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

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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.

Core College Algebra Formulas by CLEP Content Area

The College Board splits the CLEP College Algebra exam into four content areas. These are the formulas worth knowing cold for each.

Change of base is worth adding to that list: log base b of x = log(x) ÷ log(b), so log base 2 of 8 = log 8 ÷ log 2 = 3.

Transformations, Asymptotes and Interest Formulas

College algebra courses lean on three more groups of formulas that a pre-algebra sheet leaves out.

Graph transformations of y = f(x)

• f(x) + k moves the graph up k units; f(x) − k moves it down.
• f(x − h) moves the graph right h units; f(x + h) moves it left.
• −f(x) reflects it over the x-axis; f(−x) reflects it over the y-axis.
• a · f(x) stretches it vertically when a > 1 and compresses it when 0 < a < 1.

Asymptotes of a rational function

After canceling common factors, a vertical asymptote sits where the denominator equals 0. For the horizontal asymptote, compare degrees: if the top has the lower degree, it is y = 0; if the degrees match, it is y = (leading coefficient on top) ÷ (leading coefficient on bottom); if the top has the higher degree, there is none.

Interest and growth

Compound interest is A = P(1 + r/n)ⁿᵗ, and continuous growth is A = Pe^(rt). For $1,000 at 6% for 2 years, monthly compounding gives 1000(1.005)²⁴ ≈ $1,127.16, and continuous compounding gives 1000e^0.12 ≈ $1,127.50.

Frequently Asked Questions About CLEP College Algebra

Is there a formula sheet for the CLEP College Algebra exam?

No. The CLEP College Algebra exam does not provide a formula sheet, though it does show a built-in non-graphing scientific calculator. That means formulas like the quadratic formula, the distance formula and logarithm rules must be memorized. The calculator helps with arithmetic, but it will not factor, graph or solve equations for you.

What formulas are used in college algebra?

The core college algebra formulas are the quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a, slope and the forms of a line, exponent and logarithm rules, factoring patterns like a² − b² = (a + b)(a − b), function composition (f ∘ g)(x) = f(g(x)), and compound interest A = P(1 + r/n)^(nt). For example, $500 at 4% compounded yearly for 2 years grows to 500 × 1.04² = $540.80.

What should be on a college algebra final exam cheat sheet?

Focus on what you are most likely to forget under pressure: the quadratic formula and discriminant, logarithm rules such as log(ab) = log a + log b and log(a^n) = n log a, change of base, vertex form y = a(x − h)² + k, and rules for graph shifts. Writing the sheet yourself is good studying, even if your exam does not allow you to bring it in.

What is on the CLEP College Algebra exam?

The CLEP College Algebra exam has about 60 questions in 90 minutes. It covers algebraic operations (factoring, rational and radical expressions), equations and inequalities, functions and their properties, and number systems. A typical item might ask you to solve |2x − 3| = 7, which gives x = 5 or x = −2. The College Board’s official examination guide lists the exact content outline.

What should you memorize for college algebra?

Memorize the formulas you use in many problem types rather than every special case. The essentials are exponent rules (a^m × a^n = a^(m+n)), log rules, the quadratic formula, slope, the vertex formula x = −b ÷ 2a, and the inverse relationship between logs and exponents: log₂ 8 = 3 because 2³ = 8. Practice each one on a few problems until it comes without effort.

How do you study for CLEP College Algebra?

Take a practice test to see which content areas are weakest, then study those first. Most students need 4 to 8 weeks of steady review if they passed Algebra 2 in high school. Make a formula sheet from memory each week, practice with the on-screen calculator style you will use, and finish with timed sets of about 60 questions in 90 minutes.

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

Official source: the full list of CLEP exams, what each one covers and how colleges award credit for them are published by the College Board at clep.collegeboard.org.