Post on 01-Apr-2015
Slide R - 1 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Active Learning Lecture SlidesFor use with Classroom Response Systems
© 2009 Pearson Education, Inc.All rights reserved.
Chapter RReview
Slide R - 2 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Let U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7} and C = {1, 4, 9}, find
a. {1, 2, 3, 4, 5, 9}
b. {1, 2, 3, 5}
c. {1, 2, 3}
d. {2, 3, 5}
A B C.
Slide R - 3 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Let U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7} and C = {1, 4, 9}, find
a. {1, 2, 3, 4, 5, 9}
b. {1, 2, 3, 5}
c. {1, 2, 3}
d. {2, 3, 5}
A B C.
Slide R - 4 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
List all the elements of B that belong to the set of rational numbers.
a.
b.
c.
d.
B 15, 8, 19,0,0
1, 9,0.62, 8 ,0.999...
15, 19,0,0
1, 9,0.62,0.999...
15, 19,0,0
1,0.62
15, 19,0,0
1,0.62,0.999...
15, 19,0,0
1, 9,0.62, 8 ,0.999...
Slide R - 5 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
List all the elements of B that belong to the set of rational numbers.
a.
b.
c.
d.
B 15, 8, 19,0,0
1, 9,0.62, 8 ,0.999...
15, 19,0,0
1, 9,0.62,0.999...
15, 19,0,0
1,0.62
15, 19,0,0
1,0.62,0.999...
15, 19,0,0
1, 9,0.62, 8 ,0.999...
Slide R - 6 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Evaluate.
a.
c.
47
4
67
4
23
4b.
d.
1
2 10
1
4
7
95
8
Slide R - 7 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Evaluate.
a.
c.
47
4
67
4
23
4b.
d.
1
2 10
1
4
7
95
8
Slide R - 8 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Use the distributive property to remove parentheses.
(x – 6)(x – 2)
a.
c.
x2 8x 12x2 12x 8
x2 9x 12 x2 8x 8
b.
d.
Slide R - 9 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Use the distributive property to remove parentheses.
(x – 6)(x – 2)
a.
c.
x2 8x 12x2 12x 8
x2 9x 12 x2 8x 8
b.
d.
Slide R - 10 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Which statement expresses z is less than or equal to 7?
a. z < 7
b. z ≤ 7
c. z > 7
d. z ≥ 7
Slide R - 11 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Which statement expresses z is less than or equal to 7?
a. z < 7
b. z ≤ 7
c. z > 7
d. z ≥ 7
Slide R - 12 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Evaluate
a. 2
b. 1
c. 0
d. –1
when x = 4 and y = –5 x
x
y
y
Slide R - 13 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Evaluate
a. 2
b. 1
c. 0
d. –1
when x = 4 and y = –5 x
x
y
y
Slide R - 14 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Express the statement as an equation using the indicated variables.The area A of a triangle is one-half the product of its base b and its height h.
a.
b.
c.
d.
A 1
2b h
A 1
2bh
A 2bh
A bh
Slide R - 15 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Express the statement as an equation using the indicated variables.The area A of a triangle is one-half the product of its base b and its height h.
a.
b.
c.
d.
A 1
2b h
A 1
2bh
A 2bh
A bh
Slide R - 16 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Determine which value(s), if any, must be excluded from the domain of the variable expression.
a.
b.
c.
d.
x 4
x 5
9
x 2
x 2, x 2
9x 5
x2 4
Slide R - 17 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Determine which value(s), if any, must be excluded from the domain of the variable expression.
a.
b.
c.
d.
x 4
x 5
9
x 2
x 2, x 2
9x 5
x2 4
Slide R - 18 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Simplify the expression. Express the answer so that all exponents are positive.
a.
c.
10 10
8
25
64
y z
x
25z10
64x8 y10
64x8
25y10z10
25y10
64x8z10
8x4 y 5
5z5
2
b.
d.
Slide R - 19 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Simplify the expression. Express the answer so that all exponents are positive.
a.
c.
10 10
8
25
64
y z
x
25z10
64x8 y10
64x8
25y10z10
25y10
64x8z10
8x4 y 5
5z5
2
b.
d.
Slide R - 20 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Evaluate
a.
b.
c.
d. 3
2
5
1
x2 y2 when x = 2 and y = –1.
Slide R - 21 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Evaluate
a.
b.
c.
d. 3
2
5
1
x2 y2 when x = 2 and y = –1.
Slide R - 22 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
The lengths of the sides of a right triangle are 15, 36, 39. Determine if it is a right triangle. If it is, identify the hypotenuse.
a. right triangle; 39
b. right triangle; 36
c. right triangle; 15
d. not a right triangle
Slide R - 23 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
The lengths of the sides of a right triangle are 15, 36, 39. Determine if it is a right triangle. If it is, identify the hypotenuse.
a. right triangle; 39
b. right triangle; 36
c. right triangle; 15
d. not a right triangle
Slide R - 24 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Find the area A and circumference C of a circle of diameter 16 mi. Use 3.14 for π. Round the result to the nearest tenth.
a. A = 100.5 mi2; C = 25.1 mi
b. A = 50.2 mi2; C = 50.2 mi
c. A = 803.8 mi2; C = 25.1 mi
d. A = 201 mi2; C = 50.2 mi
Slide R - 25 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Find the area A and circumference C of a circle of diameter 16 mi. Use 3.14 for π. Round the result to the nearest tenth.
a. A = 100.5 mi2; C = 25.1 mi
b. A = 50.2 mi2; C = 50.2 mi
c. A = 803.8 mi2; C = 25.1 mi
d. A = 201 mi2; C = 50.2 mi
Slide R - 26 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Find the area of the shaded region. Express the answer in terms of π.
a. 4π – 4 square units
b. 4π – 16 square units
c. 16 square units
d. 8π – 16 square units
4
4
Slide R - 27 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Find the area of the shaded region. Express the answer in terms of π.
a. 4π – 4 square units
b. 4π – 16 square units
c. 16 square units
d. 8π – 16 square units
4
4
Slide R - 28 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
A flagpole casts a shadow of 28 feet. Nearby, a 10-foot tree casts a shadow of 5 feet. What is the height of the flagpole?
a. 14 ft
b. 56 ft
c. 1.8 ft
d. 1400 ft
Slide R - 29 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
A flagpole casts a shadow of 28 feet. Nearby, a 10-foot tree casts a shadow of 5 feet. What is the height of the flagpole?
a. 14 ft
b. 56 ft
c. 1.8 ft
d. 1400 ft
Slide R - 30 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Add.
a.
b.
c.
d.
11x2 13x 15 26x 15
11x2 13x 30
11x2 39x
11x2 39x 30
50x3
Slide R - 31 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Add.
a.
b.
c.
d.
11x2 13x 15 26x 15
11x2 13x 30
11x2 39x
11x2 39x 30
50x3
Slide R - 32 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Subtract.
a.
b.
c.
d.
3 3x3 x2 1 9 7x3 5x 2
72x3 3x2 45x 21
72x3 x2 45x 21
72x3 3x2 45x 21
72x3 3x2 45x 21
Slide R - 33 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Subtract.
a.
b.
c.
d.
3 3x3 x2 1 9 7x3 5x 2
72x3 3x2 45x 21
72x3 x2 45x 21
72x3 3x2 45x 21
72x3 3x2 45x 21
Slide R - 34 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Multiply.
a.
b.
c.
d.
3y 11 5y2 2y 8
15y3 49y2 46y 88
70y2 28y 112
15y3 6y2 24y 11
15y3 61y2 46y 88
Slide R - 35 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Multiply.
a.
b.
c.
d.
3y 11 5y2 2y 8
15y3 49y2 46y 88
70y2 28y 112
15y3 6y2 24y 11
15y3 61y2 46y 88
Slide R - 36 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Multiply.
a.
b.
c.
d.
9x 1 9x 1
81x2 1
81x2 18x 1
x2 1
81x2 18x 1
Slide R - 37 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Multiply.
a.
b.
c.
d.
9x 1 9x 1
81x2 1
81x2 18x 1
x2 1
81x2 18x 1
Slide R - 38 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Multiply.
a.
b.
c.
d.
8x 5 2
64x2 25
64x2 80x 25
8x2 80x 25
8x2 25
Slide R - 39 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Multiply.
a.
b.
c.
d.
8x 5 2
64x2 25
64x2 80x 25
8x2 80x 25
8x2 25
Slide R - 40 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Divide.
a.
b.
c.
d.
x4 81 divided by x 3
x3 3x2 9x 27; remainder 81
x3 3x2 9x 27; remainder 162
x3 3x2 9x 27; remainder 0
x3 3x2 9x 27; remainder 162
Slide R - 41 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Divide.
a.
b.
c.
d.
x4 81 divided by x 3
x3 3x2 9x 27; remainder 81
x3 3x2 9x 27; remainder 162
x3 3x2 9x 27; remainder 0
x3 3x2 9x 27; remainder 162
Slide R - 42 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Multiply.
a.
b.
c.
d.
4x 11y 2x 12y
8x2 22xy 132y2
8x2 48xy 132y2
8x2 70xy 132y2
8x2 70xy 70y2
Slide R - 43 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Multiply.
a.
b.
c.
d.
4x 11y 2x 12y
8x2 22xy 132y2
8x2 48xy 132y2
8x2 70xy 132y2
8x2 70xy 70y2
Slide R - 44 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d.
64x2 49
8x 7 2
8x 7 2
64x 1 x 49
8x 7 8x 7
Slide R - 45 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d.
64x2 49
8x 7 2
8x 7 2
64x 1 x 49
8x 7 8x 7
Slide R - 46 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d.
1000x3 343
10x 7 100x2 70x 49
1000x 7 x2 70x 49
10x 7 100x2 49
10x 7 100x2 70x 49
Slide R - 47 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d.
1000x3 343
10x 7 100x2 70x 49
1000x 7 x2 70x 49
10x 7 100x2 49
10x 7 100x2 70x 49
Slide R - 48 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d.
64 125x3
4 5x 16 20x 25x2
64 5x 1 20x 25x2
4 5x 16 25x2
4 5x2 16 20x 25x2
Slide R - 49 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d.
64 125x3
4 5x 16 20x 25x2
64 5x 1 20x 25x2
4 5x 16 25x2
4 5x2 16 20x 25x2
Slide R - 50 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d. prime
212 84 147x x
3 2x 7 2
3 2x 7 2x 7
3 2x 7 2
Slide R - 51 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d. prime
212 84 147x x
3 2x 7 2
3 2x 7 2x 7
3 2x 7 2
Slide R - 52 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d.
28 12 8 27x x
x 17 x 11
x2 8x 9 x2 8x 3
x 1 x 5
x2 8x 9 x2 8x 3
Slide R - 53 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d.
28 12 8 27x x
x 17 x 11
x2 8x 9 x2 8x 3
x 1 x 5
x2 8x 9 x2 8x 3
Slide R - 54 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d.
18x2 15xy 24xy 20y2
3x 4 6x 5
3x 4y 6x 5y
3x 4y 6x 5y
18x 4y x 5y
Slide R - 55 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d.
18x2 15xy 24xy 20y2
3x 4 6x 5
3x 4y 6x 5y
3x 4y 6x 5y
18x 4y x 5y
Slide R - 56 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d. Prime
15z2 11z 12
3z 4 5z 3
3z 4 5z 3
15z 4 z 3
Slide R - 57 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Factor.
a.
b.
c.
d. Prime
15z2 11z 12
3z 4 5z 3
3z 4 5z 3
15z 4 z 3
Slide R - 58 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Use synthetic division to find the quotient and the remainder.
a.
b.
c.
d.
x5 x3 2 is divided by x 3
x4 3x3 9x2 26x 782; r: 232
x4 2x2; r: 8
x4 2; r: 8
x4 3x3 10x2 30x 90; r: 268
Slide R - 59 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Use synthetic division to find the quotient and the remainder.
a.
b.
c.
d.
x5 x3 2 is divided by x 3
x4 3x3 9x2 26x 782; r: 232
x4 2x2; r: 8
x4 2; r: 8
x4 3x3 10x2 30x 90; r: 268
Slide R - 60 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Reduce the rational expression to lowest terms.
a.
c.
3x2 17x 10
3x2 16x 5
x 2
x 1
3x 5
3x 5
3x 2
3x 1
x 3
x 2
b.
d.
Slide R - 61 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Reduce the rational expression to lowest terms.
a.
c.
3x2 17x 10
3x2 16x 5
x 2
x 1
3x 5
3x 5
3x 2
3x 1
x 3
x 2
b.
d.
Slide R - 62 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Divide.
a.
c.
x2 12x 27
x2 14x 45
x2 3x
x2 12x 35
x 7
x 7
x x 5
x 7
x
x
x 5 x 9
b.
d.
Slide R - 63 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Divide.
a.
c.
x2 12x 27
x2 14x 45
x2 3x
x2 12x 35
x 7
x 7
x x 5
x 7
x
x
x 5 x 9
b.
d.
Slide R - 64 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Add.
a.
c.
x 4
x2 5x 24
4x 5
x2 10x 16
5x 9
2x2 15x 8
5x2 19x 7
x 8 x 3 x 2
5x2 19x 7
x 8 x 3 x 2
5x 9
b.
d.
Slide R - 65 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Add.
a.
c.
x 4
x2 5x 24
4x 5
x2 10x 16
5x 9
2x2 15x 8
5x2 19x 7
x 8 x 3 x 2
5x2 19x 7
x 8 x 3 x 2
5x 9
b.
d.
Slide R - 66 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Simplify.
a.
c.
1314 x
14
x 145x
9
x 14
x
14x 70
x
14x 70
27x
14x 70
27x
14x 70
b.
d.
Slide R - 67 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Simplify.
a.
c.
1314 x
14
x 145x
9
x 14
x
14x 70
x
14x 70
27x
14x 70
27x
14x 70
b.
d.
Slide R - 68 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Simplify. Assume all variables are positive.
a.
b.
c.
d.
1000x4 y53
3xy xy23
10xy xy3
10xy xy23
10xy xy2
Slide R - 69 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Simplify. Assume all variables are positive.
a.
b.
c.
d.
1000x4 y53
3xy xy23
10xy xy3
10xy xy23
10xy xy2
Slide R - 70 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Rationalize the denominator.
a.
c.
11 6 2
7
1
11 6 2
7
7 6 2
11
b.
d.
3 2
3 2
Slide R - 71 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Rationalize the denominator.
a.
c.
11 6 2
7
1
11 6 2
7
7 6 2
11
b.
d.
3 2
3 2
Slide R - 72 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Simplify.
a.
c.
81
625
625
81
625
81b.
d. Not a real number
125
27
4 3
Slide R - 73 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Simplify.
a.
c.
81
625
625
81
625
81b.
d. Not a real number
125
27
4 3
Slide R - 74 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Simplify. Express the answer so that only positive exponents occur. Assume that all variables are positive.
a.
b.
c.
d.
25x6 y4 1 2
5x3y
x3y2
5x3y2
5x6 y2
Slide R - 75 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Prentice Hall
Simplify. Express the answer so that only positive exponents occur. Assume that all variables are positive.
a.
b.
c.
d.
25x6 y4 1 2
5x3y
x3y2
5x3y2
5x6 y2