Algebra Formula Sheet - Utah Tech - log formula sheet

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Algebra Formula Sheet
"Story Problem Formulas" Zero Factor Property: ab = 0 a = 0 or b = 0
Formula Use Pythagorean Theorem: a2 + b2 = c2
A = lw Area of Rectangle Direct Variation: y = kx
A = 1 bh Area of a triangle k
2
A = r2 Area of a Circle Inverse Variation: y = x
A = 1 (b1 + b2)h Area of a Trapezoid Joint Variation: y = kxz
2
I = P RT Simple Interest Radical Rules:
d = rt Distance traveled Definition: am/n = n am = ( n a)m
V = lwh Volume of rectangular solid
F = ( 9 )C + 32 Temperature conversion Product Rule: n a ? n b = n ab
5
n a
Quotient Rule: n a = n
bb
y2-y1
Slope Equation: m = x2-x1 Square Root Property: a2 = b a = ? b
Point-Slope Form of a Linear Equation:
y - y1 = m(x - x1) Distance Formula: d = (x2 - x1)2 + (y2 - y1)2
Slope Intercept Form of a Linear Equation: Midpoint Formula: ( x1+x2 , y1+y2 )
22
y = mx + b Imaginary Numbers:
i = -1
Standard Form of Linear Equation: i2 = -1
Ax + By = C, A > 0 and no fractions i3 = -i
Horizontal Line: y = c i4 = 1
Vertical Line: x = c Quadratic Formula: x = -b? b2-4ac
2a
Exponent Rules: Algebra of Functions:
Product Rule: am ? an = am+n Sum: (f + g)(x) = f (x) + g(x)
Quotient Rule: am
an = am-n Difference: (f - g)(x) = f (x) - g(x)
Power Rule: (am)n = amn
Product: (f ? g)(x) = f (x) ? g(x)
Power of a Product: (ab)n = anbn
Power of a Quotient: ( a )n = an Quotient: ( f )(x) = f(x)
g g(x)
c cn Composition: (f g)(x) = f (g(x))
Zero Exponent: a0 = 1
1 = an Logarithmic Definition:
1 and a-n
Negative Exponent: a-n = an
Dividing a Polynomial by a Monomial:
y = logb(x) means x = by
b Properties of Logarithms:
a+b = a + c Product: logb(xy) = logb(x) + logb(y)
cc
Perfect Square Trinomials: Quotient: logb( x ) = logb(x) - logb(y)
a2 + 2ab + b2 = (a + b)2
y
a2 - 2ab + b2 = (a - b)2 Power: logb(xr) = r logb(x)
Difference of Squares: a2 - b2 = (a + b)(a - b) Change of Base: logb(a) = logc(a)
logc(b)
Difference of Cubes: logb(1) = 0
a3 - b3 = (a - b)(a2 + ab + b2) logb(bx) = x
Sum of Cubes: a3 + b3 = (a + b)(a2 - ab + b2) blogb(x) = x
1


How do you make a log sheet?A log sheet can be created with either Microsoft Word or Microsoft Excel. Each program has functions to make spreadsheets and log sheets quickly and easily. In Microsoft Word there is a ?Table? function with a log sheet already made. Once the program is opened, click on ?Table? at the top of the page to open the drop down bar.

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