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Syllabus and Contents of Math 140

Text Book.

Precalculus: Functions and Graphs (Mc Graw Hill), 6th Edition,  with supporting web site including materials for instructor and test bank.

Year: 2008,

Authors: Raymond A. Barnett, Michael R.  Ziegler and Karl E. Byleen.

Chapter 1: Equations and Inequalities.

We start with some the brief introduction from set theory, defining the operations and give the students the definitions of Natural numbers, Integers, Rational numbers, Irrational numbers and real numbers.

1.1.         Linear equations and applications

Definitions of the algebraic equations, domain, difference between the expressions and equations, set of solutions and solutions, identity equations and conditionally ones, linear equations, solutions of equations, solution of word problems based on the strategy given in the book and using different word problems.

Examples: 1, 2, 3, 4, 5, 8.

Exercises for teachers: 1, 4, 6, 11, 15, 19, 30, 45, 47, 49, 53.

Exercises for students: 2, 5, 9, 16, 23, 33, 50.

1.2 Linear inequalities

Understanding inequality relations and interval notations, solutions of linear inequalities, applications to chemistry. Definition 1, interval notations, definition 2. Theorem 2.1

Examples: 1, 2, 3, 4, 5, 6.

Exercises for teachers: 1, 4, 6, 8, 12, 25, 28, 33, 53, 75, 76. 79.

Exercises for students:  3, 7, 13, 27, 30, 50, 70, 80.

1.3             Absolute Value in equations and inequalities

Relating absolute value and distance, solving absolute value equations and inequalities, using absolute value to solve radical inequalities. Definition 1, Theorem 1, Definition 2, Table 1, Theorem 2, Theorem 3.

Examples 1, 2, 3, 4, 6, 7, 8

Exercises for teacher: 29, 32, 41, 43, 59, 67, 69, 70, 76, 79.

Exercises for Students:  27, 33, 45, 50, 60, 75.

1.4             Complex Numbers

Understanding complex number terminology, performing operation, solving equations involving complex numbers. Definition 1, Definition 2, Definition 3, Definition 4.

Examples: 1, 2, 4, 5, 8.

Exercises for teacher: 1, 5, 11, 13, 15, 30, 59, 73, 77

Exercises for students:  3, 6, 7, 17, 23, 25, 76, and 80.

Using factoring to solve Q.E, using the square rot property to solve Q. E., using completing the square to solve Q. E., Using Quadratic formula to solve Q. E., Solving applications involving Q. E. Definition 1, Theorem 1, Table1.

Examples: 1, 2, 4, 5, 8, 10

Exercises for teachers: 1, 11, 15, 19, 27, 34, 35, 75,

Exercises for students: 3, 8, 24, 37, 44, 47, 51, 52, 77.

Chapter 3:  (Functions)

Section 3.2: Definition of function, functions defined by equations, Function notation and applications. Examples 1, 2, Theorem 1, Examples 3, 4, 5.

Exercises for tutorial: 1. 2, 4, 28, 38, 88.

Exercises for students: 3, 27, 37, 80, 87

Section 3.2:  Graphing functions, Linear Functions. Examples 1, 2, 4, 5, Definitions 1, 2,

Exercises for tutorial: 7, 19, 24, 30.

Exercises for students: 8, 20, 28, 33.

Section 3.3: Definitions of odd and even functions, Example 6.

Exercises for tutorial: 33, 47, 56

Exercises for students: 34, 50, 57, 64, 70

Section 3.5:  Operations on Functions including additions, subtraction, multiplication, division and composition. Examples, 1, 2, 4, 6, definitions 1, 2.

Exercises for Tutorial: 5, 21, 34, 50

Exercises for Students: 8, 10, 20, 30, 34, 40, 52

Section 3.6: Inverse Functions

One-to-one functions, definitions 1, 2, Theorems 1, 2, 3, 4, 5, 6. Examples 1, 2, 4,

Exercises for tutorial: 5, 8, 24, 33

Exercises for students: 6, 9, 25, 28, 30, 36.

Chapter 5: Exponential and Logarithmic Functions.

Section 5.1: Definition and graph of exponential function, properties of the function, base e, and compound interest, Definitions 1, 2, Theorem 1.  Examples 1, 2, 3, 4, 5.

Exercises for tutorial:  15, 33, 49, 56.

Exercises for students: 14, 18, 38, 40, 50, 55.

Section 5.2: Logarithmic Functions

Definition and graph of the function, from logarithmic to exponential, properties of logarithmic functions, Definitions 1, Theorems 1, 2, Examples 1, 2, 3, 4, 5, 8, 9.

Exercises for tutorial:  2, 9, 33, 83, 90, 107.

Exercises for students: 11, 123, 43, 58, 70, 80, 85, 93, 100, 110.

Section 5.5: Exponential and logarithmic equations: Examples 1, 2, 4, 5, 7.

Exercises for tutorial: 3, 16, 22, 28, 35, and 45.

Exercises for students: 5, 8, 16, 27, 38, 48, 52.

Chapter 6: Trigonometric Functions

Section 6.1: Angels and their measure, Definitions 1, 2 and some examples and some exercises (up to the instructor).

Section 6.3: Solving right triangle including definitions and Examples 1, 2 and some exercises (up to the instructor).

Section 6.4:  Properties of the trigonometric functions including basic identities, sign properties, periodic functions, reference triangle Definitions 1, 2, Examples 1, 2, 3.

Exercises for Tutorial: 1, 13, 16, 25, 47, 51. 56,

Exercises for Students: 3, 6, 18, 37, 48, 50, 54, 55.

Chapter 9: Additional Topics in Analytic Geometry.

Section 9.1: Definition 1 of parabola and its graph and Theorem 1. Examples 1, 2, 3.

Exercises for Tutorial:  1, 8, 14, 33 36

Exercises for students: 4, 10, 15, 22, 30, 36.

Section  9.2: . Definition 1 of ellipse and its graph and Theorem 1. Examples 1, 2, 3

Exercises for Tutorial: 2, 6, 31, 33.

Exercises for Students: 3, 8, 12, 14, 16, 34.

Section 9.3: Definition 1 of hyperbola, its graph and Theorem 1. Examples ,2, 3, 4.

Exercises for Tutorial:  1, 3, 5, 8, 14.

Exercises for Students: 2, 5, 10, 12, 16.29, 35.

Chapter 10: Systems of Equations and Inequalities, Matrices.

Section 10.1: Systems of linear equations in two variables.

Examples 1, 2, 3, 4, 5

Exercises for tutorial: 5, 10, 16, 28.

Exercises for students: 6, 9, 14, 18, 27, 29.

Section 10.4:  Matrix operations (but before this we just take the definition of the matrix from section 10.3). Addition, subtraction and matrix product.

Examples 1, 3, 4, 8,

Exercises for Tutorial: 2, 4, 8, 16.

Exercises for students: 3, 5, 7, 10, 14, 18, 22, 24.