
Problems
1. 22 2. -7 3. {(1, 3)} 4. {(-8, 2)}
Worksheet 59 (10.6)
Warm-ups
1.(a) 4, 21, 10, -16, -17, 20, 80, -17, [83] 2.(a) -2, 4, 3, -23, 7, 1, -23, 14, 3, D = -40;
-2, 3, -23, 7, 1, 46, 119, 7, Dx = -80; -2, -1, -2, -1, 17, 4, -28, 7, -17, 113, -17, 9, 113, 34,
27, Dy = 120; 2, -7, 1, -2, -3, 17, 34, -7, -4, 17, 6, -13, -3, 11, -13, 6, 33, Dz = -40,
-80, -40, x = 2; 120, -40, y = -3; -40, -40, z = 1; [(2, -3, 1)]
Problems
1. 23 2. {(-1, 3, 5)}
Worksheet 60 (10.7)
Warm-ups
1.(a)
2x - 1, 2x, 3, x + 1, x + 1, 3, -1, 3, -1, 5, -3,
[Solution Set = {(3,5), (-1, -3)}] 2.(a)
ANSWERS TO WARM-UPS AND PROBLEMS
Problems
1.
{(2, 0), (-2, 0),



3 , - 1 , - 3 , - 1 } 2.
Chapter 11 Exponential and Logarithmic Functions
Worksheet 61 (11.1)
318
Warm-ups
1.(a) -4, -4, 2, [{2}] (b) x + 1, 6, 2x + 2, 2x + 2, 1, [{1}]
2.(a) 1/3, 1, 3, 9,
(b) 3, 1, 1/3, 1/9,
(d) 5, 3, 2 31 , 2 91 ,
(c) 3, 9, 27, 81,
Problems
1. {3} 2. {3/2} 3.
4.
Worksheet 62 (11.2)
Warm-ups
1.(a) .12, 4, 4, 5, 1.03, 20, 3612.22, [The total accumulation is $3,612.22.]
2.(a) 18149, .3, 6, 3000, [There were 3000 bacteria initially.]
Problems
1. A = 1500  1 + .10
12
( 12 )( 3 ) , The total accumulation is $2,022.27.
2. A = 2000 e .6 , The total accumulation is $3,644.24.
Worksheet 63 (11.3)
Warm-ups
1.(a) 3 (b) 4 (c) 5 2.(a) -3 (b) 4 (c) 4 3.(a) 5, 5, [5] (b) 2/5, 2, 4, [{4}] 4.(a) 7,
log 10 7, 1.1461 (b) 5, 7, log 2 5, log 2 7, 5.1296 5.(a) log 10 23, 0.6426 (b) log 8 5, 2,
ANSWERS TO WARM-UPS AND PROBLEMS
1.226 6. (a) 1/2, 1.64995 (b) 1/3, 1/3, log b x, log b y,  31  log b x - log b y   (c) 2x - 1,
x + 1, 2x - 1, x + 1, 2x2 + x - 1, 2x2 + x - 10, -5/2, 2, [{2}]
Problems
1. 33 = 27, 10-5 = 0.00001 2. log 10 100 = 2, log  41   641  = 3 3. 4 4. {25} 5. 1.1761
6. 4.3924 7. -0.2219 8. -2.6781 9. 2.796 10. log b x - 21 log b y 11. {6}
Worksheet 64 (11.4)
Warm-ups
319
1.(a)
(b)
2.(a) 0.0969 (b) 1.0969 (c) 2.0969
(d) 3.0969 3.(a) 0.4150, [2.6002] (b) 1.6135, [41.068] 4.(a) 0.2231 (b) 2.5257
(c) 4.8283 (d) 7.1309 5.(a) 0.4150, [1.5144] (b) 1.6135, [5.0204]
Problems
1.
2.
3. -1.6144 4. -0.6144 5. 0.3856 6. 1.3856
7. 1.0235 8. 0.000047753 9. -3.7173 10. -1.4147 11. 0.8879 12. 3.1905 13. 1.0102
14. 0.013287
Worksheet 65 (11.5)
Warm-ups
1.(a) 10x, 5, x, log 5, log 10, 0.70, [{0.70}] (b) 5x + 1, 7, x + 1, 7, log 7, log 5, 0.21,
[{0.21}] (c) x - 3, 2x - 6, 8, [{8}] 2.(a) 2000, 1000, .10, 4, 4, 1.025, 4t, 7.0, [It will take
7.0 years.] 3.(a) 15, 3, [2.465] (b) 0.004, 5, [-3.431]
Problems
1. {2.69} 2. {0.62} 3. {6} 4. 2000 = 1000 e.10t , It will take 6.9 years. 5. 2.499
6. -9.966
ANSWERS TO WARM-UPS AND PROBLEMS
Chapter 12 Sequences and Series
Worksheet 66 (12.1)
Warm-ups
1.(a) 1, 1, 2, 4, 3, 7, 4, 10, 5, 13, [1, 4, 7, 10, 13] (b) 1, 7, 2, 13, 3, 23, [7, 13, 23]
(c) 150, [-295] (d) 5, [1/9] 2.(a) -3, 3, 3, -3, [-3n + 6] (b) 21, -57, [-57] (c) 5, -7,
-7, 5, [5n -12] (d) 13, 53, [53] (e) 2, -3, 95, 95, -3, 2, 50, [50]
Problems
1. 4, 9, 14, 19, 24 2. 1, -5, -15 3. 174 4. 64 5. an = -2n + 5 6. -75 7. 36 terms
Worksheet 67 (12.2)
Warm-ups
320
1.(a) 2, 60, 2, 2, 60, 2, a60 = 120; 60, 2, 120, S60 = 3660, [3660] (b) 15, 20, 25, 600, 15,
600, 5, 600, 15, 5, n = 118; 118, 15, 600, S118 = 36,285 [36,285] (c) 1, 2, 40, 5, 7, 83, 5, 7,
83, 5, 40, 2, 83, 40, 5, 83, S40 = 1760, [1760] (d) 8500, 20, 850, a20 = 24,650; 8500, 9350,
24,650, 20, 8500, 24,650, S20 = 331,500 , [$331,500]
Problems
1. a50 = 150, S50 = 3825 2. n = 147, S147 = 45,276
Worksheet 68 (12.3)
Warm-ups
1.(a) 3, 3, 3, 3, [3n] (b) 10, [59,049] (c) -1/5, -50, -50, -1/5, an = (-50)(-1/5)n - 1
(d) 8, a8 = 2/3125 2.(a) -5, -2, 10, -5, -2, 10, -5, -2, [S10 = 1705] (b) 6, 1/2, 6, 6, 1/2, 6, 6,
1/2, [S6 = 189/16]
Problems
1. an = -2n - 1 2. a12 = -2048 3. an = -16(-1/4)n - 1 4. a9 = -1/4096 5. S9 = 2555
6. S7 = -215/32
Worksheet 69 (12.4)
Warm-ups
1.(a) 1/4, 1, r < 1; therefore, S  =
a1
, 1, 1/4 (b) 9, 3, r  1; therefore, the sum
1- r
does not exist [does not exist]
Problems
1. r = 1/3, S = 3 2. r = 4, Sum does not exist.
Worksheet 70 (12.5)
Warm-ups
1. 3, 2, 24, [24] 2. 2a, -b; 5, 1, 4, 3, 4, 3, 2, 3, 4, 3, 2, 1, 4, 5; 32, 80, a3, 40a2b3, 10, b5;
[32a5 - 80a4b + 80a3b2 - 40a2b3 + 10ab4 - b5] 3. 6, 6, 6, 4; 10, 8, 7, 6;10, 8, 7, 6, 4, -b; 210,
3360, [3360a4b6]
Problems
1. 32x5 + 80x4y + 80x3y2 + 40x2y3 + 10xy4 - y5 2. a6 - 12a5 + 60a4 - 160a3 + 240a2 - 192a
+ 64 3. 375x4 4. -2880x2
321