# Linear_Equations_and_Inequalities

# Math 103-1 Final Exam Review Sheet

The final exam is comprehensive. It covers chapters 2, 3,
4, 5, 6, 7, and 8. Specific sections

and content is listed below. You may bring a simple scientific calculator, but
no

graphing/symbolic/cell phone calculators are allowed . You may use a 5×7 inch
hand

written note card. Don't be late.

## Chapter 2: Linear Equations and Inequalities

**x2.1: Linear Equations :** Be able to solve linear
equations. Be able to find the LCD in

case that there are fractions. Be able to check your answer.

**x2.2: Linear Equations and Problem Solving:** Be able to work with
percentages

and proportions . Two shapes that are the same shape, but a different size are
what?

**x2.3: Business and Scientific Problems:** Be able to set up and solve a
simply rate

problems. I could ask a business, mixture, or distance problem. What is d = r×t?
Know

the equations for a square, rectangle, circle , and triangle. Be able to solve
given formulas

for another variable . Be able to do a word problem that deals with geometry.

**x2.4: Linear Inequalities:** Be able to solve linear inequalities of one
variable. When

does the inequality change direction? Be able to state the answer using an
inequality,

interval notation, and on a number line . Be able to solve compound equalities of
the form

5 < 2x - 5 < 10 and of the form 2x > 1 or - 6 > 3x.

**x2.5: Absolute Value Equations and Inequalities:** Be able to solve basic
absolute

value problems like|2x - 4 |
+ 3 = 6 and like| x + 5|
= |x + 11|.
Make sure and check your

answers because sometimes the ones you find won't work. Be able to solve
absolute value

inequalities like |3x - 4|≥5
and |2 - 1/3x| ≤1/100. Be able to express your
answers on a

number line, with interval notation, and with inequalities.

## Chapter 3: Graphs and Functions

**x3.1: The Rectangular Coordinate System :** Be able to
plot points (ordered pairs).

Be able to build tables from given equations, like lines . Be able to find the
distance between

two given points. What is the Pythagorean Theorem? Be able to find the midpoint
(average)

between two points.

**x3.2: Graphs of Equations:** Be able to graph a given function by building
a table of

values and plotting those values. Be abe to find intercepts of equations, both x
and y.

**x3.3: Slope and Graphs of Linear Equations:** Given two points, be able to
find the

slope of the line that passes through them. What kind of lines have zero slope ?
Vertical

(undefined) slope? Given the equation of a line, be able to find its slope. Know
the slope-

intercept form of a line y = mx + b. What is m? What is b? When are two lines
parallel?

Perpendicular? What is m_{1} = -1=m_{2} for? Note that slope represents the average
rate of

change of a process .

**x3.4: Equations of Lines:** Be familiar with the point-slope form of a line
y - y_{1} =

m(x - x_{1}). What is m? What is (x_{1}; y_{1})? Be familiar with the general form of a
line

ax + by + c = 0. What is x = a? y = b?

**x3.5 Graphs of Linear Inequalities:** Be able to sketch the solutions of
linear inequal-

ities.

**x3.6 Relations and Functions: **What is a relation? What is domain? What is
range?

What is a function? Be familiar with function notation. Be able to evaluation
functions at

a given number, a variable, a smiley face, a tree, or an expression . Be able to
find both the

domain and range of a function. Be able to find the domain of functions like f(x)
= x^{2}-4x,

**x7. Graphs of Functions:** Be able to sketch a function. Be able to use a
table of

values to sketch a graph. Be able to sketch piecewise functions. Be able to
sketch functions

with a given domain. Be able to use the vertical line test to determine whether
a graph is a

function or not (relation). Be familiar with shifts and reflections. Be familiar
with the six

basic functions and their graphs.

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