About This Course
With the aid of technology, students study fundamental algebraic concepts and graphical analysis of functions.
Course Objectives
Upon successful completion of this course, students will be able to:
- Solve linear, quadratic, radical, absolute-value equations and inequalities;
- determine the equations of lines and circles and sketch their graphs;
- compose, graph and perform operations on functions;
- solve exponential and logarithmic equations;
- model real-world problems with linear, quadratic, exponential and logarithmic functions; and
- demonstrate proficiency in the use of a graphing calculator and educational software.
Material Includes
- Sullivan, M. & Sullivan, M. (2013). Algebra & trigonometry enhanced with graphing utilities. (6th ed.). New Jersey: Upper Saddle River, Pearson.
- SUPPLEMENTARY READINGS/MATERIALS
- Stewart, J., Redlin, L., & Watson, S. (2011). Algebra and trigonometry (3rd ed.). Pacific Grove: CA: Brooks/Cole Publishers.
- Stewart, J., Redlin, L., & Watson, S (2011). Precalculus mathematics for cal-culus. (6th ed.). Pacific Grove, CA: Brooks/Cole Publishers.
Curriculum
Week 1: Fundamental Concepts
A. Real numbers
i. Classification
ii. The real number line
iii. Properties
B. Polynomials
i. Factorization
ii. Operations
iii. Long and synthetic division
C. Rational expressions
i. Simplification
ii. Operations
D. Roots and rational exponents
E. Complex numbers
Week 2: Equations
A. Linear
B. Quadratic
C. Solution of polynomial equations by factoring
D. Rational
E. Complex Solutions
F. Other types
i. Radical
ii. Quadratic-form
iii. Absolute value
Week 2: Inequalities
A. Linear
B. Quadratic
C. Polynomial
D. Rational
E. Absolute value
Week 3 – 10: Coordinate Geometry
A. Distance and midpoint formulae
B. Intercepts and symmetry
C. Lines
D. Circles
Week 3 – 10: Relations and Functions
A. Distinguishing characteristics
B. Graphs and the vertical line test
C. Properties
i. Domain and range
ii. Even and odd
iii. Monotonicity
iv. Extreme values
D. Operations
i. Addition
ii. Subtraction
iii. Multiplication
iv. Division
v. Composition
vi. Inversion
E. Features of special functions
i. Constant
ii. Identity
iii. Square
iv. Cube
v. Square root
vi. Cube root
vii. Reciprocal
viii. Absolute Value
ix. Rational
x. Piecewise-defined
F. Transformations
i. Shifts
ii. Stretches
iii. Compressions
iv. Reflections
G. Linear and Quadratics
i. Properties and graphs
ii. Models
Week 11: Revision and Midterm Exam
Week 12: Polynomial Functions
A. Power functions
B. Zeros
i. Real
ii. Complex
C. Properties and graphs
Week 13: Rational Functions
A. Domain
B. Asymptotes
i. Ver-tical
ii. Horizontal
iii. Oblique
C. Graphs
Week 13: Exponential and Logarithmic Functions
A. Properties and graphs
B. Equations
C.
Week 14: Revision
Week 15: Finals
Your Instructors
Free
Enrollment validity:
Lifetime
