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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 #3-18
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
non linear 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 denominators /ratio-help-like-algebra-help.html">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 y-intercept.

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 y-intercept, 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 work-rate 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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