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Absolute Value Inequality: |x| < a iff -a < x <a; |x| > a iff x < -a or x > a
Area of a Circle: A = PI(r)²
Area of a Rectangle: A = lw
Area of a Sqare: A = s²
Area of a Triangle: A = (1/2)bh
Asymptotes of a Hyperbola: y = .(b/a)x and; y = -(b/a)x or y = (a/b)x and y = -(a/b)x
Circle: (x - h)² + (y - k)² = r²
Circumference of a Circle: C - 2πr
Completing the Square: For the equation 1x² + bx = -c, add (b/2)² to each side, then factor
Compound Interest: A = P([1 + (r/n)]^nt
Compound Interest: Balance = principle[interest + (annual interest rate/ compounding per year)]^(compounding per year × time in years)
Continuous Compounding: A = Pe^rt
Cube of a Binomial (+): (u + v)³ = u³ + 3u²v + 3uv² + v³
Cube of a Binomial (-): (u - v)³ = u³ - 3u²v + 3uv² + v³
Definition of Composition of Two Functions: ( f ⁰ g)(x) = f(g(x))
Difference of Functions: (f - g)(x) = f(x) - g(x)
Difference of Two Cubes: u³ - v³ = (u - v)(u² + uv + v²)
Difference of Two Squares: u² - v² = (u + v)(u - v)
Distance: distance traveled = rate × time
Distance Formula: d = √[( x₂ - x₁) + (y₂ - y₁)]
Distance from center of Circle: r = √[(x - h)² + (y - k)²]
Distance Problem: Distance = Rate + Time
Ellipse: an ellipse is a set of all points (x,y) in a plane the sum of whose distances from two distinct fixed points (foci) is constant
Equation of Profit: Profit = Revenue = Cost
Exponential Function: f(x) = a^x
Extracting Square Roots: The equation u² = d, u = ±√(d)
General form of the equation of a line: Ax + By + C = 0
Horizontal Line: y = b
Hyperbola: a hyperbola is the set of all points (x,y) in a plane the difference of whose distances from the two distinct fixed points (foci) is a positive constant
Linear Equation: ax + b = 0
Midpoint Theorem: m = (x₁ + x₂)/2, (y₁ + y₂)/2
Percent of a Raise: Raise - Percent × Old Wage
Percent of Monthly Expenses: Monthly Expenses = Percent × Income
Perimeter of a Rectangle: P = 2l + 2w
Perimeter of a Square: P = 4s
Perimeter of a Triangle: P = a + b + c
Point-Slope Form of the Equation of a Line: y - y₁ = m(x - x₁)
Principal Square Root of a Negative Number: √(-a) = √(ai)
Product of Functions: (fg)(x) = f(x) × g(x)
Pythagorean Theorem: a² + b² = c²
Quadratic Equation: ax² + bx + c = 0
Quadratic Formula: x = -b ± √(b² - 4ac)/2a
Quadratic Functions: f(x) = ax² + bx + c
Quotient of Functions: (f/g)(x) = f(x)/g(x), g(x) ≠ 0
Rational Zero Test: Rational zero = (a factor of the constant term a₀)/( a facetor of the leading coefficient asubn)
Similar Triangles: (Height of A)/(Length of A's shadow) = (Height of B)/(Length of B's shadow"
Simple Interest: Interest = principle × annual interest rate × time in years
Slope of a Line Passing Through Two Points: m = (y₂ - y₁)/(x₂ - x₁)
Slope-Intercept Form: y = mx + b
Square of a Binomial (+): (u + v)² = u² + 2uv + v²
Square of Binomial (-): (u - v)² = u² - 2uv + v²
Standard Equation of a Hyperbola: (x²/a²) - (y²/b²) = 1; (x²/b²) - (y²/a²) = 1
Standard Equation of an Ellipse: (x²/a²) + (y²/b²) = 1 ; (x²/b²) + (y²/a²) = 1
Standard Form of a Quadratic Function: f(x) - a(x - h)² + k, a ≠ 0
Sum of Functions: (f + g)(x) = f(x) + g(x)
Sum of Two Cubes: u³ + v³ = (u + v)(u² - uv + v²)
Temperature: F = 9/5C + 32
Test for Even Function: f(-x) = f(x)
Test for Odd Function: f(-x) = -f(x)
The Equation of a Circle: (x - h)² + (y - k)² = r²
The Fundamental Theroem of Algebra: If f(x) is a polynomial of degree n, where n > 0, then f has at least one zero in the complex number system
Vertical Line: x = a
Volume of a Circular Cyloander: V = πr²h
Volume of a Cube: V = s³
Volume of a Rectangular Solid: V = lwh
Volume of a Sphere: V = (4/3)πr³
Zeros of a Function: the x-values for which f(x) = 0