These CLEP Precalculus practice questions are meant to help students find weak areas before committing to a full-length practice test. The official College Board CLEP Precalculus page describes an exam of about 48 questions in about 90 minutes, with a graphing calculator provided for one section and no calculator for the other section. That means your practice should include both calculator-friendly graph interpretation and no-calculator exact work.
ViewMath is an independent publisher and is not affiliated with or endorsed by College Board or the CLEP program. CLEP is a trademark of College Board. For current official details, visit the College Board CLEP Precalculus page.
How to Use This Mini Practice Set
Set a timer for 30-35 minutes. Work without notes. If you do not know how to start a question within one minute, mark it and move on. Afterward, sort missed questions by topic: functions, equations, trigonometry, analytic geometry, or modeling.
CLEP Precalculus Practice Questions
1. Find the domain of f(x) = sqrt(x – 5).
2. If f(x) = 2x – 3 and g(x) = x^2 + 1, find f(g(4)).
3. Solve x^2 – 5x – 14 = 0.
4. Find the inverse of f(x) = (x – 4) / 3.
5. Solve log2(x) = 5.
6. If 3^x = 81, find x.
7. Find the x-intercepts of y = x^2 – 9.
8. A function has vertical asymptote x = 2 and horizontal asymptote y = 0. Which parent type is most likely: linear, quadratic, rational, or exponential?
9. Find sin(30 degrees).
10. Find cos(2pi/3).
11. Simplify tan(theta) if sin(theta) = 3/5 and cos(theta) = 4/5.
12. A circle has equation (x – 2)^2 + (y + 1)^2 = 25. What are its center and radius?
13. A parabola has equation y = (x – 3)^2 – 4. What is its vertex?
14. The function h(x) = 4(1.2)^x models growth. What is h(0)?
15. A car rental costs $45 per day plus a fixed $60 fee. Write a function C(d) for the cost of d days, then find C(5).
Answer Key with Explanations
1. The expression under a square root must be nonnegative: x – 5 >= 0, so x >= 5.
2. g(4) = 4^2 + 1 = 17. Then f(17) = 34 – 3 = 31.
3. x^2 – 5x – 14 = (x – 7)(x + 2), so x = 7 or -2.
4. Let y = (x – 4) / 3. Then 3y = x – 4, so x = 3y + 4. The inverse is f^-1(x) = 3x + 4.
5. log2(x) = 5 means 2^5 = x, so x = 32.
6. 81 = 3^4, so x = 4.
7. Set y = 0: x^2 – 9 = 0, so x = -3 or 3.
8. A vertical asymptote and horizontal asymptote are common in rational functions.
9. sin(30 degrees) = 1/2.
10. 2pi/3 is 120 degrees, so cos(2pi/3) = -1/2.
11. tan(theta) = sin(theta) / cos(theta) = (3/5) / (4/5) = 3/4.
12. Standard form is (x – h)^2 + (y – k)^2 = r^2. Center = (2, -1), radius = 5.
13. Vertex form y = (x – h)^2 + k gives vertex (3, -4).
14. h(0) = 4(1.2)^0 = 4.
15. C(d) = 45d + 60. C(5) = 225 + 60 = $285.
Five Extra Diagnostic Questions
Try these after reviewing the answer key. They are short, but each one points to a high-value review area.
A. If f(x) = x^2 – 4x, find f(-2).
B. Solve 2^(x+1) = 16.
C. Find the period of y = sin(3x).
D. A line has slope 5 and passes through (0, -2). Write its equation.
E. Which expression is undefined: 1/(x – 4) when x = 4 or sqrt(x – 4) when x = 9?
A. f(-2) = (-2)^2 – 4(-2) = 4 + 8 = 12. B. 16 = 2^4, so x + 1 = 4 and x = 3. C. The period is 2pi / 3. D. y = 5x – 2. E. 1/(x – 4) is undefined at x = 4 because the denominator is 0.
What Your Score Tells You
| Correct Out of 15 | Interpretation | Next Step |
|---|---|---|
| 12-15 | Strong first pass | Move into timed full practice tests and calculator-section strategy. |
| 8-11 | Some gaps | Review the topics you missed, especially functions and trig. |
| 0-7 | Foundational review needed | Rebuild Algebra 2, function transformations, and unit-circle basics before full tests. |
Common CLEP Precalculus Mistakes
Doing Calculator Work Before Algebra Work
Some questions are faster when you simplify first. For example, composition, inverse functions, logarithm equations, and exact trig values often reward clean symbolic work before graphing or numerical checking.
Forgetting Domain Restrictions
Radicals, rational expressions, logarithms, and inverse functions all have restrictions. When you miss a function question, write the domain rule that applies before reworking the problem.
Memorizing Trig Values Without Quadrants
Knowing that cos(pi/3) = 1/2 is not enough. You also need signs by quadrant, reference angles, and radian-degree conversion. A quick unit-circle sketch can prevent sign errors.
High-Priority CLEP Precalculus Topics
- Function notation, composition, inverses, domain, and range
- Graph transformations for linear, quadratic, rational, exponential, logarithmic, and trigonometric functions
- Exact trigonometric values and identities
- Equations involving radicals, rational expressions, exponentials, and logarithms
- Conic sections, especially circles and parabolas in standard form
Two-Week Review Plan
If the diagnostic set felt uneven, do not jump straight into full tests. Use this two-week plan first.
- Days 1-2: functions, domain, range, composition, inverse functions, and transformations.
- Days 3-4: polynomial, rational, exponential, and logarithmic equations.
- Days 5-6: unit circle values, trig graphs, identities, and right-triangle applications.
- Days 7-8: circles, parabolas, lines, systems, and analytic geometry.
- Days 9-10: mixed modeling problems and calculator-section graph interpretation.
- Days 11-12: timed practice sets with a written error log.
- Days 13-14: redo missed problems without notes, then take a longer mixed review.
For every missed problem, record the topic, the first wrong step, and the corrected method. That error log is usually more valuable than rereading an entire chapter.
ViewMath CLEP Precalculus Resources
For a more complete review path, use a CLEP Precalculus study guide or workbook before full-length timed practice tests. A study guide is best for rebuilding topics, a workbook is best for repetition, and practice tests are best after you can complete mixed sets without checking notes. Browse ViewMath CLEP Precalculus resources for topic review, guided practice, formula review, and test-style practice.
