CLEP College Algebra study plan
CLEP College Algebra · Give each week a clear focus.
8 weeks · About 6 hours per week
Functions and their properties
Define a function, evaluate it at numeric and symbolic inputs, and determine its domain and range from a formula or a verbal description.
Compute and simplify difference quotients for linear and quadratic functions, showing each algebraic step.
Identify whether a relation given as a table, set of ordered pairs, or equation represents a function, and justify the conclusion.
Sketch parent functions (linear, quadratic, cubic, absolute value, square root, reciprocal) and state their key features: intercepts, symmetry, end behavior, and extrema.
Your checkpoint
A one-page reference sheet of the six parent functions with hand-drawn graphs, plus 20 worked function-evaluation and domain/range problems scored at 80% or better.
Functions and their properties
Apply vertical and horizontal shifts, reflections, and stretches/compressions to parent graphs and write the transformed equation.
Determine whether a function is even, odd, or neither using both algebraic and graphical tests.
Find and simplify the composition of two functions and state the domain of the composite.
Construct the inverse of a one-to-one function algebraically and verify it using composition.
Your checkpoint
A transformations and inverses problem set of 25 items (graphing, equation writing, composition, inverse verification) with a corrected error log for every miss.
Equations and inequalities
Solve linear equations and inequalities, including compound inequalities, and express solution sets in interval notation.
Solve absolute value equations and inequalities and interpret the solutions on a number line.
Solve quadratic equations by factoring, completing the square, and the quadratic formula, choosing the most efficient method.
Set up and solve word problems that translate into linear or quadratic equations (rate, mixture, area, projectile).
Your checkpoint
A 30-problem mixed equation/inequality set, with a written justification of method choice for each quadratic, scored at 80% or better.
Equations and inequalities & Algebraic operations
Solve rational equations and check for extraneous solutions.
Solve radical equations and identify extraneous roots introduced by squaring.
Solve systems of two linear equations by substitution and elimination, and interpret the geometric meaning of no solution or infinitely many.
Simplify polynomial and rational expressions by factoring, expanding, and canceling common factors.
Your checkpoint
A timed 25-minute, 15-question quiz covering rational, radical, and system problems, plus a review of every incorrect item with the corrected solution written out.
Algebraic operations
Perform addition, subtraction, multiplication, and division of polynomials and state the degree and leading coefficient of the result.
Factor polynomials completely, including difference of squares, sum/difference of cubes, and grouping.
Apply the remainder and factor theorems to test candidate roots and factor higher-degree polynomials.
Simplify complex rational expressions by finding a common denominator and reducing.
Your checkpoint
A factoring and polynomial-operations portfolio of 30 problems organized by technique, with a short note explaining when each technique applies.
Algebraic operations & Number systems and operations
Apply the laws of exponents and radicals to simplify expressions with rational exponents.
Convert between radical and rational-exponent form and evaluate numerical expressions without a calculator.
Classify numbers within the real number system (natural, integer, rational, irrational) and place them on a number line.
Perform operations with complex numbers and simplify powers of i.
Your checkpoint
A two-column cheat sheet (exponent/radical rules on one side, number-system and complex-number rules on the other) plus 20 simplification problems scored at 85% or better.
Number systems and operations & Functions and their properties
Use function notation to model and solve applied problems involving exponential growth and decay.
Evaluate and simplify logarithmic expressions using the definition of a logarithm and its properties.
Solve exponential and logarithmic equations, including those requiring the same-base technique or rewriting.
Interpret slope and rate of change in context and connect linear functions to proportional reasoning.
Your checkpoint
A full-length, timed 60-minute practice test (all four domains, 60 questions) with a score report by domain identifying the two weakest subtopics.
Algebraic operations & Equations and inequalities & Functions and their properties & Number systems and operations
Review the two weakest subtopics identified in week 7 and rework missed problems until each is solved correctly without notes.
Complete a second timed 60-minute practice test under exam conditions, including the on-screen calculator policy.
Build a one-page formula and strategy sheet from memory to confirm retention of key rules.
Practice pacing by completing 20 mixed problems in 25 minutes with at least 80% accuracy.
Your checkpoint
Two timed practice-test score reports showing improvement over week 7, plus a final one-page handwritten formula sheet and a list of remaining weak areas with a plan to review them before test day.
Milestones
Week 2: Can graph all six parent functions and their transformations from memory and correctly find an inverse function, verified by composition, on 8 of 10 problems.
Week 4: Scores 80% or better on the timed mixed equation/inequality quiz and can explain why a rational or radical solution is extraneous.
Week 6: Simplifies rational-exponent and complex-number expressions with 85% accuracy and can classify any given real number correctly.
Week 7: Completes the first full-length timed practice test with a domain-by-domain score report and identifies the two weakest subtopics.
Week 8: Improves the full-length practice-test score by at least 10 percentage points over week 7 and solves 20 mixed problems in 25 minutes at 80% or better.