INSTRUCTOR’S TESTING
MANUAL
College Algebra and Trigonometry, 7th edition
by Margaret L. Lial, John Hornsby
TU
TO
R
G
U
R
U
, Table of Content
R. Review of Basic Concepts
R-1 Fractions, Decimals, and Percents
R-2 Sets and Real Numbers
R-3 Real Number Operations and Properties
R-4 Integer and Rational Exponents
R-5 Polynomials
R-6 Factoring Polynomials
R-7 Rational Expressions
R-8 Radical Expressions
1. Equations and Inequalities
1-1 Linear Equations
TU
1-2 Applications and Modeling with Linear Equations
1-3 Complex Numbers
1-4 Quadratic Equations
1-5 Applications and Modeling with Quadratic Equations
1-6 Other Types of Equations and Applications
1-7 Inequalities
TO
1-8 Absolute Value Equations and Inequalities
2. Graphs and Functions
2-1 Rectangular Coordinates and Graphs
2-2 Circles
2-3 Functions
2-4 Linear Functions
2-5 Equations of Lines and Linear Models
R
2-6 Graphs of Basic Functions
2-7 Graphing Techniques
2-8 Function Operations and Composition
G
3. Polynomial and Rational Functions
3-1 Quadratic Functions and Models
3-2 Synthetic Division
U
3-3 Zeros of Polynomial Functions
3-4 Polynomial Functions: Graphs, Applications, and Models
3-5 Rational Functions: Graphs, Applications, and Models
R
3-6 Polynomial and Rational Inequalities
3-7 Variation
4. Inverse, Exponential, and Logarithmic Functions
4-1 Inverse Functions
U
4-2 Exponential Functions
4-3 Logarithmic Functions
4-4 Evaluating Logarithms and the Change-of-Base Theorem
4-5 Exponential and Logarithmic Equations
4-6 Applications of Models of Exponential Growth and Decay
5. Trigonometric Functions
5-1 Angles
5-2 Trigonometric Functions
5-3 Trigonometric Function Values and Angle Measures
5-4 Solutions and Applications of Right Triangles
6. The Circular Functions and Their Graphs
6-1 Radian Measure
,6-2 The Unit Circle and Circular Functions
6-3 Graphs of the Sine and Cosine Functions
6-4 Translations of the Graphs of the Sine and Cosine Functions
6-5 Graphs of the Tangent and Cotangent Functions
6-6 Graphs of the Secant and Cosecant Functions
6-7 Harmonic Motion
7. Trigonometric Identities and Equations
7-1 Fundamental Identities
7-2 Verifying Trigonometric Identities
7-3 Sum and Difference Identities
7-4 Double-Angle and Half-Angle Identities
7-5 Inverse Circular Functions
7-6 Trigonometric Equations
TU
7-7 Equations Involving Inverse Trigonometric Functions
8. Applications of Trigonometry
8-1 The Law of Sines
8-2 The Law of Cosines
8-3 Geometrically Defined Vectors and Applications
8-4 Algebraically Defined Vectors and the Dot Product
TO
8-5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients
8-6 De Moivre's Theorem; Powers and Roots of Complex Numbers
8-7 Polar Equations and Graphs
8-8 Parametric Equations, Graphs, and Applications
9. Systems and Matrices
9-1 Systems of Linear Equations
9-2 Matrix Solution of Linear Systems
R
9-3 Determinant Solution of Linear Systems
9-4 Partial Fractions
9-5 Nonlinear Systems of Equations
G
9-6 Systems of Inequalities and Linear Programming
9-7 Properties of Matrices
9-8 Matrix Inverses
U
10. Analytic Geometry
10-1 Parabolas
10-2 Ellipses
R
10-3 Hyperbolas
10-4 Summary of the Conic Sections
11. Further Topics in Algebra
11-1 Sequences and Series
U
11-2 Arithmetic Sequences and Series
11-3 Geometric Sequences and Series
11-4 The Binomial Theorem
11-5 Mathematical Induction
11-6 Basics of Counting Theory
11-7 Basics of Probability
, JHGFDSA
1
CHAPTER R, FORM A NAME
COLLEGE ALGEBRA AND TRIGONOMETRY DATE
¹' 54 16 '¹
1. Let A = (- 9.6, , 6 , 0, 13, 2.15, ,
't 7 5 'j
List the elements of A that belong to the given set.
a. Natural numbers 1. a.
b. Rational numbers b.
c. Irrational numbers c.
2. Evaluate the expression if x = -2 , y = -4 , and z = 1 : 2.
TU
2y - x 2
( y - 3z)
2
3. Identify the property illustrated. Let a, b, and c represent any
real numbers.
a. (a + b)c = ac + bc 3. a.
TO
b. a + Fb +(-b)l = a + 0 b.
L ⎦
l'1 2ıh 3 1 'l2 3ıh
c. ⋅ ⋅ = ⋅ ⋅
'y2 3jı 4 2 y' 3 4jı
c.
1 1
( p + 3) = ( p + 3)⋅
R
d. d.
2 2
Perform the indicated operations.
G
4. F l
2
L (3a + b)- 2 ⎦ 4.
5. (3x2 - 2x -5)-(2x3 + x - 7)+ 2x2 (x -3) 5.
U
6. (x2 - x + 2)(2x -3) 6.
R
7. F lF l
L (x - y ) -7 ⎦ L (x - y)+ 7 ⎦ 7.
8. (2x + 5)
3
8.
U
3y4 -5 y3 -14 y2 +10 y
9. 9.
y2 - 2
10. x2 -9 ⋅ x -1 10.
x2 - x x2 -3x
3x x 3x +1
11. - - 11.
x - 4 x + 4 16 - x2
Copyright © 2021 Pearson Education, Inc.
MANUAL
College Algebra and Trigonometry, 7th edition
by Margaret L. Lial, John Hornsby
TU
TO
R
G
U
R
U
, Table of Content
R. Review of Basic Concepts
R-1 Fractions, Decimals, and Percents
R-2 Sets and Real Numbers
R-3 Real Number Operations and Properties
R-4 Integer and Rational Exponents
R-5 Polynomials
R-6 Factoring Polynomials
R-7 Rational Expressions
R-8 Radical Expressions
1. Equations and Inequalities
1-1 Linear Equations
TU
1-2 Applications and Modeling with Linear Equations
1-3 Complex Numbers
1-4 Quadratic Equations
1-5 Applications and Modeling with Quadratic Equations
1-6 Other Types of Equations and Applications
1-7 Inequalities
TO
1-8 Absolute Value Equations and Inequalities
2. Graphs and Functions
2-1 Rectangular Coordinates and Graphs
2-2 Circles
2-3 Functions
2-4 Linear Functions
2-5 Equations of Lines and Linear Models
R
2-6 Graphs of Basic Functions
2-7 Graphing Techniques
2-8 Function Operations and Composition
G
3. Polynomial and Rational Functions
3-1 Quadratic Functions and Models
3-2 Synthetic Division
U
3-3 Zeros of Polynomial Functions
3-4 Polynomial Functions: Graphs, Applications, and Models
3-5 Rational Functions: Graphs, Applications, and Models
R
3-6 Polynomial and Rational Inequalities
3-7 Variation
4. Inverse, Exponential, and Logarithmic Functions
4-1 Inverse Functions
U
4-2 Exponential Functions
4-3 Logarithmic Functions
4-4 Evaluating Logarithms and the Change-of-Base Theorem
4-5 Exponential and Logarithmic Equations
4-6 Applications of Models of Exponential Growth and Decay
5. Trigonometric Functions
5-1 Angles
5-2 Trigonometric Functions
5-3 Trigonometric Function Values and Angle Measures
5-4 Solutions and Applications of Right Triangles
6. The Circular Functions and Their Graphs
6-1 Radian Measure
,6-2 The Unit Circle and Circular Functions
6-3 Graphs of the Sine and Cosine Functions
6-4 Translations of the Graphs of the Sine and Cosine Functions
6-5 Graphs of the Tangent and Cotangent Functions
6-6 Graphs of the Secant and Cosecant Functions
6-7 Harmonic Motion
7. Trigonometric Identities and Equations
7-1 Fundamental Identities
7-2 Verifying Trigonometric Identities
7-3 Sum and Difference Identities
7-4 Double-Angle and Half-Angle Identities
7-5 Inverse Circular Functions
7-6 Trigonometric Equations
TU
7-7 Equations Involving Inverse Trigonometric Functions
8. Applications of Trigonometry
8-1 The Law of Sines
8-2 The Law of Cosines
8-3 Geometrically Defined Vectors and Applications
8-4 Algebraically Defined Vectors and the Dot Product
TO
8-5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients
8-6 De Moivre's Theorem; Powers and Roots of Complex Numbers
8-7 Polar Equations and Graphs
8-8 Parametric Equations, Graphs, and Applications
9. Systems and Matrices
9-1 Systems of Linear Equations
9-2 Matrix Solution of Linear Systems
R
9-3 Determinant Solution of Linear Systems
9-4 Partial Fractions
9-5 Nonlinear Systems of Equations
G
9-6 Systems of Inequalities and Linear Programming
9-7 Properties of Matrices
9-8 Matrix Inverses
U
10. Analytic Geometry
10-1 Parabolas
10-2 Ellipses
R
10-3 Hyperbolas
10-4 Summary of the Conic Sections
11. Further Topics in Algebra
11-1 Sequences and Series
U
11-2 Arithmetic Sequences and Series
11-3 Geometric Sequences and Series
11-4 The Binomial Theorem
11-5 Mathematical Induction
11-6 Basics of Counting Theory
11-7 Basics of Probability
, JHGFDSA
1
CHAPTER R, FORM A NAME
COLLEGE ALGEBRA AND TRIGONOMETRY DATE
¹' 54 16 '¹
1. Let A = (- 9.6, , 6 , 0, 13, 2.15, ,
't 7 5 'j
List the elements of A that belong to the given set.
a. Natural numbers 1. a.
b. Rational numbers b.
c. Irrational numbers c.
2. Evaluate the expression if x = -2 , y = -4 , and z = 1 : 2.
TU
2y - x 2
( y - 3z)
2
3. Identify the property illustrated. Let a, b, and c represent any
real numbers.
a. (a + b)c = ac + bc 3. a.
TO
b. a + Fb +(-b)l = a + 0 b.
L ⎦
l'1 2ıh 3 1 'l2 3ıh
c. ⋅ ⋅ = ⋅ ⋅
'y2 3jı 4 2 y' 3 4jı
c.
1 1
( p + 3) = ( p + 3)⋅
R
d. d.
2 2
Perform the indicated operations.
G
4. F l
2
L (3a + b)- 2 ⎦ 4.
5. (3x2 - 2x -5)-(2x3 + x - 7)+ 2x2 (x -3) 5.
U
6. (x2 - x + 2)(2x -3) 6.
R
7. F lF l
L (x - y ) -7 ⎦ L (x - y)+ 7 ⎦ 7.
8. (2x + 5)
3
8.
U
3y4 -5 y3 -14 y2 +10 y
9. 9.
y2 - 2
10. x2 -9 ⋅ x -1 10.
x2 - x x2 -3x
3x x 3x +1
11. - - 11.
x - 4 x + 4 16 - x2
Copyright © 2021 Pearson Education, Inc.
