Ch. 2 Pretest
Quantities & Relationships
Name ______________________________
Period _________
Show all of your work on a separate piece of paper!
In each problem situation, do the following:
(a) Write a function
(b) Identify the independent and dependent
quantities
(c) Identify the rate of change and the yIntercept.
1. Rachel is walking to the mall at a rate of 3
miles per hour.
2. Maria is stuffing envelopes with invitations
to the school's Sober Grad Night. She stuffs
5 envelopes each minute.
3. The baseball booster club sells t-shirts at the
varsity baseball games. Each t-shirt costs
$12.
Use each scenario to complete the table of
values.
6. a. Owen is riding his bike to his friend's
house at a rate of 6 miles per hour.
Independent
Quantity
Quantity
Units
0
2
4
8
Expression
b. Draw an accurate graph of this scenario, and
label the axes.
8. a. A hot tub containing 400 gallons of water
is drained. The water drains at a rate of 5
gallons per minute.
Independent
Quantity
4. A hot air balloon cruising 1000 feet begins
to ascend. It ascends at a rate of 200 feet per
minute.
Dependent
Quantity
Dependent
Quantity
Quantity
Units
0
10
20
200
Expression
5. A submarine is traveling at a depth of -300
feet. It begins ascending at a rate of 25 feet
per minute.
b. Draw a graph of this scenario and label
the axes.
c. When will the hot tub have 200 gallons of
water in it?
12. A helicopter flying at 3505 feet begins its
descent at a rate of 470 feet per minute.
The function 𝐷(𝑡) = −470𝑡 + 3505
represents the height of the helicopter as it
descends.
d. Determine the amount of water in the hot
tub after 10 minutes.
Find when 𝐷(𝑡) = 1155 and describe what
the answer means in words.
Solve each of the following scenarios.
9. The function 𝐴(𝑡) = 7𝑡 represents the total
amount of money in dollars Laura earns
babysitting as a function of time in hours.
Solve for 𝐴(5) and describe the answer in
words.
10. The function 𝐴(𝑡) = 7𝑡 represents the
total amount of money in dollars Laura earns
babysitting as a function of time in hours.
Find when 𝐴(𝑡) = 42 and describe what
the answer means in words.
11. A helicopter flying at 3505 feet begins its
descent at a rate of 470 feet per minute.
The function 𝐷(𝑡) = −470𝑡 + 3505
represents the height of the helicopter as it
descends.
13. A bathtub contains 5 gallons of
water. It is filled with additional water at a
rate of 4 gallons per minute.
Write a function and find the time it will
take to fill the tub up with 33 gallons of
water.
14. A backyard pool contains 500 gallons of
water. It is filled with additional water at a
rate of 6 gallons per minute.
Write a function and find the time it will
take to fill the pool up with 632 gallons
of water.
Write an algebraic inequality to represent
the following scenarios. (Use a variable, and
DEFINE what that variable means)
17. Leslie has to earn more than $500 in
fundraising money.
Solve for 𝐷(6) and describe what the
answer means in words.
18. Americans must be at least 16 years old to
drive.
19. Jake plays in the under 17 (U17) soccer
team. How old is Jake?
Solve each equation.
25. 2𝑥 + 1 = 7
20. Your sibling must be 5 or under to get into
the fair for free.
26. 2𝑥 − 5𝑥 + 6 = 12 + 2𝑥 − 1
Write a simplified compound algebraic
inequality to represent the following
scenarios:
27. 2 − 5(𝑥 − 3) = −7𝑥 + 9
21. The number of houses that will be built in
the new neighborhood must be at least 14
AND no more than 28.
28. |𝑥 − 5| = 7
22. The flowers in the garden are 6 inches or
taller OR shorter than 3 inches.
29. |2𝑥 + 3| + 2 = 11
Write the algebraic solution for each
inequality.
Solve and graph each inequality.
23.
30. 3𝑥 + 7 ≥ 10
24.
31. 10 − 2𝑥 < 18
32. |2𝑥 + 3| > 5
33. |4𝑥 + 2| ≤ 22
38. Explain the difference between an open and
closed circle when graphing an inequality.
39. What is the error made on the following
problem.
12 − 3𝑥 > −6
−12
− 12
−3𝑥 > −18
−3𝑥 −18
>
−3
−3
34. |𝑥 − 3| + 5 > 25
𝑥>6
35. 2|𝑥 + 2| − 4 ≤ 10
40. What is the error made on the following
problem?
|𝑥 + 2| < 2
𝑥+2 <2
𝑥<0
36. |𝑥| ≥ 9
37. |3𝑥 − 4| < −20
𝑜𝑟
𝑜𝑟
𝑥 + 2 > −2
𝑥 > −4
Review
41. Is this a graph of a function? Justify your
answer with words.
43. Simplify each of the following expressions:
8
7
a. +
3
b.
2
4
2
11
÷3
5
6
2
3
.
c
42. Graph 2 examples of each of the 5 function
families that you know.
1. Linear
d.
2. Exponential
3. Quadratic
4. Absolute Value
5. Piecewise
3
5
7
−3