Elementary Algebra -- MTH065
Elementary Algebra -- MTH065
Preparing for the Module 1 Retest
Getting Ready
Prior to retesting for Module 1, you should have gone over your test with your instructor
or an instructional assistant in the Learning Center, so you may already have a good
idea of what topics you need to review. To study for the retest, examine the problems
below. They represent a sample of problems like the ones covered in Module 1. Which
ones are similar to the problems you missed on the test? To help you review for the test,
practice those problems, referring to the appropriate section as needed for specific
examples, rules, or more practice problems.
NOTE: Your instructor may have specific retest instructions for you. Be sure to talk with
your instructor about what you will need to do prior to retaking the test. Your instructor
must validate your ticket again so you can retake the test.
REMINDER: You must pass each module test with a score of at least 70%. The best
score that you may earn on the first retest for this module is 80%. This means that any
score of 80% or better will be recorded as 80%. It is the instructor's decision whether to
allow more than one retest per module. If a second retest is allowed, the best score that
can be earned is 70%.
Problems to Practice
Section 1.1: Use the order of operations to completely simplify each of the following expressions. Check your answers using a calculator.
I. Grouping Symbols: parentheses, brackets, fraction bar
II. Exponents
III. Multiplication and Division in order from left to right
IV. Addition and Subtraction in order from left to right
1. [pic] 2. [pic] 3. [pic]
4. [pic] 5. 15 ( 6(2)3 6. [pic]
Section 1.1: Translate the calculator keystrokes given into an equivalent algebraic statement.
7. ( [pic] + [pic] ) ( ( [pic] – 7 ) 8. [pic] – ( [pic] ^ [pic] + [pic] )
9. ( 16 ( 2 ^ 3 ) ( 4 + 1 ( 2 10. 7 + √ ( 13 + 3 ) ( 2
Section 1.2: Determine whether each phrase represents a constant or variable quantity. Give reasons for your answers.
CONSTANT: A quantity whose value does not change
VARIABLE: A quantity whose value may change
11. The number of days in a week
12. The area of a rectangle with a 6-inch width and a length of x
13. The cost of a gallon of gas
14. The number of minutes in a day
15. The number of days in a year
Section 1.2: Combine like terms in the expressions. Identify the coefficient of each term in your answer.
LIKE TERMS: Terms that have identical variable parts
COFFICIENT: A constant when multiplied by a variable
16. [pic] 17. [pic]
18. [pic] 19. [pic]
Section 1.3: Determine which equations are linear.
LINEAR EQUATIONS: A linear equation can be put into the form [pic], where [pic].
20. [pic] 21. [pic] 22. [pic] 23. [pic]
Section 1.3: Solve each equation. Check your answers.
SOLUTION: A solution to a linear equation is any value that, when plugged in for the variable, makes the equation a true statement.
OPTIONAL: Clear fractions and clear decimals
24. [pic]–[pic] 25. –[pic]
26. [pic] 27. [pic]
Section 1.4: Translate the written statements into symbols and the statements written in symbols into words.
28. The product of 3 and the sum of [pic] and 4 is 6
29. 2 less than 3 times a number is not more than 7
30. [pic]
31. [pic]
Section 1.4: Follow the directions. Graph each solution set on a number line. Also use interval notation to indicate the solution set.
CHECK THE BOUNDARY POINT: Plug the number into the original. If an equality results, then the correct boundary point has been found.
CHECK THE DIRECTION: Pick a number in the solution set. If this results in a true inequality, then the direction is correct.
32. For [pic], check the boundary and direction for the solution [pic].
33. For [pic], check the boundary and direction for the solution [pic].
34. Solve the inequality and check. [pic]
35. Solve the inequality and check. [pic]–[pic]
Section 1.5: For the relation below:
a. Identify the independent and dependent variables.
b. Write the relation as a table of values.
DEPENDENT VARIABLE: The variable that depends on the input value and the rule to get its value.
INDEPENDENT VARIABLE: The variable whose value is selected to input into the equation to produce an output.
36. Jerry bought 5 loads of gravel for $550.00. The dollar amount needed to buy gravel
is related to the number of loads of gravel purchased.
37. You walk 150 feet per minute. The distance you walk is related to the time you travel.
Section 1.5: For the following tables decide whether the relation is a function. Provide a reason. State the domain and range for each.
FUNCTION: A relation where each input is assigned exactly one output.
DOMAIN: The set of input values, top row is standard
RANGE: The set of output values, bottom row is standard
38.
| p |(3 |(2 |0 |1 |2 |
| l |5 |3 |2 |(1 |5 |
39.
| m |0 |1 |4 |7 |4 |
| n |1 |2 |1 |2 |3 |
40.
| x | (3 | (2 | 0 | 1 | 2 |
| y | 8 | 8 | 8 | 8 | 8 |
41.
| p | (3 | (3 | (3 | (3 | (3 |
| l | 0 | 1 | 2 | 3 | 4 |
Sections 1.5 and 1.6:
a. Identify the independent and dependent variables.
b. Graph the relation by plotting the ordered pairs.
c. State the domain and range.
d. Decide whether the relation is a function. Provide a reason.
e. If the relation is a function, is it linear? Explain.
42. 43.
|a |(6 |(3 |0 |3 |6 |9 |
|t | 4 |2 |0 |(2 |(4 |(6 |
|g |(2 |(1 |0 |(1 |(2 |(3 |
|r | 5 | 3 |1 |(1 |(3 |(5 |
Section 1.6:. Explain why the relation described is a function. Identify the independent and dependent variables and write an equation using function notation.
44. Jon picks grapes to sell at the produce stand. He sells them for $6.00 for [pic] bushel, $12.00
for [pic] bushel, and $24.00 for [pic] bushels. The cost of the grapes is a function of the number of
bushels of grapes sold.
Sections 1.5 and 1.6: For each graph:
a. Identify the graph as that of a function or not a function.
b. If the graph represents a function, decide if the function is linear.
c. Give the domain and the range.
VERTICAL LINE TEST: A relation is not a function if a vertical line would intersect the graph in more than one point.
45. 46.
47. Section 1.5: Sketch the graph of a function that is increasing.
48. Section 1.5: Sketch the graph of a function that is decreasing.
49. Section 1.5: Sketch the graph of a function that is constant.
Section 1.6: Evaluate the function [pic] for the given values of the independent variable.
50. [pic] 51. [pic] 52. [pic]
Section 1.6: The relation in the table represents a function. Decide whether the function is linear. Provide a reason.
LINEAR FUNCTION: For a function to be linear, equal steps in the independent variable must always produce equal steps in the dependent variable.
COMMON ERROR: Students often will not read directions and will check to see if a table represents a function when the directions specify to check for a linear function.
53.
| t |(2 |0 |2 |4 |6 |
| y |5 |2 |(1 |(4 |(7 |
Section 1.7: Use the table feature of your calculator to complete the table.
54. [pic]
|x |y |
|(2 | |
|(1 | |
|0 | |
|1 | |
Section 1.7: For each of the functions below:
a. What window setting is necessary to see all of the horizontal and vertical
intercepts?
b. Sketch the graph showing all of the horizontal and vertical intercepts.
c. Find the x-coordinates of all the horizontal intercepts. Round answers to [pic]
decimal places.
55. [pic]–[pic] 56. [pic]
Section 1.8: Translate each phrase or sentence into a mathematical expression. Clearly
indicate what each variable represents. Do not solve the equations.
57. Five times the difference of a number and ([pic]
58. Eight is the quotient of [pic] and the difference of 4 and the number.
59. Judy’s age is 5 years less than 6 times Peter’s age.
60. Fifteen percent of a number is 5.
Section 1.8: Use VESI or a similar process to solve each of the following problems.
VESI: Identify the VARIABLE.
Write an EQUATION.
SOLVE the equation.
INTERPRET the results.
61. Jerry works at two part-time jobs. At the first job, he works 12 hours per week and earns
$7.68 per hour. The second job pays $10.61 per hour. How many hours did Jerry work at his
second job the week that he earned $145.31?
62. Jennifer is investing in stamps and gold. She currently has invested $3020 in gold and
$1550 in stamps. She has the opportunity to buy several classic stamps at $91.00 per
stamp. How many stamps did she purchase if her total investment after the purchase
is $5389?
63. The amount of material needed to cover the sides and bottom of a box whose length
is [pic] inches and whose width is [pic] inches is a function of its height. The model that
expresses this relationship is:
[pic], where h is the height of the box in inches.
a. Use the model to find the amount of material (in square inches) needed when the
height is [pic] inches. Round your answer to two decimal places.
b. If the amount of material used is [pic]square inches, what is the height of the box?
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