CLEP Algebra

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Last updated 12:19 AM on 9/30/26
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37 Terms

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Slope Formula
m = (y2 - y1) / (x2 - x1)
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Slope-Intercept Form
y = mx + b
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Point-Slope Form
y - y1 = m(x - x1)
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Standard Form of a Line
Ax + By = C
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Distance Formula
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
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Midpoint Formula
M = ((x1 + x2)/2
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Perpendicular Slope Rule
m1 * m2 = -1 (m2 = -1 / m1)
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Quadratic Formula
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
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Discriminant & Meaning
D = b^2 - 4ac (D > 0: 2 real roots | D = 0: 1 real root | D < 0: 2 complex roots)
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Vertex Form of a Quadratic
y = a(x - h)^2 + k with vertex (h
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Vertex x-coordinate (Standard Form)
x = -b / (2a)
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Difference of Squares
a^2 - b^2 = (a - b)(a + b)
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Perfect Square Trinomial
(a ± b)^2 = a^2 ± 2ab + b^2
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Sum of Cubes
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
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Difference of Cubes
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
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Product Rule of Exponents
a^m * a^n = a^(m+n)
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Quotient Rule of Exponents
a^m / a^n = a^(m-n)
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Power of a Power Rule
(a^m)^n = a^(mn)
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Negative Exponent Rule
a^(-n) = 1 / (a^n)
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Rational Exponents
a^(m/n) = nth-root(a^m)
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Zero Exponent Rule
a^0 = 1 (where a ≠ 0)
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Definition of a Logarithm
log_b(x) = y <-> b^y = x
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Product Rule of Logarithms
log_b(xy) = log_b(x) + log_b(y)
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Quotient Rule of Logarithms
log_b(x/y) = log_b(x) - log_b(y)
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Power Rule of Logarithms
log_b(x^p) = p * log_b(x)
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Change of Base Formula
log_b(x) = log_c(x) / log_c(b) = ln(x) / ln(b)
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Arithmetic Sequence n-th Term
a_n = a_1 + (n - 1)d
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Arithmetic Series Sum
S_n = (n / 2)(a_1 + a_n)
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Geometric Sequence n-th Term
a_n = a_1 * r^(n-1)
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Finite Geometric Series Sum
S_n = a_1 * (1 - r^n) / (1 - r) [where r ≠ 1]
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Infinite Geometric Series Sum
S_infinity = a_1 / (1 - r) [where |r| < 1]
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Horizontal Shift Rules
f(x - h) shifts right h | f(x + h) shifts left h
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Vertical Shift Rules
f(x) + k shifts up k | f(x) - k shifts down k
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Reflection Rules
-f(x) reflects across x-axis | f(-x) reflects across y-axis
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Simple Interest Formula
I = P * r * t
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Compound Interest Formula
A = P(1 + r/n)^(nt)
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Continuous Compound Interest Formula
A = P * e^(rt)