The Mathematics Department has adopted the following best practices for teaching this course: offering or awarding extra-credit is forbidden, the allowance of multiple attempts at exams is forbidden, and an approved on-site proctor for online course exams is required.
A. Linear Equations and Inequalities
1. Linear equations in one variable.
3. Applications-word problems.
4. Linear inequalities in one variable.
5. Absolute value equations.
6. Compound inequalities.
7. Absolute value inequalities.
B. Exponents and Polynomials
1. Integer Exponents-zero exponent, product rule, quotient rule, power rule.
2. Polynomials – addition and subtraction.
3. Multiplication of polynomials.
4. Greatest common factors; factoring by grouping.
5. Factoring trinomials.
6. Special factoring – difference of squares, sum of cubes, difference of cubes.
7. General methods of factoring.
8. Solving equations by factoring.
C. Rational Expressions
1. Basics of rational expressions.
2. Multiplication and division of rational expressions.
3. Addition and subtraction of rational expressions.
4. Complex fractions.
5. Dividing polynomials by monomials and by polynomials.
6. Synthetic division.
7. Equations and rational expressions.
8. Applications-work problems and motion problems.
D. Rational Exponents and Radicals
1. Rational exponents.
3. Simplifying radicals.
4. Adding and subtracting radical expressions.
5. Equations with numbers.
6. Complex numbers.
E. Quadratic Equations and Inequalities
1. Solving quadratic equations by completing the square.
2. The quadratic formula.
3. The discriminant and the sum and product of solutions.
4. Equations and quadratic in form.
5. Formulas and applications.
6. Nonlinear inequalities.
F. The Straight Line
1. The rectangular coordinate system.
2. The slope of a line.
3. Linear equations.
4. Linear inequalities.
G. Systems of Linear Equations
1. Linear systems of equations in two variables.
2. Applications of linear systems of equations.
3. Linear systems of equations in three variables.
5. Solution of linear systems of equations by determinants – Cramer’s Rule.
6. Solution of linear systems of equations by Matrix Methods (optional).
H. Exponential and Logarithmic Functions
1. Graphs of the exponential and logarithmic functions.
2. Properties of logarithms.
3. Solving equations involving exponents and logarithms.
4. Application problems.
I. Introduction to Conic Sections
1. The parabola.
2. The circle and the ellipse.
3. The hyperbola.
4. Nonlinear systems of equations.
5. Second-degree inequalities.
J. Selected Algebraic Applications To Be Chosen From:
1. Mathematics: other branches.
2. Biological Sciences: e.g., general biology, anatomy, physiology, microbiology.
3. Physical Sciences: e.g., chemistry, physics, geology, astronomy, oceanography.
4. Computer Sciences: e.g., computer graphics, computer animation.