Precalculus Exam Info
The Precalculus exam assesses student mastery of skills and concepts required for success in a first-semester calculus course. A large portion of the exam is devoted to testing a student’s understanding of functions and their properties. Many of the questions test a student’s knowledge of specific properties of the following types of functions: linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise defined. Questions on the exam will present these types of functions symbolically, graphically, verbally or in tabular form. A solid understanding of these types of functions is at the core of all precalculus courses, and it is a prerequisite for enrolling in calculus and other college-level mathematics courses.
Knowledge and Skills Required
Algebraic Expressions, Equations, and Inequalities20%
- Ability to perform operations on algebraic expressions
- Ability to solve equations and inequalities, including linear, quadratic, absolute value, polynomial, rational, radical, exponential, logarithmic, and trigonometric
- Ability to solve systems of equations, including linear and nonlinear
Functions: Concept, Properties, and Operations15%
- Ability to demonstrate an understanding of the concept of a function, the general properties of functions (e.g., domain and range), function notation, and to perform symbolic operations with functions (e.g., evaluation and inverse functions)
Representations of Functions: Symbolic, Graphical, and Tabular30%
- Ability to recognize and perform operations and transformations on functions presented symbolically, graphically, or in tabular form
- Ability to demonstrate an understanding of basic properties of functions and to recognize elementary functions (linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions) that are presented symbolically, graphically, or in tabular form
Analytic Geometry10%
- Ability to demonstrate an understanding of the analytic geometry of lines, circles, parabolas, ellipses, and hyperbolas
Trigonometry and its Applications*15%
- Ability to demonstrate an understanding of the basic trigonometric functions and their inverses and to apply the basic trigonometric ratios and identities (in right triangles and on the unit circle)
- Ability to apply trigonometry in various problem-solving contexts
Functions as Models10%
- Ability to interpret and construct functions as models and to translate ideas among symbolic, graphical, tabular, and verbal representations of functions
*Note that trigonometry permeates most of the major topics and accounts for more than 15% of the exam. The actual proportion of exam questions that requires knowledge of either right triangle trigonometry or the properties of the trigonometric functions is approximately 30%–40%.