Core algebra concepts and formulas tested on the CLEP College Algebra exam. Front: the term or formula. Back: definition or formula with a brief usage note.
40 cards · basic cards · AI-written, checked twice. Edit anything.
- Quadratic formula
Show answer
x = (-b ± sqrt(b^2 - 4ac)) / 2a, used to find roots of ax^2 + bx + c = 0- Discriminant
Show answer
b^2 - 4ac; determines the nature of roots: positive = 2 real roots, zero = 1 real root, negative = 2 complex roots- Completing the square
Show answer
Transform ax^2 + bx + c by adding and subtracting (b/2a)^2 to create a perfect square trinomial- Difference of squares
Show answer
a^2 - b^2 = (a + b)(a - b)- Sum of cubes
Show answer
a^3 + b^3 = (a + b)(a^2 - ab + b^2)- Difference of cubes
Show answer
a^3 - b^3 = (a - b)(a^2 + ab + b^2)- Slope formula
Show answer
m = (y2 - y1) / (x2 - x1), the rate of change between two points- Point-slope form
Show answer
y - y1 = m(x - x1), equation of a line given a point and slope- Distance formula
Show answer
d = sqrt((x2 - x1)^2 + (y2 - y1)^2), the distance between two points- Midpoint formula
Show answer
M = ((x1 + x2)/2, (y1 + y2)/2), the point halfway between two points- Vertex form of a parabola
Show answer
y = a(x - h)^2 + k, where (h, k) is the vertex and a determines direction and width- Standard form of a circle
Show answer
(x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius- Rational exponent rule
Show answer
a^(m/n) = (n-th root of a)^m = n-th root of (a^m)- Product rule for exponents
Show answer
a^m * a^n = a^(m+n), when multiplying powers with the same base, add the exponents- Quotient rule for exponents
Show answer
a^m / a^n = a^(m-n), when dividing powers with the same base, subtract the exponents
FlashKeepers