Fundamentals of College Algebra Course Structure
I. Fundamental Algebraic Operations – 20%
- Operations with algebraic expressions
- Operations with polynomials (including factoring and expanding polynomials)
- Rational expressions
- Operations with positive, negative and fractional exponents
II. Complex Numbers – 4%
- Conjugate
- Basic Operations
III. Equations and Inequalities – 44%
- Linear equations and inequalities
- Quadratic equations and inequalities (including quadratic forms and solving quadratic inequalities)
- Absolute value equations and inequalities
- Systems of linear equations and inequalities
- Exponential and logarithmic equations
- Equations involving radicals
IV. Properties of Functions and their Graphs – 32%
- Coordinate systems
- Domain and range
- Operations of functions
- Inverse functions
- Linear functions
- Quadratic functions
- Polynomial functions
- Rational functions
- Exponential and logarithmic functions
Sample Questions
All test questions are in a multiple-choice format, with one correct answer and three incorrect options. The following are samples of the types of questions that may appear on the exam.
1. If x² ≠ 1, then
2. Which of the following is a solution of the equation x² + 3x – 2 = 0?
3. An experimental formula for the number of hours of sleep a child needs is S = 13.5 – (y/3), where S is the number of hours of sleep needed and y is the age of the child in years. According to this formula, with each passing year, a child needs:
- 1/3 hour less sleep
- 1/3 hour more sleep
- 1 hour less sleep
- 1 hour more sleep
4.
. 
5. Which of the following could be the equation of the graph below?
- y = 2 x2
- y = – x2 + 2
- y = x2 + 2
- x=y2 +2
Answers to sample questions:
1-C; 2-C; 3-A; 4-A; 5-C