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Linear_Equations_and_Inequalities
Math 1031 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 like2x  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 pointslope 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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