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