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.
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- Quadratic formula
- x = (-b ± sqrt(b^2 - 4ac)) / 2a, used to find roots of ax^2 + bx + c = 0
- Discriminant
- b^2 - 4ac; determines the nature of roots: positive = 2 real roots, zero = 1 real root, negative = 2 complex roots
- Completing the square
- Transform ax^2 + bx + c by adding and subtracting (b/2a)^2 to create a perfect square trinomial
- 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)
- Slope formula
- m = (y2 - y1) / (x2 - x1), the rate of change between two points
- Point-slope form
- y - y1 = m(x - x1), equation of a line given a point and slope
- Distance formula
- d = sqrt((x2 - x1)^2 + (y2 - y1)^2), the distance between two points
- Midpoint formula
- M = ((x1 + x2)/2, (y1 + y2)/2), the point halfway between two points
- Vertex form of a parabola
- y = a(x - h)^2 + k, where (h, k) is the vertex and a determines direction and width
- Standard form of a circle
- (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius
- Rational exponent rule
- a^(m/n) = (n-th root of a)^m = n-th root of (a^m)
- Product rule for exponents
- a^m * a^n = a^(m+n), when multiplying powers with the same base, add the exponents
- Quotient rule for exponents
- a^m / a^n = a^(m-n), when dividing powers with the same base, subtract the exponents