$5one-time
- 29-page printable PDF
- 181 terms with examples
- 40 practice questions, answers explained
- 2-page cram sheet and study plans
← CLEP College Algebra course
CLEP® Study Guide
Printable PDF · 29 pages
CLEP College Algebra Study Guide
Everything the CLEP College Algebra exam tests, in one PDF you can print. Built from the College Board's official outline, heaviest topics first.
- 181 key terms, each with an example
- 40 practice questions with every answer explained
- A 2-page cram sheet for the night before
- 2-, 4- and 8-week study plans built from the exam weights
Last updated 2026 · exam details checked against the College Board's published exam information in 2026
Look inside the guide
Real pages from the 29-page PDF.
What you get for $5
One chapter for each official content area, in the order the exam weighs them.
- 📘29pages, printable
- 🧭4chapters, heaviest first
- 🔑181terms with examples
- ✍️40practice questions, answers explained
- ⚠️12exam traps to avoid
- 📄2page cram sheet
Try 10 free College Algebra questions
In the style of the real exam, from all 4 areas. About 15 minutes, with every answer explained and a score by area.
10 questions
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Question 1 · Functions and their properties
For x = 1, 2, 3 and 4, the function f takes the values 3, 1, 4, 2 and the function g takes the values 4, 3, 1, 2. What is the value of f(g(1))?
Show the answer
Answer: A. 2. g(1) = 4, and then f(4) = 2. The inner function is evaluated first.
The trap: 1 is g(f(1)): f(1) = 3, then g(3) = 1. That runs the composition in the wrong order.
g(1) = 4, and then f(4) = 2. The inner function is evaluated first.
The trap: 1 is g(f(1)): f(1) = 3, then g(3) = 1. That runs the composition in the wrong order.
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Question 2 · Algebraic operations
What is the remainder when p(x) = 2x³ − 5x² + x − 4 is divided by x − 3?
Show the answer
Answer: C. 8. By the Remainder Theorem the remainder is p(3) = 54 − 45 + 3 − 4 = 8.
The trap: −106 is p(−3), which is the remainder for division by x + 3, not x − 3. The divisor x − 3 means c = 3.
By the Remainder Theorem the remainder is p(3) = 54 − 45 + 3 − 4 = 8.
The trap: −106 is p(−3), which is the remainder for division by x + 3, not x − 3. The divisor x − 3 means c = 3.
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Question 3 · Equations and inequalities
For which positive value of k does the equation 2x² − kx + 8 = 0 have exactly one real solution?
Show the answer
Answer: B. 8. One real solution requires a discriminant of 0: k² − 4(2)(8) = k² − 64 = 0, so k = 8 (the positive value).
The trap: 64 sets k² − 64 = 0 but stops there. It is k², so a square root is still needed.
One real solution requires a discriminant of 0: k² − 4(2)(8) = k² − 64 = 0, so k = 8 (the positive value).
The trap: 64 sets k² − 64 = 0 but stops there. It is k², so a square root is still needed.
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Question 4 · Number systems and operations
What is the value of (4 + 3i)(2 − i)?
Show the answer
Answer: D. 11 + 2i. Expand: 8 − 4i + 6i − 3i². Since i² = −1, −3i² = +3. The sum is 11 + 2i.
The trap: 5 + 2i comes from treating i² as +1, which gives 8 − 3 = 5.
Expand: 8 − 4i + 6i − 3i². Since i² = −1, −3i² = +3. The sum is 11 + 2i.
The trap: 5 + 2i comes from treating i² as +1, which gives 8 − 3 = 5.
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Question 5 · Functions and their properties
What is the domain of f(x) = √(x + 3)/(x − 1)?
Show the answer
Answer: E. [−3, 1) ∪ (1, ∞). The root needs x + 3 ≥ 0, so x ≥ −3. The denominator excludes x = 1. Together: [−3, 1) ∪ (1, ∞).
The trap: [−3, ∞) keeps x = 1, where the denominator is zero.
The root needs x + 3 ≥ 0, so x ≥ −3. The denominator excludes x = 1. Together: [−3, 1) ∪ (1, ∞).
The trap: [−3, ∞) keeps x = 1, where the denominator is zero.
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Question 6 · Algebraic operations
Which expression is equivalent to (3x²y⁻¹)³ / (9x⁻¹y²), for x and y not 0?
Show the answer
Answer: E. 3x⁷/y⁵. The numerator is 27x⁶y⁻³. Dividing: 27/9 = 3, x⁶ − (−1) = x⁷, and y⁻³ − 2 = y⁻⁵, so the result is 3x⁷/y⁵.
The trap: 3x⁵/y⁵ subtracts 6 − 1 instead of 6 − (−1). Subtracting a negative exponent adds 1.
The numerator is 27x⁶y⁻³. Dividing: 27/9 = 3, x⁶ − (−1) = x⁷, and y⁻³ − 2 = y⁻⁵, so the result is 3x⁷/y⁵.
The trap: 3x⁵/y⁵ subtracts 6 − 1 instead of 6 − (−1). Subtracting a negative exponent adds 1.
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Question 7 · Equations and inequalities
A ball thrown upward from a height of 4 feet has height h = −16t² + 48t + 4 feet after t seconds. To the nearest hundredth of a second, when does it hit the ground?
Show the answer
Answer: C. 3.08. Set −16t² + 48t + 4 = 0, or 16t² − 48t − 4 = 0. The quadratic formula gives t = (48 ± √2560)/32, about 3.08 or −0.08. Time cannot be negative, so t ≈ 3.08.
The trap: 6.16 divides by 16 instead of 2a = 32. The denominator is twice the leading coefficient.
Set −16t² + 48t + 4 = 0, or 16t² − 48t − 4 = 0. The quadratic formula gives t = (48 ± √2560)/32, about 3.08 or −0.08. Time cannot be negative, so t ≈ 3.08.
The trap: 6.16 divides by 16 instead of 2a = 32. The denominator is twice the leading coefficient.
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Question 8 · Number systems and operations
Which expression equals (7 + 4i)/(1 + 2i)?
Show the answer
Answer: D. 3 − 2i. Multiply top and bottom by 1 − 2i: (7 + 4i)(1 − 2i) = 15 − 10i, and (1 + 2i)(1 − 2i) = 5. The result is 3 − 2i.
The trap: 15 − 10i is the numerator alone. The denominator 5 must also be divided out.
Multiply top and bottom by 1 − 2i: (7 + 4i)(1 − 2i) = 15 − 10i, and (1 + 2i)(1 − 2i) = 5. The result is 3 − 2i.
The trap: 15 − 10i is the numerator alone. The denominator 5 must also be divided out.
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Question 9 · Functions and their properties
A farmer has 120 meters of fence for a rectangular pen against a long barn wall. The side along the wall is not fenced. What is the largest possible area of the pen, in square meters?
Show the answer
Answer: B. 1,800. Let w be each side that meets the wall, so the far side is 120 − 2w. A = w(120 − 2w) = −2w² + 120w has its vertex at w = 30, giving 30 · 60 = 1,800.
The trap: 1,600 splits the fence into three equal 40-meter sides. The vertex shows the best width is 30, not 40.
Let w be each side that meets the wall, so the far side is 120 − 2w. A = w(120 − 2w) = −2w² + 120w has its vertex at w = 30, giving 30 · 60 = 1,800.
The trap: 1,600 splits the fence into three equal 40-meter sides. The vertex shows the best width is 30, not 40.
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Question 10 · Algebraic operations
What is the value of 16^(3/4) · 27^(−2/3)?
Show the answer
Answer: A. 8/9. 16^(3/4) = (⁴√16)³ = 2³ = 8 and 27^(−2/3) = 1/(∛27)² = 1/9, so the product is 8/9.
The trap: 72 ignores the negative sign on the second exponent and multiplies by 9 instead of 1/9.
16^(3/4) = (⁴√16)³ = 2³ = 8 and 27^(−2/3) = 1/(∛27)² = 1/9, so the product is 8/9.
The trap: 72 ignores the negative sign on the second exponent and multiplies by 9 instead of 1/9.
The CLEP College Algebra exam at a glance
The CLEP College Algebra exam is a computer-based test from the College Board. The exam has approximately 60 questions to be answered in 90 minutes, and some are pretest questions that will not be scored. A score of 50 on the 20–80 scale earns an ACE credit recommendation of 3 semester hours, though each college sets its own policy. The exam covers 4 content areas; the heaviest is Functions and their properties at 30%.
- Questions
- About 60mostly multiple choice
- Time
- 90 minabout 2 minutes a question
- Passing score
- 50on a 20–80 scale
- ACE credit
- 3semester hours
- Exam fee
- $97paid to College Board
- Calculator
- Yeson-screen calculator provided
What the exam covers
4 areas, heaviest first. The guide's chapters follow this order.
- Functions and their properties30%
- Algebraic operations25%
- Equations and inequalities25%
- Number systems and operations20%
How it works
- 1Buy once, $5Secure checkout. No subscription needed.
- 2Download the PDFFrom your TransferCredit.org account, right away and any time later.
- 3Study the heaviest areas firstFollow the 2-, 4- or 8-week plan, then read the cram sheet the night before.
Questions students ask
What's in the full CLEP College Algebra study guide?
29 pages: 4 chapters, one per official content area, heaviest first. 181 terms, each with a plain-English definition and an example, common traps and memory tricks, 40 practice questions with an answer key that explains every answer, question tactics, 2-, 4- and 8-week study plans and a 2-page cram sheet.
How much is the full CLEP College Algebra study guide?
The full 29-page PDF is $5, a one-time payment. The 10 practice questions on this page are free, with no account.
What does the $29 plan include?
$29 a month gives you all 28 CLEP subjects: every CLEP study guide plus the full prep course for each subject, and you can cancel anytime. If you only need this exam, the guide on its own is a one-time $5.
How do I get the full guide?
Choose Buy this guide ($5) and check out. Then sign in to your TransferCredit.org account, then open the course and its Download Your Study Guide lesson. The PDF is yours to keep, and you can download it again from your account at any time.
Can I print the guide or use it on my phone?
Yes. It's a PDF, so it opens on phones, tablets and computers, and printing is allowed. Its tick boxes and answer bubbles work in PDF readers that support forms. Copying and editing are turned off.
Is this an official CLEP study guide?
No. CLEP® is a registered trademark of the College Board, which was not involved in producing this guide and does not endorse it. TransferCredit.org is independent. We built the guide from the official exam outline, and the exam details were checked against the College Board's published exam information in 2026.
Why is this study guide better than a generic review?
It follows the official outline area by area and spends the most pages on what the exam weighs most. Every term comes with an example, each chapter names the traps the exam sets, and the answer key explains why the most tempting wrong answer is wrong, not just which answer is right. It ends with a 2-page cram sheet for the night before.
What is the CLEP College Algebra exam?
The CLEP College Algebra exam is a computer-based test from the College Board. The exam has approximately 60 questions to be answered in 90 minutes, and some are pretest questions that will not be scored. A score of 50 on the 20–80 scale earns an ACE credit recommendation of 3 semester hours, though each college sets its own policy. The exam covers 4 content areas; the heaviest is Functions and their properties at 30%.
More questions about the CLEP College Algebra exam (21)
How many questions are on the CLEP College Algebra exam, and how long is it?
The exam has approximately 60 questions to be answered in 90 minutes, and some are pretest questions that will not be scored.
What is the passing score for CLEP College Algebra?
The passing score is 50 on a 20–80 scale. At 50 or above, the American Council on Education (ACE) recommends 3 semester hours. Each college sets its own passing score and credit award, so check your school's policy before you book.
How much does the CLEP College Algebra exam cost?
The exam fee is $97, paid to the College Board. Test centers may add their own administration fee. Eligible U.S. military service members can usually test for free through DANTES.
How many college credits is CLEP College Algebra worth?
ACE recommends 3 semester hours for a passing score of 50. Your college decides how many credits it awards and which course they replace. Check your college's policy.
Can I use a calculator on the CLEP College Algebra exam?
A scientific (nongraphing) calculator, the TI-30XS MultiView, is built into the exam software for the whole test.
Is there a penalty for guessing on CLEP College Algebra?
No. Your score counts only correct answers, so a wrong answer costs nothing. Never leave a question blank: rule out what you can and pick your best guess.
What topics are on the CLEP College Algebra exam?
4 content areas, from the official outline: Functions and their properties (30%); Algebraic operations (25%); Equations and inequalities (25%); Number systems and operations (20%).
Which CLEP College Algebra topics should I study first?
Start with the three heaviest: Functions and their properties (30%), Algebraic operations (25%) and Equations and inequalities (25%). Together they are about 80% of the exam, roughly 48 of 60 questions. The guide's chapters run in that order, heaviest first.
Is the CLEP College Algebra exam hard?
It depends on what you already know. The exam has only 4 content areas, so each one carries real weight: Functions and their properties (30%), Algebraic operations (25%), Equations and inequalities (25%) and Number systems and operations (20%). Take the free diagnostic above to see where you stand in about 15 minutes.
What kinds of questions are on the CLEP College Algebra exam?
The guide sorts them into 5 types: “Simplify or rewrite”, “Solve and select”, “Model a situation”, “Which statement must be true” and “Read a table or composition”. Multiple-choice questions have 5 answer choices, and some items use other formats. Try the 10 free questions above to see the style.
How long should I study for CLEP College Algebra?
Use the diagnostic to decide. If you already know most areas, two weeks of daily review is often enough; if the subject is new to you, plan on eight. The full guide has 2-, 4- and 8-week plans built from the exam weights.
How should I pace myself on the CLEP College Algebra exam?
On average you have about 2 minutes per question (90 minutes for 60 questions). Be past question 20 a third of the way through and past question 40 two-thirds through. If a question takes more than about 3 minutes, pick your best guess, mark it and come back.
What happens if I don't pass CLEP College Algebra?
You can retake a CLEP exam after three months. Use the wait to work through the areas the score report and the diagnostic show you missed.
Do colleges accept CLEP College Algebra for credit?
CLEP exams are accepted at more than 2,900 U.S. colleges and universities, but each school decides which exams it accepts, the score it requires and the credit it gives. Look up your college's CLEP policy before you book.
How is the guide different from the CLEP College Algebra course?
The guide is a 29-page PDF for review and self-testing. The CLEP College Algebra course is a full online course with lessons, quizzes and a practice exam, for $19 with lifetime access. Many students use the guide first, then take the course for the areas the diagnostic flags.
Should I take CLEP College Algebra or DSST Fundamentals of College Algebra?
Both cover the same subject. CLEP College Algebra: about 60 questions, 90 minutes, passing score 50, fee $97. DSST Fundamentals of College Algebra: about 100 questions, 120 minutes, passing score 400, fee $100. Take the one your college accepts; most colleges award the credit once, not for both. See the DSST Fundamentals of College Algebra study guide.
How up to date is this CLEP College Algebra guide?
Last updated 2026. The exam details were checked against the College Board's published exam information in 2026. Exams change, so confirm the details on the official exam page before you register.
What should I do the night before the exam?
Read the cram sheet once, slowly. Check your test time, the location or remote-proctoring setup, and the ID you need. Then sleep: a rested brain recalls more than a crammed one. In the morning, skim the memory tricks and common traps, then stop studying.
Which formulas should I know for CLEP College Algebra?
Know the quadratic formula and discriminant, the rules of exponents, the product, quotient and power rules of logarithms and the change-of-base formula, the difference of squares and sum and difference of cubes factoring patterns, and factorials and the binomial theorem.
Are there word problems on CLEP College Algebra?
Yes. The functions area includes modeling situations described in words, tables and graphs, and about half the questions are nonroutine problems that apply concepts.
Are complex numbers on CLEP College Algebra?
Yes. Complex numbers are part of Number systems and operations (20%), alongside real numbers, factorials and the binomial theorem. Know that i² = −1 and how to multiply by a conjugate.
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- Quizzes and a practice final exam
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CLEP® is a registered trademark of the College Board, which was not involved in producing this guide and does not endorse it. TransferCredit.org is independent and not affiliated with the College Board. © 2026 UPI Globale Edu Inc.