Algebra Formula Sheet
”Story Problem Formulas”
Formula Use
A=lw Area of Rectangle
A=1
2bh Area of a triangle
A=πr2Area of a Circle
A=1
2(b1+b2)hArea of a Trapezoid
I=P RT Simple Interest
d=rt Distance traveled
V=lwh Volume of rectangular solid
F= (9
5)C+ 32 Temperature conversion
Slope Equation: m=y2−y1
x2−x1
Point-Slope Form of a Linear Equation:
y−y1=m(x−x1)
Slope Intercept Form of a Linear Equation:
y=mx +b
Standard Form of Linear Equation:
Ax +By =C,A > 0 and no fractions
Horizontal Line: y=c
Vertical Line: x=c
Exponent Rules:
Product Rule: am·an=am+n
Quotient Rule: am
an=am−n
Power Rule: (am)n=amn
Power of a Product: (ab)n=anbn
Power of a Quotient: (a
c)n=an
cn
Zero Exponent: a0= 1
Negative Exponent: a−n=1
anand 1
a−n=an
Dividing a Polynomial by a Monomial:
a+b
c=a
c+b
c
Perfect Square Trinomials:
a2+ 2ab +b2= (a+b)2
a2−2ab +b2= (a−b)2
Difference of Squares: a2−b2= (a+b)(a−b)
Difference of Cubes:
a3−b3= (a−b)(a2+ab +b2)
Sum of Cubes: a3+b3= (a+b)(a2−ab +b2)
Zero Factor Property: ab = 0 ⇒a= 0 or b= 0
Pythagorean Theorem: a2+b2=c2
Direct Variation: y=kx
Inverse Variation: y=k
x
Joint Variation: y=kxz
Radical Rules:
Definition: am/n =n
√am= ( n
√a)m
Product Rule: n
√a·n
√b=n
√ab
Quotient Rule: n
qa
b=n
√a
n
√b
Square Root Property: a2=b⇒a=±√b
Distance Formula: d=q(x2−x1)2+ (y2−y1)2
Midpoint Formula: (x1+x2
2,y1+y2
2)
Imaginary Numbers:
i=√−1
i2=−1
i3=−i
i4= 1
Quadratic Formula: x=−b±√b2−4ac
2a
Algebra of Functions:
Sum: (f+g)(x) = f(x) + g(x)
Difference: (f−g)(x) = f(x)−g(x)
Product: (f·g)(x) = f(x)·g(x)
Quotient: (f
g)(x) = f(x)
g(x)
Composition: (f◦g)(x) = f(g(x))
Logarithmic Definition:
y= logb(x) means x=by
Properties of Logarithms:
Product: logb(xy) = logb(x) + logb(y)
Quotient: logb(x
y) = logb(x)−logb(y)
Power: logb(xr) = rlogb(x)
Change of Base: logb(a) = logc(a)
logc(b)
logb(1) = 0
logb(bx) = x
blogb(x)=x
1
