PERT Math cheat sheet

Slope between two points: m = (y2 - y1) / (x2 - x1).

Slope-intercept form: y = mx + b, where m is slope and b is y-intercept.

Point-slope form: y - y1 = m(x - x1).

Parallel lines have equal slopes; perpendicular lines have slopes whose product is -1.

Standard form Ax + By = C has slope -A/B when B is not zero.

Solve linear equations by applying inverse operations to isolate the variable.

When multiplying or dividing an inequality by a negative number, reverse the inequality symbol.

For a > 0, |x| < a is equivalent to -a < x < a, and |x| > a means x < -a or x > a.

A two-variable linear system has no solution when the lines are parallel and distinct.

Distributive property: a(b + c) = ab + ac; combine like terms after distributing.

Product rule: x^a · x^b = x^(a+b); quotient rule: x^a / x^b = x^(a-b).

Power rule: (x^a)^b = x^(ab); negative exponent: x^-a = 1/x^a for x not zero.

Difference of squares: a^2 - b^2 = (a - b)(a + b).

A function assigns exactly one output to each input; the vertical line test identifies functions.

Domain restrictions: exclude values making a denominator zero, and require even-root radicands to be nonnegative.

Composition: (f ∘ g)(x) = f(g(x)); evaluate the inner function first.

Direct variation is y = kx; inverse variation is y = k/x, with k a nonzero constant.

Nonlinear systems can often be solved by substitution or by setting expressions equal.

Standard quadratic form: ax^2 + bx + c = 0, with a not zero.

Quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Discriminant b^2 - 4ac: positive gives two real solutions, zero gives one, negative gives none.

Zero product property: if ab = 0, then a = 0 or b = 0.

The vertex x-coordinate for y = ax^2 + bx + c is -b/(2a).

Axis of symmetry: x = -b/(2a); the y-intercept is c.

Vertex form y = a(x - h)^2 + k has vertex (h, k).

The parabola opens upward when a > 0 and downward when a < 0.

Rectangle area A = lw and perimeter P = 2l + 2w.

Triangle area A = (1/2)bh; circle area A = πr^2 and circumference C = 2πr.

Pythagorean theorem: a^2 + b^2 = c^2 for a right triangle with hypotenuse c.

Triangle angles sum to 180 degrees; complementary angles sum to 90 and supplementary to 180.

Volume formulas include rectangular prism V = lwh and cylinder V = πr^2h.

Similar figures with side ratio k have area ratio k^2 and volume ratio k^3.

Mean = sum / count; median = middle ordered value; mode = most frequent value; range = maximum - minimum.

Probability = favorable outcomes / total outcomes; for independent events, P(A and B) = P(A)P(B).