Name_____________________
Topics in College Math
Midterm Review
Linear Equations:
Solve each equation:
1. −3𝑚 + 29 = 4(𝑚 − 5)
2. 24 + 𝑥 = 8(−8 + 5𝑥) + 𝑥
3. 36 + 8𝑎 = 2(6𝑎 + 8)
4. 8 + 3𝑟 = −7𝑟 − 4(−3𝑟 + 1)
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5. − 2 𝑥 + 9 = 3(4𝑥 − 5)
6. If 𝑥 = 9 and 𝑦 = 5, then 8𝑥 + 4𝑦 =
For the following set of problems, solve for y:
7. −7𝑥 − 2𝑦 = −15
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8. 2𝑥 − 5𝑦 = 20
9. 4𝑥 + 3𝑦 = −15
Application Problem:
10. Demetria and Demetrius own a company together to create painted t-shirts. Demetria painted 20
more than twice the number of t-shirts that Demetrius painted. Together they painted 170 shirts.
Create an equation and solve it to find the number of shirts (𝑥) that Demetria painted?
11. Demetria and Demetrius’s business model for making t-shirts 𝐶 = 5𝑥 + 1080 represents the cost in
dollars for painting 𝑥 t-shirts during a month. Based on this, how much does it cost to produce 75 tshirts?
12. A company will break even as long as the revenue exactly equals the cost. The value of x is called
the break-even point when x equals the number of items sold when
C(x) = R(x).
Demetria and Demetrius sell their t-shirts to college students and have determined that the total
cost in dollars, C(x), of producing x t-shirts is given by C( x) = 5x + 1080, while the revenue in
dollars, R(x) from the sale of the t-shirts is given by R( x) = 25 x.
a. State in words what the cost and revenue functions represent.
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b. How many t-shirts must be sold to break even and what is the total cost/revenue at this
point?
c. Determine the domain where the revenue will exceed the cost.
13. Glenna wants to rent a car for a trip to Key West for one week. She calls two car rental companies to
get prices. Mr. Kotter’s Rentals rent a Cadillac Escalade for $99 for one week plus $0.11 per mile.
Barbarino’s Rental has the same vehicle for $75 per week and $0.15 per mile. If it is 432 miles to Key
West, which company has the better deal? How many miles would Glenna drive before she would
be spending the same amount at either company.
14. Veeral’s car needed body parts due to his latest accident. He was told the body parts cost $925. The
mechanic charges $80 per hour. If he received an estimate for at least $1165 and at most $1325 for
fixing his car, what is the time interval, in hours that the mechanic will be working on his car?
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Interpreting data in graphs and graphing
15. The graph below illustrates the number of acres used for farming in Piscataway, New Jersey, over
several years. Create a line of best fit.
A. What does 𝑥 represent? ______________ What does 𝑦 represent?_____________________
B. What is the slope of the line of best fit and what does it represent?
C. Using a line of best fit, approximately how many acres will be used for farming in the 5th
year?
D. What is an estimate of the change in farming acres between years 1 & 3?
What is an estimate of the change in farming acres between years 2 & 3?
E. Is the size of the land farmed increasing or decreasing?
How can you tell?
16. You are renting a car and they require a $50 deposit and $25 a day.
a. Create a table of values for the cost of the car for the first week including the deposit.
n (no. of weeks)
0
1
2
3
4
5
6
7
8
c (cost in dollars)
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b. Graph these points.
c. Determine the y-intercept or vertical intercept.
d. What is the practical meaning of the vertical intercept?
e. Determine the equation of the line.
Systems of Equations:
17. Solve for the coordinate point that is a solution to this system of equations.
3𝑥 + 2𝑦 = 13
3𝑥 − 4𝑦 = 1
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18. Solve this system of equations:
𝑥 = 2𝑦 − 8
4𝑥 + 𝑦 = 31
19. Give an visual example of a systems of equations and also create a set of equations which have:
a. 1 solution
b. No solution
c. Infinite solutions
20. Write a system of equations and then solve by the method of your choice.
An exam worth 145 points contains 50 questions. Some of the questions are worth two points and
some are worth 5 points. How many two point questions are on the test? How many five point
questions are on the test?
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21. Cody’s school is selling tickets to a choral performance. On the first day of ticket sales the school
sold 4 adult tickets and 2 child tickets for a total of $62. The school took in $272 on the second day
by selling 14 adult tickets and 12 child tickets. Find the price of an adult ticket and the price of a
child ticket.
22. Solve the system
3𝑥 − 4𝑦 = 7
𝑥+𝑦 =7
Quadratics
23. If 𝑥 = −5, which of the following is greatest in value?
A.
(𝑥 + 1)(𝑥 + 2)
B. (𝑥 + 1)(𝑥 − 1)
C. (𝑥 − 2)(𝑥 + 2)
D. (𝑥 − 2)(𝑥 + 1)
E. (𝑥 − 4)(𝑥 + 4)
24. A common factor of
x 2  7 x  10
and
x 2  25
is:
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25. One of the factors of 36𝑥 2 – 9 is 6𝑥 – 3. Find the other factor.
26. 7𝑥2 + 11𝑎 + 4
27. 4𝑥2 − 10𝑥 − 126
28. 4𝑥 3 + 20𝑥2
4𝑥 3 + 𝑥2
Absolute Value:
29. Solve for 𝑥: |3𝑥 + 7| < 25
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30. Solve for 𝑥: |2𝑥 − 4| ≥ 8
31. Solve |5𝑥 + 3 | = 28.
32. Solve the inequality |110𝑥 + 7| < −9876
33. |5𝑥 − 9| > 91 Solve the inequality.
Graph the inequality on the number line below.
34. Find the vertex for the following absolute value functions:
a. 𝑓(𝑥) = −|𝑥 − 3|
𝑔(𝑥) = |−𝑥 + 2| + 4
b. 𝑓(𝑥) = |𝑥 + 1|
𝑔(𝑥) = |−2𝑥 + 2| + 4
c. 𝑓(𝑥) = −|3𝑥 + 4|
𝑔(𝑥) = |2𝑥 − 3| − 4
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35. Graph any two on the same graph by selecting a pair (a, b, or c) and describe the differences. Make
sure you label each graph with its function name. Use the vertex values for the center of your
function tables.
a.
What is the domain and range of 𝑓(𝑥)?
b. What is the domain and range of 𝑔(𝑥)?
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Piecewise Functions:
36. Graph the function:
𝑥 + 2 if 𝑥 < 2
𝑓(𝑥) = {
7
if 𝑥 ≥ 2
37. Graph the piecewise function.
−8
𝑓(𝑥) = {
−3 − 𝑥
𝑥≥1
𝑥<1
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38. Graph the piecewise function. State both the domain and range
2𝑥 + 1 if 𝑥 < 3
𝑓(𝑥) = {
−2𝑥 − 1 if 𝑥 ≥ 3
a. Domain:
b. Range:
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SAT questions
39. Za’iyr was recording how many slam dunks his favorite teams scored. He organized the information
in the pictograph below.






Which team had the largest number of slam dunks?
Which team had the largest number of slam dunks?
Which team had the fewest number of slam dunks?
Which team had more slam dunks, Rockets or Hawks?
How many slam dunks did the Bulls make?
How many slam dunks did the Warriors make?
40. In the sequence below, the first term is 5 and each term after the first is 2 more than 3 times the
previous term. What is the value of 𝑡?
5, 17, 53, 𝑡, 485, …
41. It takes 30 minutes to fill up a cotton candy making machine, and it produces 2 cotton candies per
minute once it is set up. Use an inequality to find the number of cotton candies that can be
produced in 2 hours.
42. If the average (arithmetic mean) of 3𝑥 9𝑥, and 6𝑥 is 12, what is the value of 𝑥?
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43. We can grade can fill 12 final exams in 1 hour. At this rate, how many final exams can be graded in
15 minutes?
44. The diameter of circle 𝐴 is 4 times the diameter of circle 𝐵. What is the ratio of the radius of circle 𝐴
to the radius of circle 𝐵?
45. List 5 fractions between -1 and 0. List 5 decimals between -1 and 0. List one fraction less than -1.
List one decimal less than -1.
5 fractions: ____________________________________________________________
5 decimals: ____________________________________________________________
One fraction less than -1_______________
One decimal less than -1 ________________
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