Your Algebra Homework Can Now Be Easier Than Ever!

Math Final Exam Reference Sheet

Distance between two points

Midpoint between two points

Slope between two points

Average rate of change of a function

Inverse functions

Transformations of graph of f(x)

f(x − h) + k translates h units ”to the right”,
and k units vertically

−f(x) reflects across x−axis; f(−x) across y−
cf(x) dilates by factor of c vertically
f(cx) dilates by factor of horizontally


General Form
Factored Form

Rational Functions

Definition where f, g are polynomials with no common factors
Domain all real numbers except where g(x) = 0
x- intercepts at zeros of f
vertical asymptotes at zeros of g

Exponents and Logarithms
Exp onential Function
Definition of Logarithm is equivalent to b y = x
Properties of Logs

Trigonometric Functions
Of acute angles:
Of any angle: (circle radius r)

Radians and Degrees
180° =π (radians)

Linear equations

General Form: Ax + By =C
Slope-intercept form y = mx + b
Point-slope form
Double-intercept form

Quadratic equations

Forms: General
Vertex General
Roots General

Translations, Reflections, Dilations y = Asin(B(x − C)) + D, y = Acos(B(x − C)) + D
Horizontal Translation (phase shift) C units
Vertical Translation (vertical shift) D units
Horizontal Dilation By a factor of (period becomes )
Vertical Dilation (amplitude) By a factor of A
Reflections −f(x) reflect across y−axis; f(−x) reflect across x−axis

Trig Identities
Opposite Angle


Half-Angle s


Inverse Trig Functions
Domain restrictions: sin restricts to , cos restricts to [0,π ], tan restricts to
for all θ

only for
only for
only for

Position(radius) Given and
Unit Components If =< x, y >, then
Magnitude (length) If =< x, y >, then Unit vector
Scalar Multiplication If =< x, y >, then k =< kx, ky >
Addition If =< a, b > and =< c, d > then + =< a + c, b + d >
Dot Product If =< a, b > and =< c, d > then · = ac + bd
Angle between and

Polar Coordinates

Trigonometric (polar) form of Complex Numbers
z = r(cosθ + i sinθ ) is the trigonometric form of the complex number a + bi, where
a = r cosθ , b = r sinθ and
zn = rn(cos nθ + i sin nθ ) with z as above

Matrix Multiplication If and , then
Identity Matrix . For any 2 × n matrix A,
Inverse Matrices and
Matrix equations If AX = B, then

Polynomial Functions and Equations
Division Algorithm
Let p(x) and d(x) be polynomials, and assume that d(x) is not the zero polynomial. Then there
are unique polynomials q(x) and R(x) such that p(x) = d(x) · q(x) + R(x), where the degree of
R is less than the degree of d. R(x) is called the remainder.
Remainder Theorem
When a polynomial f(x) is divided by x − r, the remainder is f(r).
Factor Theorem
Let f(x) be a polynomial. If f(r) = 0, then x − r is a factor of f(x). Conversely, if x − r is a
factor of f(x), then f(r) = 0.
Linear Factors Theorem
Any polynomial f(x) of degree n can be be ex pressed as a product of n linear factors, f(x) =
, where each is a root of f(x), and may be a real or complex number.
Some roots may be repeated.
Rational Roots Theorem
If , and all the coefficients are integers . Then any root of the
equation f(x) = 0 must be of the form , where p is a factor of (the constant term of f ) and
q is a factor of (the leading coefficient of f), and p and q have no common factors (so is in
lowest terms ).
Complex Conjugate Roots Theorem
Let f(x) be a polynomial whose coefficients are real numbers. If a + bi is a root of f(x) = 0,
and b ≠ 0, then a − bi is also a root of f(x) = 0).
Linear and Quadratic Factors Theorem
Any polynomial with real roots can be factored into linear and quadratic factors with real coefficients.

Partial Fractions Decompositions

In the following, we always assume the degree of p(x) is smaller than the degree on the bottom:

,where ax2 + bx + c is irreducible

,where ax2 + bx + c
is irreducible

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

OR is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for visitors -- if you order Algebra Helper by midnight of May 26th you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)


Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

OR is an authorized reseller
of goods provided by Sofmath
Check out our demo!
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2018, Algebra-Answer.Com.  All rights reserved.