The Ultimate CLEP College Algebra Formula Cheat Sheet

The CLEP College Algebra exam is one of the most worthwhile tests a student can take — pass it, and most colleges will give you credit for an entire College Algebra course. That can save real money and a full semester of work. The catch: the test covers a lot of algebra, and the on-screen scientific calculator helps with arithmetic but won’t graph, factor, or solve equations for you — and there’s no formula sheet provided.

This page is the working formula reference I use with my CLEP College Algebra students. The reference grid below covers the standard algebra and geometry building blocks, and the appendix that follows fills in the CLEP-specific College Algebra material — quadratic equations, logarithm rules, function composition, sequences, and the rest of what the official content outline tests.

Best way to use it: read through the whole list first to see the full scope. Then go back and identify the formulas that feel rusty. Most students find that about a third of the list is already solid; the remaining two-thirds is where focused study time pays off.

The CLEP College Algebra Formula Cheat Sheet

Circles

Area \(=πr^2\)
Circumference \(=2πr\)
Full circle \(=360^\circ\)

Rectangles

(Square if l=w)
Area=lw

Surface Area and Volume of a Sphere  

\(SA =4πr^2\)
\(V =\frac{4}{3} \ πr^3\)
(p \(=\) perimeter of base B; \(π ~ 3.14 \))

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What the CLEP Tests That High-School Algebra Often Skips

Here’s what trips students up: CLEP College Algebra goes a little deeper than a typical high-school Algebra II course. You’ll see more on logarithms, more on inverse functions, more on transformations of graphs (shifts, stretches, reflections), and a real focus on rational expressions and complex numbers. None of it is genuinely hard — but the breadth means you can’t skip topics.

The other thing the CLEP loves: word problems that test your understanding of how a formula works, not just whether you can plug numbers into it. For example, you might see a question about exponential growth that gives you the half-life and asks for the decay constant. The formula is the same one above, but you have to read the question carefully and pick the right pieces.

Books That Pair With This Cheat Sheet

For a slow, step-by-step walkthrough of every concept on this sheet, Algebra II for Beginners is a strong starting point — it covers most of what the CLEP tests, with worked examples and short practice sets after each topic.

When you’re closer to test day and want timed, realistic practice, 10 Full Length CLEP College Algebra Practice Tests gives you exactly that — ten complete tests with answer explanations, written to match the real exam’s pacing and difficulty.

The CLEP College Algebra Appendix — Formulas the Above Grid Doesn’t Cover

The reference above gives you the geometry, arithmetic, and intro-algebra building blocks. The CLEP College Algebra test goes further. Here are the formulas the official content outline requires that aren’t in the grid.

Quadratic Formula and Discriminant

For \(ax^2 + bx + c = 0\): \(x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}\). The discriminant \(b^2 – 4ac\) tells you whether you get two real, one repeated, or two complex solutions.

Vertex Form and Completing the Square

Vertex form: \(y = a(x – h)^2 + k\), where \((h, k)\) is the vertex of the parabola. Convert from standard form using \(h = -\frac{b}{2a}\), then \(k = f(h)\).

Factoring Patterns

Difference of squares: \(a^2 – b^2 = (a-b)(a+b)\). Sum of cubes: \(a^3 + b^3 = (a+b)(a^2 – ab + b^2)\). Difference of cubes: \(a^3 – b^3 = (a-b)(a^2 + ab + b^2)\). These three patterns cover most of the CLEP factoring questions.

Exponent and Radical Rules

Product: \(a^m \cdot a^n = a^{m+n}\). Quotient: \(\frac{a^m}{a^n} = a^{m-n}\). Power: \((a^m)^n = a^{mn}\). Negative: \(a^{-n} = \frac{1}{a^n}\). Fractional: \(a^{m/n} = \sqrt[n]{a^m}\). Zero: \(a^0 = 1\) (for any \(a \neq 0\)).

Logarithm Rules

Product: \(\log_b(xy) = \log_b x + \log_b y\). Quotient: \(\log_b(x/y) = \log_b x – \log_b y\). Power: \(\log_b(x^n) = n \cdot \log_b x\). Change of base: \(\log_b x = \frac{\log x}{\log b}\). Definition: \(\log_b x = y \iff b^y = x\).

Functions and Function Composition

Composition: \((f \circ g)(x) = f(g(x))\). Inverse: \(f^{-1}(f(x)) = x\) and \(f(f^{-1}(x)) = x\). To find an inverse, swap \(x\) and \(y\), then solve for \(y\). Horizontal and vertical line tests determine whether a relation is a function and whether it’s one-to-one.

Sequences

Arithmetic sequence \(n\)-th term: \(a_n = a_1 + (n-1)d\), where \(d\) is the common difference. Geometric sequence \(n\)-th term: \(a_n = a_1 \cdot r^{n-1}\), where \(r\) is the common ratio. Sum of an arithmetic series: \(S_n = \frac{n}{2}(a_1 + a_n)\). Sum of a finite geometric series: \(S_n = a_1 \cdot \frac{1 – r^n}{1 – r}\).

Complex Numbers

\(i = \sqrt{-1}\), so \(i^2 = -1\), \(i^3 = -i\), \(i^4 = 1\). The conjugate of \(a + bi\) is \(a – bi\). Multiplying a complex number by its conjugate gives a real number: \((a + bi)(a – bi) = a^2 + b^2\).

Exponential Growth and Decay

Growth: \(A = A_0 \cdot e^{kt}\) for continuous, or \(A = A_0 (1 + r)^t\) for periodic. Half-life decay: \(A = A_0 \cdot (1/2)^{t/h}\), where \(h\) is the half-life.

Frequently Asked Questions About CLEP College Algebra

Is there a formula sheet on the CLEP College Algebra test?

No. The CLEP College Algebra exam does not provide a formula sheet. You’ll have a built-in scientific calculator for some sections, but every formula — quadratic formula, distance formula, logarithm rules, exponent rules — has to be in your memory.

How hard is the CLEP College Algebra test?

It’s roughly equivalent to a one-semester college algebra course. Most students who passed Algebra II in high school can pass the CLEP with about four to eight weeks of focused review. If algebra has been a struggle, plan on a longer runway — twelve weeks of consistent study is realistic.

What score do I need to pass CLEP College Algebra?

The American Council on Education recommends a passing score of 50 (on the CLEP’s 20–80 scale). Individual colleges set their own minimums, and some require a higher score (often 55 or 60) for credit. Check with the college whose credit you want before you take the test.

Can I use a calculator on the CLEP College Algebra?

Yes — but only the built-in non-graphing scientific calculator on the test interface. You cannot bring your own. The calculator handles arithmetic, square roots, exponents, and basic functions, but it won’t graph or solve equations for you. Knowing your formulas still matters.

Which topics are most heavily tested on CLEP College Algebra?

Roughly 25% of the test is on algebraic operations (factoring, simplifying expressions, working with rational and radical expressions). About 25% covers equations and inequalities (linear, quadratic, absolute value, systems). Another 30% is on functions and their graphs (including logs, exponents, and transformations). The final 20% is on number systems, sequences, and matrices.

How long do I have to take the CLEP College Algebra?

You get 90 minutes for 60 multiple-choice questions. That works out to roughly 90 seconds per question — fast enough that you can’t afford to look up formulas mentally. The cheat sheet above needs to be in instant-recall mode by test day.

What is the difference between log_b and ln on the CLEP?

\(\log_b\) is logarithm with base \(b\); \(\log\) (no base shown) usually means \(\log_{10}\); \(\ln\) means \(\log_e\), where \(e \approx 2.71828\). The CLEP uses all three. The change-of-base formula \(\log_b x = \frac{\ln x}{\ln b}\) lets you compute any log with the natural-log button on the test’s built-in calculator.

How do I find the inverse of a function on the CLEP?

Three steps: (1) Replace \(f(x)\) with \(y\). (2) Swap \(x\) and \(y\). (3) Solve for \(y\) — that’s your inverse. Then check by computing \(f(f^{-1}(x))\); it should equal \(x\). Not every function has an inverse; one-to-one functions do (they pass the horizontal line test).

What’s the difference between an arithmetic and geometric sequence on the CLEP?

An arithmetic sequence adds the same number each step (\(2, 5, 8, 11, \ldots\) — common difference 3). A geometric sequence multiplies by the same number each step (\(2, 6, 18, 54, \ldots\) — common ratio 3). The CLEP gives you both and expects you to identify which kind from the pattern, then apply the right \(n\)-th-term formula.

What is i squared and why does it matter on the CLEP?

\(i^2 = -1\). This is the definition of the imaginary unit, and it powers everything you’ll see with complex numbers. When you simplify expressions like \(i^{15}\), reduce the exponent mod 4: \(i^{15} = i^{4 \cdot 3 + 3} = i^3 = -i\).

Related EffortlessMath Lessons

• How to use the quadratic formula
• How to use the change-of-base formula for logarithms
• Composition of functions
• How to verify inverse functions
• Arithmetic sequences
• Geometric sequences
• Exponential growth and decay
• Top 10 CLEP College Algebra study tips