CLEP Precalculus study plan

Simplify and expand polynomial, rational, radical, and negative-exponent expressions without a calculator, checking each result by substitution

Solve linear and quadratic equations by factoring, completing the square, and the quadratic formula, and classify roots using the discriminant

Solve linear, polynomial, rational, and absolute-value inequalities and express solution sets in interval notation

Set up and solve work, mixture, and distance word problems by translating them into a single equation in one variable

Solve systems of two and three linear equations by substitution and elimination, and identify inconsistent or dependent systems

Compute domain and range of polynomial, rational, radical, and piecewise-defined functions from their formulas

Evaluate and simplify difference quotients for quadratic and rational functions

Combine functions by addition, subtraction, multiplication, division, and composition, and state the domain of each result

Classify functions as even, odd, or neither algebraically and confirm the classification graphically

Find inverse functions for one-to-one functions, verify with composition, and restrict domains where needed

Sketch parent graphs (linear, quadratic, cubic, absolute value, square root, reciprocal, exponential, logarithmic) and apply shifts, stretches, and reflections

Read domain, range, intercepts, intervals of increase and decrease, and extrema from a given graph

Sketch polynomial functions using end behavior, multiplicity of zeros, and sign analysis

Divide polynomials using synthetic division and apply the Remainder and Factor Theorems

Find all real and complex zeros of polynomial functions using the Rational Root Theorem and the Fundamental Theorem of Algebra

Graph rational functions by locating vertical, horizontal, and slant asymptotes and holes

Convert between exponential and logarithmic form and apply the product, quotient, and power properties of logarithms

Solve exponential and logarithmic equations, including those requiring domain checks for extraneous solutions

Model growth and decay problems using exponential functions and solve for time or rate

Interpret tabular data by identifying the function family (linear, exponential, logarithmic, polynomial) that best fits a table of values

Find distance and midpoint between points and write equations of circles, parabolas, ellipses, and hyperbolas in standard form by completing the square

Identify the conic section from a general second-degree equation and state its key features

Convert angles between degrees and radians and compute arc length and sector area

Define the six trigonometric functions using right triangles and the unit circle, and evaluate them at standard angles

Prove and apply Pythagorean, sum, difference, double-angle, and half-angle identities to simplify expressions

Solve trigonometric equations over a stated interval and express general solutions

Graph sine, cosine, and tangent functions with amplitude, period, phase shift, and vertical shift

Solve right and oblique triangle application problems using the Law of Sines, Law of Cosines, and inverse trigonometric functions

Build a function model from a described scenario, state its domain, and justify why the model fits

Complete two full-length timed practice tests under exam conditions and record domain-level accuracy

Re-teach the two weakest domains by rewriting their core rules in your own words and redoing missed problems

Memorize and apply a calculator strategy sheet covering graphing, tables, and root finding