Math 40 Final Exam Review
Notice that topics here are arranged a little bit differently
than the order in which you learned them. This is to help you to see the
similarities and contrasts between all the different topics you have learned
over the semester. Example problems are listed with each topic; all chosen
problems are those that have solutions in the back of the textbook.
Suggested study plan: Plan on studying for seven days. Each
day, practice the problems in one category and work through a couple of problems
in the “Applications” category. In this manner, you can prepare for your final
exam over one week. Certainly, if you are having trouble with a topic, you will
want to do more than the suggested problems to gain a mastery of the topic.
Simplifying 
Simplify a numeric expression using the order of
operations and simplify absolute values. 
1.7 #67, 77, 87 
Convert between decimal and scientific
notation. 
5.3 #15, 27, 31, 35 
Simplify signed numbers and fractions raised to
exponents. 
1.7 #27, 28, 31,
5.2 #15, 65 
Simplify an exponential expression using the
various rules of exponents. 
5.1 #39, 51, 75 
Simplify terms with negative and zero
exponents. 
5.2 #19, 33, 43, 55, 57, 65 
Completely factor a polynomial.

547 #318 
Simplify a rational expression . 
7.1 #45, 47, 81, 83 
Simplify complex fractions .

7.5 #29, 33, 57, 61 
Evaluate 
Evaluate an algebraic expression for given
variable values . 
1.8 #87, 91
5.5 #57 6.1 #21 
Determine whether a number is a solution to a
given equation.

2.1 #19, 29, 31 
Determine whether a point is a solution to a linear
equation.

3.2 #19, 27 
Construct a table of values for a given linear
equation and graph the equation . 
3.2 #49, 55 
Construct a table of values for a given simple
nonlinear equation and graph the equation. 
5.4 #69, 75 
Solve 
Solve linear equations in one variable, including
those with parentheses. 
2.2 #27, 39, 47, 61, 87 
Solve a linear inequality. Use interval
notation 
2.7 #37, 45, 53, 67 
Solve literal equations. 
2.4 #39, 45, 53, 61, 71
7.6 #59, 67 
Clear fractions from linear equations. 
2.2 #67, 69, 79 
Solve a quadratic equation that can be solved by
factoring. 
6.7 #23, 33, 39, 49, 63, 65 
Solve a proportion 
7.8 # 35, 39, 47 
Solve a rational equation 
7.6 #25, 37, 51, 53 
Add or Subtract 
Add or subtract signed
numbers and fractions 
1.4 #35, 53 1.5 #37, 53 
Add or subtract variable
expressions using like
terms. 
5.5 #21, 33 
Add or subtract polynomials 
5.5 #39, 61, 65, 81, 93 
Add or subtract rational expressions with like or
unlike denominators . 
7.3 #41, 43, 51
7.4 #39, 45, 53, 55 
Multiply 
Multiply signed numbers 
1.6 #41, 43 
Multiply fractions 
1.2 #87, 93 1.6 #85 
Multiply numbers written in
scientific notation. 
5.3 #61, 63, 71 
Multiply two exponential expressions and apply
the correct exponent rules. 
5.1 #41
5.6 #19, 21, 23 
Multiply polynomials of
various sizes. 
5.6 #29, 53, 59, 71 
Multiply rational
expressions and simplify. 
7.2 #21, 27, 31 
Simplify an exponential expression that is raised
to a power. 
5.1 #79, 109, 115
5.2 #87, 97 
Simplify a squared
binomial. 
5.7 #15, 23, 27 
Divide 
Divide signed numbers. Evaluate zero in
quotients. 
1.6 #63, 73, 75 
Divide fractions 
1.2 #77, 91 1.6 #77 
Divide two exponential
expressions 
5.1 #57, 97 5.2 #91, 107,115 
Divide numbers written in
scientific notation. 
5.3 #67, 69 
Divide a polynomial by a
monomial. 
5.8 #35, 47 
Divide a polynomial by a binomial using
polynomial long division. 
5.8 #49, 71, 77, 95 
Divide rational expressions
and simplify. 
7.2 #49, 53, 59 
Lines 
Calculate the slope between two points or from
the graph of a line. 
3.4 #23, 25, 35, 41, 47 
Understand the equations and slopes of horizontal
and vertical lines. 
3.2 #69, 71
3.4 #45, 61, 67 
Rearrange and interpret the equation of a line to
find the slope and yintercept. 
3.5 #13, 37, 43 
Find the intercepts of a line . Use intercepts to
graph. 
3.2 #21, 37 
Find the equations of a line in various
circumstances. 
3.6 #13, 21, 25, 35, 43, 47 
Given the slope and yintercept, write the
equation for the line and graph it. 
3.5 #51, 57 
Graph a line given its
equations. 
3.5 #67, 73 
Graph a linear inequality. 
3.7 #39, 49, 63 
Applications 
Translate words into an algebraic equation and
solve. 
2.5 #13, 15, 41 2.7 #99 
Plot data and interpret the meaning of a specific
point. 
3.1 #37, 39 
Solve percent problems.

2.3 #31, 39, 45 
Given a mathematical equation that models a
real world situation, evaluate the equation for
specific data and interpret the result. Note: You
will be given the appropriate equation to use. 
2.4 #15, 23
3.2 #77, 79 3.3 #81
5.4 #83
7.1 #97 
Solve problems that involve area and perimeter of
simple geometric figures. 
2.4 #81, 85 
Translate words describing a linear relationship
into a linear equation. 
3.5 #95, 97
3.6 #77 
Solve workrate problems. 
7.7 #35, 39 
Solve distance, rate, time
problems. 
2.4 #19
7.7 #23, 29 
Solve proportion problems

7.8 #53, 79, 85, 87 
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