December 2023
GUIDED SELF-PLACEMENT MATH TEST
STUDY GUIDES
GSP MATH STUDY GUIDE
TEST 0: FOUNDATIONS OF ALGEBRA READINESS CHECK
Study Guide………………………………………………………………………………..………….………..page 1
Answer Key…………………………………………………………………………..……………………..… page 6
TEST 1: COLLEGE MATH READINESS CHECK
Study Guide ………………………………………………………………………….…..…………………..page 7
Answer Key…………………………………………………………………………….….………………… page 16
TEST 2: COLLEGE ALGEBRA READINESS CHECK
Study Guide ……………………………………………………………………………………….…….…. page 22
Test 2 Answer Key………………………………………………………………………………..……….page 29
HOW THE TEST WORKS:
Start with TEST 1 (13 ques�ons/90 minutes).
If your score is 84% or more (11 or more correct) placement is MAT 099
TEST 2 for
Less than 84% /11 correct= taTEST 0
TEST 0
84% or more ( 11 or more correct) placement is MAT 097
Less than 84% = placement is MAT 093
TEST 2
84% or more (11 or more correct) placement is MAT 194
Less than 84% placement is MAT 099
The Guided Self-
of the visit
Precalculus and Calculus:
-For
to
Study Guide for Test 0: "Foundations of Algebra Readiness Check" (MAT093 Skills)
Work through this study guide to help you prepare for the "Foundations of Algebra Readiness Check", or "Test
0". This content aligns with the MAT093 (Foundations of Mathematics) course offered at BHCC. You will need
to score an 84% or higher on the actual test to enroll in MAT097 (Foundations of Algebra).
1. Find the area of the rectangle shown
ft
ft
__________________ square feet
2. If elephant grass grows inches a day, how many inches will it grow in 9 days?
__________________ inches
3. It took Danna hours to get from Portland to Kansas City. Then it took Danna
another hours to get from Kansas City to Sacramento. How long did Danna travel in total?
Write your answer as a mixed number. Remember to type , enter 3_2/5.
Danna traveled a total of __________________ hours.
4. A chewy fruit bar recipe calls for cups of brown sugar and cups of granulated sugar.
How many cups of sugar are in the recipe?
There are __________________ cups in the recipe.
How many MORE cups of brown sugar are there then granulated sugar?
There are __________________ more cups of brown sugar.
5. Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local
stores. You mix the Gazebo blend with the Tanzanian blend, but always in the same proportion.
Yesterday, you mixed 130 pounds of the Gazebo blend with 247 pounds of the Tanzanian blend.
Today, there is 60 pounds of the Gazebo coffee left in stock. How many pounds of the Tanzanian
1
coffee should you mix with it to get your secret blend?
Answer: __________________ pounds
6. In Tacoma, the tax on a property assessed at $840,000 is $15,960. If tax rates are proportional in
this city, how much would the tax be on a property assessed at $380,000?
Answer: $ __________________
7. Solve the proportion
(round to the hundredths place)
__________________
8. Find the unknown number in the proportion
Round your answer to the nearest hundredth.
__________________
9. A person who wants to get in shape goes to a local gym that advertises 64 training sessions for
$1105. Find the cost of 162 training sessions.
Round your answer to the nearest cent.
$__________________
10. Solve the proportion. Leave the answer as a fraction.
__________________
11. If the first chapter of a certain book is 26 pages long and makes up 2% of the book, how many
pages does the entire book have?
2
__________________ pages
12. What is percent of ?
Your answers is : __________________
13. 8.2% of 35 is what number?
__________________
14. 120% of 110 is what number?
__________________
15. If the sales tax rate for the state of Arizona was 7.5%, what would the state sales tax on a $2,400
car be in Arizona?
$__________________
What would the final cost of the car, including tax, be?
$__________________
16. The sales tax rate for South Salt Lake is 7.05%.
What is the state sales tax on a $26,500 car in South Salt Lake?
$__________________
What is the final cost of the car, including tax?
$__________________
The sales tax rate for Morgan County is 5.95%.
What is the state sales tax on that same car purchase in Morgan County?
$__________________
What is the final cost of the car in Morgan County, including tax?
$__________________
How much money would you save by driving to Morgan County to purchase the vehicle?
3
$__________________
17. Divide. Write your answer in lowest terms.
__________________
18. Divide and simplify: = __________________
Write all products as integers or reduced fractions - NOT MIXED NUMBERS.
If the expression is undefined use the word undefined in the answer box.
19. Subtract:
__________________
20. Subtract:
Give your answer in reduced terms.
__________________
21. Solve each proportion:
(round answers to nearest tenth)
__________________
(round answers to nearest whole person)
__________________
4
22. Solve for the variable in
__________________
23. Find the least common multiple of and using the prime factors method.
__________________
24. Find the least common multiple of 7 and 11
__________________
25. Solve for the variable in
__________________
26. A person who wants to get in shape goes to a local gym that advertises 85 training sessions for
$923. Find the cost of 127 training sessions.
Round your answer to the nearest cent.
$____________________
27. 31 % is equivalent to what decimal value?
__________________
28. 5.9% is equivalent to what fraction in reduced terms?
__________________
29. After visiting the Titanic, Captain Brain and Mr. Pinky are taking the Alvin submarine back to
the surface of the water. After ascending for 3 hours, they are 1898 feet below the surface of the
water. Then, at 8 hours they are 1728 feet below the surface. (Note: under the water is negative)
What is the rate of the submarine? __________________ feet per hour
What depth did the submarine start at? __________________ feet
Write an equation to model this situation (use for depth in meters and for hours).
__________________
5
30. You are in a submarine and are at a depth of 47 feet below sea level. Your depth changes to 51
feet below sea level. Did you go up or down?
A. __Up
B. __Down
Answer Key to Study Guide for Test 0: "Foundations of Algebra Readiness Check" (MAT093 Skills)
1.
2.
3.
4. ~
5. 114
6. 7220
7. 26.15
8. 90.29
9. 2797.03
10.
11. 1300
12. 182
13. 2.87
14. 132
15. 180.00 ~ 2,580.00
16. 1,868.25 ~ 28,368.25 ~ 1,576.75 ~ 28,076.75 ~ 291.50
17.
18.
19.
20.
21. 119.2 ~ 19
22.
23. 330
24. 77
25. 0.2625
26. 1379.07
27. 0.31
28.
29. 34 ~ 2000 ~
30. B: Down
License info at: https://ohm.lumenlearning.com/course/showlicense.php?id=582-1196-29953-38023-880-117894-803-879-883-16049-841-70274-953-955-
30775-43687-38005-42035-623-630-38038-42467-234117-234119-42460-51583-903-906-3266-34595
6
Study Guide for Test 1: "College Math Readiness Check" (MAT097 Skills)
Work through this study guide to help you prepare for the "College Math Readiness Check", or "Test 1". This
content aligns with the MAT097 (Foundations of Algebra) course offered at BHCC. You will need to score an
84% or higher on the actual test to place into a non-STEM college math course (MAT171/172/174/181) -or- into
MAT099 (Intermediate Algebra) -or- to move on to the next test ("College Algebra Readiness Check" for
students needing MAT194).
1. Evaluate: where , and
__________________
2. Evaluate
for and
__________________
Write the answer as a reduced fraction.
3.
Simplifying Algebraic Expressions
Simplify by using the distributive property and combining like terms.
__________________
__________________
__________________
__________________
4. Simplify __________________
5. Solve for
__________________
6. Solve the equation for
__________________
7
7. Solve for :
You can enter your answer as an improper fraction (like 13/4), but not as a mixed number.
__________________
8. Complete the table for the equation . Then use two of your points to create its graph.
__________________
__________________
__________________
__________________
9.
Field Trip
The Aquarium charges $16 for adult admission and $9 for each child.
The Aquarium bill for a school field trip was $377.
Write a linear equation in general form to represent this situation. Let C represent the number of children
and A represent the number of adults attending the field trip.
Equation: __________________
If 33 children attended the field trip, how many adults were there?
There were __________________ adults.
10. Find the x-intercept and y-intercept of the graph of . Then graph.
x-intercept = (__________________,0)
y-intercept = (0,__________________)
8
11. Use the slope-intercept form of a line to graph the equation .
The slope is __________________
The y-intercept is __________________. (Remember to write the intercept as an ordered pair)
9
12. Consider the following equation:
A) Write the above equation in the form Enter the values of and in the appropriate
boxes below as integers or reduced fractions (in the form A/B.)
Answer: __________________ + __________________
B) Use your answer in part (A) to find the ordered pair that lies on this line when
Answer: ( ,__________________)
Enter your answer as an integer or a reduced fraction in the form A/B.
13.
Graphing Inequalities
Graph the following inequality.
Note: To graph the inequality:
1. Select the type of line below (solid or dashed).
2. Plot two points on the line.
3. Click on the side that should be shaded.
10
14.
Graphing Inequalities
Graph the following inequality. Be sure to use a solid/dashed line as appropriate and to shade the
appropriate region of the coordinate plane.
15.
Graphing Inequalities
Graph the following inequality. Be sure to use a solid/dashed line as appropriate and to shade the
appropriate region of the coordinate plane.
11
16. Solve the system of equations by graphing:
First graph each line, then place a dot indicating the solution to the system.
12
17. Solve the system of equations by graphing:
First graph each line, then place a dot indicating the solution to the system.
18. Solve the system by substitution:
Answer: (__________________ ,__________________ )
Enter your answers as integers or as reduced fraction(s) in the form A/B.
19. Solve the system by elimination.
= (__________________,__________________)
13
20. Solve the system by elimination.
= (__________________,__________________)
21. Solve the system of equations. Give your solution as an ordered pair.
__________________
22. Evaluate:
-|17| = __________________ -|-17| = __________________
|-(-17)| = ___________________________
23. Find the absolute value of 7. __________________
Find the opposite of 7. __________________
Find the reciprocal of 7. __________________
24. Rewrite this number in appropriate scientific notation:
answer = __________________
25. Simplify:
__________________
26. Simplify the following expression completely:
Answer: __________________
27. Simplify the following expression completely:
Answer: __________________
14
28. Simplify the following expression completely:
Answer: __________________
29. Graph the equation by completing a table of values.
30.
Find the equation of the line above.
__________________
15
Answer Key to Study Guide for Test 1: “College Math Readiness Check” (MAT097 Skills)
1. 33
2.
3. ~ ~ ~
4.
5.
51
2
or 25.5
6. −
6
7
7.
8. -3 ~ -4 ~ -5 ~ -6 ~
9. ~ 5
10. -2 ~ -4 ~
16
11. ~ ~
12. ~ ~
17
13.
14.
18
15.
16.
19
17.
18. ~
19. -2 ~ 1
20. 1 ~ -4
21.
22. -17 ~ -17 ~ 17
23. 7 ~ -7 ~
24.
25.
26.
27.
28.
20
Study Guide for "College Algebra Readiness Check" (MAT099 Skills)
Work through this study guide to help you prepare for the "College Algebra Readiness Check", or "Test
2". This content aligns with the MAT099 (Intermediate Algebra) course offered at BHCC. You will need to
score an 84% or higher on the actual test in order to enroll in MAT194 (College Algebra). **Only students
who need to take MAT194 need to take this test**
1. Graph the inequality and give interval notation for the solution.
OR
Interval notation for the above inequality and graph is __________________
2.
Graph:
3. Simplify
Write your answer with positive exponents only.
__________________
22
4. Write the polynomial that represents the perimeter of the figure pictured below.
Perimeter = __________________
5. Multiply and simplify: = __________________
6. Solve
_________________
7. Solve by completing the square. Enter exact values.
If you have two solutions, list them separated by commas.
For example: for and , type "2-sqrt(5),2+sqrt(5)"
If there is no solution, write "DNE" (does not exist)
__________________
8. Which of the expressions below is equal to the expression when written using a
rational exponent?
A. __
B. __
C. __
D. __
9. Simplify:
__________________
23
10.
Graph:
11. Simplify completely. Do not use any parentheses in your answer.
__________________
12. Add the polynomials:
__________________
13. Find the area of the triangle. Simplify your answer.
The area is __________________ square inches.
24
14. Solve the following equation:
__________________
15. Solve the equation given by completing the square. If there are more than one answers, separate
them by a comma. If there is no solution, enter DNE (short for does not exist.)
__________________
16. Simplify:
__________________
17. Solve for
__________________
18. Solve for :
__________________
19. Add and simplify:
__________________
20. Simplify and give the domain.
__________________
State the sum in simplest form.
__________________
25
21. What is the family of the equation ?
A. __exponential
B. __linear
C. __quadratic
Create a table of values for the equation on paper and use it to help you graph the equation.
22. You are working with a quadratic equation and construct the following graph.
Identify the vertex of the parabola: __________________
Remember that the vertex is a point!
Identify the y-intercept of the parabola: __________________
Remember that the y-intercept is a point!
26
Identify the x-intercepts: __________________ and __________________
Remember that the x-intercepts represent points on the graph!
Given the x-intercepts above, write an equation for the parabola in factored form:
__________________
Hint: Think about the zero-product property.
Write an equation for the axis of symmetry: __________________
23. An object is thrown upward at a speed of 110 feet per second by a machine from a height of 8
feet off the ground. The height of the object after seconds can be found using the
equation
When will the height be 182 feet?
__________________ (choose the units for your answer: feet / Ft/sec / sec/ft / seconds)
When will the object reach the ground?
__________________ (choose the units for your answer: feet / ft/sec / sec/ft / seconds)
24. The equation gives the number of diagonals for a polygon with sides. Find
the number of sides for polygon that has 90 diagonals.
__________________
25. Solve for x. If there is more than one solution, separate the solutions with a comma.
__________________
26. For the following rational equation , first state the restriction(s):
__________________
Next provide the solution(s) as a single fraction in lowest terms. If there is no solution, type "DNE".
__________________
27
27. Solve for
__________________
28. Wilma can mow a lawn in 60 minutes. Vanessa can mow the same lawn in 40 minutes. How
long does it take for both Wilma and Vanessa to mow the lawn if they are working together?
__________________ minutes
29. Simplify:
__________________
30. (Simplify the expression
__________________
28
Answer Key for “College Algebra Readiness Check” (MAT099 Skills)
1.
~ (-oo,-3)U[4,oo)
2.
3.
4.
5.
6.
7.
8. B:
9.
10.
29
11.
12.
13.
14.
15.
16.
17. 39
18.
19.
20. 4 ~
21. C: quadratic ~
22. ~ ~ ~ ~ ~
23. 2.47, 4.41 ~ seconds ~ 6.95 ~ seconds
24. 15
25. -7
26. ~
27.
28.
29.
30.
License info at: https://ohm.lumenlearning.com/course/showlicense.php?id=7752-91195-1304-48356-40167-7945-59203-91529-3861-3552-
3597-1863-40157-29557-73540-38375-2863-38409-1988-93862-65528-133363-17065-96790-18992-231981-38411-3402-18631-55320
30
