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 
1.7 #67, 77, 87 
Convert between decimal and scientific notation.  5.3 #15, 27, 31, 35  
Simplify signed numbers and fractions raised to 
1.7 #27, 28, 31, 5.2 #15, 65 

Simplify an exponential expression using the 
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 
1.8 #87, 91 
Determine whether a number is a solution to a 
2.1 #19, 29, 31 

Determine whether a point is a solution to a linear 
3.2 #19, 27 

Construct a table of values for a given linear 
3.2 #49, 55  
Construct a table of values for a given simple 
5.4 #69, 75  
Solve 
Solve linear equations in one variable, including 
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 
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 
7.3 #41, 43, 51 

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 
5.1 #41 

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 
5.1 #79, 109, 115 

Simplify a squared binomial.  5.7 #15, 23, 27  
Divide 
Divide signed numbers. Evaluate zero in 
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 
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 
3.4 #23, 25, 35, 41, 47 
Understand the equations and slopes of horizontal 
3.2 #69, 71 

Rearrange and interpret the equation of a line to 
3.5 #13, 37, 43 

Find the intercepts of a line. Use intercepts to 
3.2 #21, 37  
Find the equations of a line in various 
3.6 #13, 21, 25, 35, 43, 47  
Given the slope and yintercept, write the 
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 
2.5 #13, 15, 41 2.7 #99 
Plot data and interpret the meaning of a specific 
3.1 #37, 39  
Solve percent problems.  2.3 #31, 39, 45  
Given a mathematical equation that models a 
2.4 #15, 23 

Solve problems that involve area and perimeter of 
2.4 #81, 85  
Translate words describing a linear relationship 
3.5 #95, 97 

Solve workrate problems.  7.7 #35, 39  
Solve distance, rate, time problems. 
2.4 #19 

Solve proportion problems  7.8 #53, 79, 85, 87 