CLEP: Precalculus

Algebraic Expressions, Equations and Inequalities - 20%

• Operations on algebraic expressions

According to Western Technical College, this might include:

• adds, subtracts, multiplies and divides monomial expressions
• adds, subtracts, multiplies, and divides algebraic fractions
• adds, subtracts, multiplies, and divides polynomials containing rational terms
• simplifies complex fractions containing variables
• Solving equations and inequalities, inc. linear, quadratic, absolute value, polynomial, rational, radical, exponential, logarithmic and trigonometric

Linear Functions
Quadratic Functions
Factorise quadratic expressions
Polynomials of Higher Degree
Rational Functions and Solving Rational Inequalities
Exponential Functions and The Natural Exponential Function
Logarithmic Functions and Exponential and Logarithmic Equations

• Solving systems of equations, inc. linear and nonlinear

Systems of Equations
According to Western Technical College, this might include:

• solves systems of equations using addition/subtraction
• solves systems of equations graphically
• solves systems of equations using substitution
• solves applied problems requiring the solution to a system of equations
• solves systems using determinants

Functions: concepts, properties and operations - 15%

• Concept of a function

What is a function?

• Properties of functions (e.g. domain, range)

The Domain and Range of a Function

• Function notation

Function Notation

• Performing symbolic operations with functions (e.g. evaluation, inverse functions)

Inverse Functions

Representations of Functions - 30%

• Operations and transformations on functions presented symbolically, graphically or in tabular form

Graphs of Functions
Graphing Shortcuts

• Basic properties of functions


• Recognizing elementary functions (linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, piecewise-defined) that are presented symbolically, graphically or tabulated

Analytic Geometry - 10%

• Analytic geometry of lines, circles, parabolas, ellipses and hyperbolas

Parabolas
Ellipses
Hyperbolas

Trigonometry and its Applications - 15%

• Basic trigonometric functions and their inverses

Trigonometric Functions
Inverse Trigonometric Functions

• Basic trigonometric ratios and identities (in right triangles and on the unit circle)

Trigonometric Identities

• Application of trigonometry in various problem-solving contexts

Applications of Trigonometry

Functions as Models - 10%

• Interpreting and constructing functions as models and translating ideas among symbolic, graphical, tabular and verbal representations of functions