Introductory Algebra
- Fall 2008 -
MATH 125 - Exam 3 Guide
Earl Rodd
erodd@malone.edu Extension 8546 www.malone.edu/erodd
Summary
Exam 3 will include these review and current items:
Includes some questions on past material, and sections:
You may bring one page (1 side) of hand written notes. You may
bring a calculator.
Note: Don't be scared by the number of pages in the exam
(8). Graphs take a lot of space!
Details
- Identify kinds of numbers (eg. irrational, rational, integer,
natural)
- The exam shows an example of converting an equation from standard
form (e.g. x + y = 10) to slope intercept form (e.g. y = -x + 10).
For each step of the process, you are to write which principle
(e.g. Equality, Commutative etc.) is used.
The example below shows the format:
4(x + 2) + 3y = 13
4x + 8 + 3y = 13 Distributive was used to get to this step
from the prior step.
4x + 3y = 5 Equality (subtract 8 from each side)
3y = 5 - 4x Equality (subtract 4x from each side)
3y = -4x + 5 Commutative (reversed 5 and -4x)
y = -4/3 x + 5/3 Equality (divide both sides by 3)
- Graph an equation and indicate its slope and y-intercept.
- Solve 3 absolute value equations. All have answers.
- Given some equations, write which ones have the null
set as an answer. Equations we have dealt with which have the null
set (no answer) as an answer are:
|x + 10| = -1
because absolute values cannot be less than zero.
x2 < 0 because a number times itself is alwasy positive.
- Solve 3 inequalities and graph them on number lines.
- Plot a number points (e.g. (4,3)) on an x-y coordinate graph.
- Identify the coordinates (e.g. (4,3)) of a set of points
shown on an x-y coordinate graph.
- Solve an equation for y (i.e. convert from standard form to
slope intercept form). For example:
2x - 3y = 6
-3y = 6 - 2x (subtract 2x from both sides)
-3y = -2x + 6 (reverse order to slope intercept form)
y = 2/3 x - 2 (divide both sides by -3)
- Fill in a table of x/y values for a simple equation and then graph
the equation.
- Graph several simple cases (e.g. x=2).
- Given several lines on a graph, compute the slope and y-intercepts
of the lines.
- Compute the slope of a line given 2 points on the line.
- Given the slope of a line know that the slope of a parallel line is
the same and that of a perpendicular line is the negative inverse.
Examples
| Equation | Slope | Slope of parallel line> |
Slope of perpendicular line |
| y = 4x + 2 | 4 | 4 | -1/4 |
| y = 4/5 x - 22 | 4/5 | 4/5 | -5/4 |
| y = -5x - 2 | -5 | -5 | 1/5 |
| y = -2/7 x + 7/2 | -2/7 | -2/7 | 7/2 |
- Draw a freehand graph from some values in a table.
- Given intercepts, graph lines.
- Given some lines on a graph, identify them by criteria (e.g.
slope is positive).
There are 3 BONUS questions worth 5 points in addition to the
64 points on which your grade is based.