A good CLEP Precalculus 30-day study plan should spend most of its time on functions. College Board describes the CLEP Precalculus exam as about 48 questions in about 90 minutes, split into a calculator section and a no-calculator section. The official topic weights put the largest emphasis on representations of functions, followed by algebraic equations and inequalities, function properties, trigonometry, analytic geometry, and modeling.
Use the official College Board CLEP Precalculus page for current exam details. ViewMath is an independent publisher and is not affiliated with or endorsed by College Board or CLEP.
Before Day 1: Take a Diagnostic
Before reviewing, answer 20 mixed questions without notes: five algebra questions, five function questions, four trigonometry questions, three analytic geometry questions, and three modeling or graph questions. Sort your misses by topic. If you miss more than half of the algebra questions, add extra Algebra 2 review before moving quickly through precalculus.
30-Day CLEP Precalculus Plan
| Days | Focus | Daily Task | Checkpoint |
|---|---|---|---|
| 1-5 | Algebra foundations | Equations, inequalities, exponents, radicals, rational expressions, logarithms | Can solve mixed equations without a calculator |
| 6-12 | Functions | Domain, range, notation, composition, inverses, transformations | Can move between equation, graph, table, and words |
| 13-18 | Graph representations | Polynomial, rational, exponential, logarithmic, piecewise, and trig graphs | Can identify intercepts, asymptotes, zeros, and end behavior |
| 19-23 | Trigonometry | Unit circle, right-triangle trig, identities, inverse trig, applications | Can work in radians and degrees |
| 24-26 | Analytic geometry | Lines, circles, parabolas, ellipses, hyperbolas | Can read standard forms |
| 27-30 | Full review | Timed practice, calculator practice, error log, formula refresh | Can explain every missed problem |
Week 1: Algebra Foundations
Do not skip algebra. CLEP Precalculus questions often look like function questions, but the work underneath is equation solving. Review factoring, rational equations, exponent rules, radicals, and logarithms.
Example: Solve log2(x – 1) = 4. Convert to exponential form: x – 1 = 16, so x = 17. Then check the domain: x – 1 must be positive, so 17 is valid.
Week 2: Functions and Transformations
Functions are the center of the exam. Practice evaluating functions, composing functions, finding inverses, and identifying transformations.
Example: If f(x) = x^2 – 3 and g(x) = 2x + 1, find f(g(2)). First g(2) = 5. Then f(5) = 25 – 3 = 22.
Week 3: Graphs and Trigonometry
College Board notes that questions may present functions symbolically, graphically, verbally, or in tables. Practice reading features from graphs: zeros, intercepts, maximums, minimums, asymptotes, increasing intervals, and transformations.
For trigonometry, memorize the unit-circle values, but do not stop there. You also need quadrant signs, radians, inverse trig restrictions, and applications.
Week 4: Analytic Geometry and Timed Practice
Review conic sections in standard form. You do not need a full analytic geometry course, but you should recognize circles, parabolas, ellipses, and hyperbolas and know what the key numbers mean.
Example: (x – 3)^2 + (y + 2)^2 = 49 is a circle with center (3, -2) and radius 7.
Daily Schedule
- 10 minutes: Formula and vocabulary review.
- 30 minutes: Topic practice from the current week.
- 20 minutes: Mixed problems from older topics.
- 10 minutes: Error log. Rewrite one missed problem correctly.
Final Four Days
Day 27: Timed half test. Simulate calculator and no-calculator work separately.
Day 28: Review every missed question. Sort misses by topic and cause.
Day 29: Target the two weakest areas only. Do not scatter your attention.
Day 30: Light review, calculator familiarization, exact trig values, and rest.
Calculator and No-Calculator Balance
The official CLEP Precalculus format makes calculator strategy important, but the calculator should not replace algebra. During the calculator section, practice graphing functions, finding zeros, checking intersections, and using tables. During no-calculator practice, focus on exact values, symbolic manipulation, domains, factoring, and simple logarithm or exponential equations.
A useful rule is 70/30: spend about 70% of your study time solving by hand and 30% learning when the graphing calculator is faster. If you use a calculator on every practice problem, the no-calculator section will feel much harder than it should.
Priority Topic Checklist
- Can you identify domain restrictions for square roots, rational functions, and logarithms?
- Can you compose two functions and find a simple inverse?
- Can you recognize parent functions from graphs?
- Can you use radians and degrees without mixing them?
- Can you find circle centers and radii from standard form?
- Can you explain whether a model is linear, exponential, logarithmic, or trigonometric?
Practice Questions
- Find the domain of f(x) = sqrt(2x – 6).
- Solve 3^(x + 1) = 81.
- Find the inverse of f(x) = 4x – 7.
- Find cos(pi).
- Find the vertex of y = (x + 5)^2 – 9.
Answers: 1. x >= 3. 2. x = 3. 3. f^-1(x) = (x + 7)/4. 4. -1. 5. (-5, -9).
ViewMath CLEP Precalculus Resources
Use a CLEP Precalculus study guide for the first two weeks, a workbook or question set for topic practice, and practice tests near the end. A 30-day plan works best when you do not spend all 30 days reading; most days should include active problem solving and correction.
If you fall behind, do not restart the whole plan. Preserve the order: algebra foundations, functions, graph representations, trigonometry, analytic geometry, then mixed practice. Skip lower-priority repetition before you skip full mixed review, because the last week is when students learn how topics appear together on the exam.
Keep every missed question until you can solve it twice: once immediately after review and once again two or three days later. That second attempt is what shows whether the skill is actually retained.
