2. Ordering symbols : < (remember that "less than" means "to the left of" on the
number line: -10<-5 since -10
is to the left of -5),> greater than, ≤ , ≥ (remember that a line
underneath means "or equal to": 10 ≤ 10 is a true statement
since 10 is less than OR EQUAL TO 10)
3. Absolute Value: Remember that l#l measures the distance from that # to 0 and
distance is always positive!
4. Prime factors: prime numbers are evenly divisible by themselves and 1 only. 9
is not prime since 3 goes evenly into 9
1. Solve Equations:
Distribute to remove parantheses
Clear fractions by multiplying BOTH SIDES OF EQUATION by the LCD
Move variable terms to left side, non variable terms to the other
Divide by coefficient of variable.
2. Solve word problems: Remember to DEFINE THE VARIABLE, and ANSWER IN WORDS
3. Solve Inequalities: Graphing on a number line...use open circle for < or >
use closed circle for ≤ or ≥
Remember that multiplying or dividing by a negative switches the direction of
Example: -2x> 6, solve by dividing both sides by –2, and you get x <-3
Topics from Chapters 3
1. Plot points: plot any given point, identify the quadrant in which it
lies, know the form of x-intercepts (a, 0)
and y-intercepts (0, b)
2. Find distance (from Section 11.1): Find the
distance between two points by using the Distance Formula
(also be able to plot the points and show
the line segment that represents the distance
between the points)
4. Graph line equations by
a. plotting points (create a table of values, i.e. t-chart)
b. finding x-intercept and y-intercept: set x = 0 and find y; set y = 0 and find
c. plotting the y-intercept (or any other point) and using theslope
as rise over run to find another point on the line
5. Find the Slope of a line: Remember that
(you have to rise before you can run...think
a. given two points:
b. given an equation: solve the equationfor y to get the point
slope equation y = mx + b.
6. Write the equation of a line: As soon as you see the words "FIND THE
EQUATION OF THE LINE ..."
WRITE DOWN the point-slope equation:
Find the slope if necessary, then substitute in a point and the slope.
7. Horizontal lines: Equation is of the form y = some constant (e.g., y =
1). Graph by making a t-chart by letting y = 1 for
several points, x can be anything! SLOPE IS 0.
8. Vertical lines: Equation is of the form x = some constant (e.g. x =
2). Graph by making a t-chart by letting x = 2 for several
points, y can be anything! SLOPE IS UNDEFINED.
9. Graph the solution toLinear Inequalitiesin two variables (example:
2x + 3y > 6):
(1) Graph the line (the =),
(2) Choose a dashed line for < , > solid line for ≤ , ≥ .
(3) Shade: Check a point in the inequality. If you get a true statement (like 0
< 5), shade the side containing the check
point. If you get a false statement (like 0 > 5), shade the OTHER side of the
Topics from Chapter 4.
1. Solve two-variable systems of linear equations
Methods of solution: Elimination, Substitution, Graphing: The solution
you find by using substitution or elimination is the
intersection point when you graph the equations! ALL SOLUTIONS WILL HAVE BOTH AN
X AND A Y VALUE!! Once
you have solved for one variable, be sure to go back and solve for the other!!!
Graphing: Graph each line (use the checkerboard), find the point at which
they cross. This is the solution. CHECK IT in
Substitution: solve for one variable in one equation, substitute into the
Addition/ Elimination: multiply one or both equations to get opposite
coefficients on one variable. Add equations.
Types of systems: Consistent (with one solution, two intersecting lines), Dependent
(with infinite solutions, one single line-variables drop
out, true statement) Inconsistent (with no solutions, parallel
lines-variables drop out, false statement)
Word problems using two variables: Interest, Money, Mixture and Solution
Interest and Money problems are alike. Mixture and Solution problems are alike.
On the latter, DON'T
FORGET to have the final percent or price per pound TIMES the final amount!!!
As always, DEFINE YOUR VARIABLES in words, set up and solve and equation and
Topics from Chapter 5:
1. Know the definition of exponents:
2. Apply the Properties of Exponentsin simplifying
1. Product rule: (add powers when
multiplying like bases)
2. Quotient rule: (subtract powers when
dividing like bases)
3. Power to Power rule: (multiply powers
when power to power)
4. Distributive Property:
This DOESN'T work for addition!! I.e.,
In working with exponents, IF IN DOUBT, EXPAND IT OUT.
c. no radicals in the denominator; Multiply bottom and top by “what’s missing”
to make 2 of a kind, 3 of a kind, etc.
(i)Rationalizing the denominator (SINLGE TERM): multiply numerator and
denominator by "what's
missing" under the radical in the given denominator. "What's missing" are the
factors needed to create a
perfect power (power = root or multiple of the root)
(ii) Rationalizing the denominator (TWO TERMS): Multiply numerator and
denominator by the
CONJUGATE of the denominator. Ex. Given ,
the conjugate is
Be sure to simplify and reduce your final answer.
2. Combining radical expressions:
a. simplify all radicals as much as possible
b. identify like radicals (same radicand)
c. combine COEFFICIENTS in front of like radicals
3. Solving radical equations:
a. isolate radical, if possible (otherwise put one radical on each side of
b. raise both sides to power = root (for example: for a square root, square both
c. solve for x (linear equation: isolate x / quadratic equation: set = 0,
factor, set factors = 0)
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