Try the Free Math Solver or Scroll down to Resources!












Please use this form if you would like
to have this math solver on your website,
free of charge.

Fri 5 Dec — Review for Final Exam (Appendix and Cpt 1)

Final is in 100 Smith Hall on Fri 12 Dec at 1:30 pm.
There are 15 multiple choice questions and 6 fill-in. The MC get no partial credit but the fill in do.
In the MC questions, work out the solution, circle the answer on the test sheet, and fill in the bubble
on the answer sheet.
In the MC, some of the questions are set up to make it difficult to guess. For example a question
might read:

Solve x2+ 5x + 6 = 0. Then, add the two answers to get one of the following:
a. –1
b. 2
c. –5
d. 6
e. None of these.

So, you would add –2 + (–3) to get –5. Circle choice C and fill in the bubble on the answer sheet.
Check my web site for the finals and keys from Spring 2003 and Spring 2005. I did not write those but
they are good practice for mine.
Now, let’s do some review from the Appendix and Chapter 1.

A.2 Geometry Essentials

Be sure to memorize the formulas in this section.
Pythagorean Theorem
Geometry formulas (area, perimeter, volume)
Congruent and similar triangles

Similar triangles - they are the same shape (the angles are the same but the lengths of the legs
can be different).
The corresponding sides of similar triangles are proportional.
For example, given these triangles:

The two are similar since all the angles are the same. So, we can write the following proportion:
4/r = 16/h We could then solve for r in terms of h or h in terms of r.

A.3 Polynomials

Factor using FOIL (First, Outer, Inner, Last)
Special product formulas (difference of squares, square of binomial, sum and difference of
Divide polynomials using long division
Factor polynomials

A.5 Rational Expressions

Be sure to factor first and then cancel common factors.
Multiply and divide
Add and subtract

Find LCD and then combine:
EX: Combine into a single fraction:

Complex rational expressions

A.6 Solving Equations

Quadratic and higher order

Solve: x4 = 2+x2

Let u = x2

Absolute value
Complete the square
Quadratic formula

A.8 Problem Solving: Interest, Mixture, Motion Applications

Translate Verbal Descriptions into Mathematical Expressions
Simple Interest Problems
Mixture Problems

How many gallons of a 25% acid solution must be mixed with 5 gallons of a 10% solution to obtain
an 18% solution?
Let x = # gal of 25% solution

Uniform Motion Problems
Constant Rate Job Problems

A.10 nth Roots; Rational Exponents; Radical Equations

Simplify radicals


Add and subtract radicals


Rationalize denominators of radicals
Solve radical equations
Rational exponents


1.1 Rectangular coordinates; Distance & Midpoint Formulas

Rectangular (xy)
Distance formula
Midpoint formula

1.2 Graphs of Equations in Two Variables

Graph equation by plotting points
Intercepts of a graph
Test for symmetry with respect to xaxis,
yaxis, and origin

Symmetric with respect to x-axis: f(x) = -f(x)

Symmetric with respect to y-axis: f(x) = f(-x)

EX: y = x2-9

 f(x) = x2-9

 f(-x) = (-x)2-9

 = x2-9

 = f(x)

Symmetric with respect to origin: f(x) = -f(-x)

EX: y = 2/x

 f(x) = 2/x

 f(-x) = 2/-x

 = -2/x

 = -f(x)

1.3 Lines

Calculate and interpret the slope of a line
Graph lines given a point and the slope
Equation of a vertical line
Equation of a horizontal line
form of a line
Find equation of a line given two points
form of a line
Identify slope and yintercept
of a line given its equation
General form of a line
Parallel lines
Perpendicular lines

Find the equation of a line that passes through the point (5, 0) and which is perpendicular to the
line that passes through (2, 3) and (1, -5).
First, find slope of the line that passes through the points (2, 3) and (1, -5):

The perpendicular slope is m= negative reciprocal = -1/8

Now, use y = mx + b to find b.

1.4 Circles

Standard form

Graph a circle
General form and completing the square

Find the center and radius of the circle described by:

Put this in standard form by completing the square of both x and y.

The center is (1, –2) and the radius is sqrt(11) .