UCS Algebra 1
Midterm Review #2
1
Which family of function does each graph belong?
__
___
___
___
__
___
___
___
A. Linear
E. Exponential
2
3
Name: _____________________________
Date: ________________ Hour: _______
B. Quadratic
F. Inverse
C. Cubic
G. Square Root
D. Absolute Value
Name the coefficients and constants for the following expressions
a) 8𝑥 7 − 14𝑥 5 + 34𝑥 3 − 𝑥 2 + 54
b) 5𝑥 2
Coefficients: ___________________
Coefficients: ___________________
Constants: ____________________
Constants: ____________________
The coach of a basketball team gathered data on each player’s height, in inches, and shoe
size. He organized the data using ordered pairs in the form
. The set of
ordered pairs below shows this relation.
Is this relation a function? Explain your reasoning in terms of the definition of a function.
4
5
The following diagrams show relationships among a group of students. Which relationship
is a function?
A
C
B
D
a. A store bought a case of disposable cameras for $300.The store’s profit on the cameras
is a function of the number of cameras sold. Find the range of the function 𝑝 = 6𝑐 − 300
when the domain is {0, 15, 50, 62}.
b. In this situation, what do the domain and range represent?
6
A hardware store rents a carpet-cleaning machine for $50 plus $10 per hour of use. The
cost to rent the machine is graphed below.
Which point is the y-intercept of this graph?
7
A hot tub manufacturer uses this equation to estimate the cost 𝐶(𝑑) of making a hot tub
given the diameter 𝑑 in meters.
𝐶(𝑑) = 200𝑑 + 400
If the hot tub manufacturer makes hot tubs with diameters of 2𝑚, 2.5𝑚, 3𝑚, 3.5𝑚,
𝑎𝑛𝑑 4𝑚, what is the range of the function?
8
Graph the equation y  3x  4?
9
Using the graph below, determine the tax rate used on the items purchased.
10
The table below shows the change in temperature over 12 hours.
What is the rate of change per hour?
11
Jennifer wrote this equation to model how she expects the price, p , of a stock will change:
𝑝 = −0.25𝑤 + 15
Explain the relationship that this model represents.
A
As w increases, the value of p
increases
C
As w increases, the value of p stays the
same
B
As w increases, the value of p
decreases
D
As w increases, the value of p
increases on some days
12
Ms. Nguyen is an energy analyst consultant. The equation below represents Ms. Nguyen’s
earnings,
, while working
hours at a site.
For each additional hour that Ms. Nguyen works, how does the value of
13
change?
The sign below shows the costs for one ice cream sundae with toppings.
Number
of
Toppings
c
1
2
3
4
$3.25
$3.75
$4.25
$4.75
Write an equation to model this relationship.
14
Based on the information in the graph, how much will A & J Plumbing charge for an 8-hour
job?
15
The two equivalent sides of an isosceles triangle are 3 more than twice the base. If the
perimeter is 106 in., find the length of the base.
A
length = 5 in.
C
length = 20 in.
B
length = 10 in.
D
length = 30 in.
16
The width of a rectangular map is 12 inches more than the length and the perimeter is 60
inches. Find the length and the width.
17
Larry runs at an average a rate of 8 miles per hour. He walks at an average rate of 3
miles per hour.
a. Let x = time running and y = time walking. Write an equation, in standard form,
to relate the times he spends running and walking if he travels a distance of 15
miles.
b. Graph the equation
18
Suppose you have a job in an ice cream shop that pays $6 per hour. You also have a
babysitting job that pays $4 per hour. You want to earn at least $60 per week but would
like to work no more than 12 hours per week.
Write a system to model this situation.
19. At Wagner’s Rentals, the cost of renting a car is $0.15 per mile plus $25.
a. Write an equation that you can use to determine the cost, C(x), of renting a car from
Wagner’s Rentals for, x miles.
b. Graph your equation on the grid below. Be sure to include the following:
 an informative title for your graph,
 labels for your x-axis and y-axis,
 a consistent and appropriate scale, and
 accurately graphed data.
20
A generic linear function written in standard form is shown below. Rewrite the equation
solved for x.
𝐴𝑥 + 𝐵𝑦 = 𝐶
21
Circle which steps contain an error based on the previous step.
𝟏
(𝒙 − 𝟗) = −𝟔
𝟑
1
𝑥 − 9 = −6
3
1
Step 2:
𝑥 = −6 + 9
3
1
Step 3:
𝑥=3
3
Step 4:
𝑥 =3÷3
Step 1:
Step 5:
𝑥=1
What is the correct solution?
22
Find the solutions for the following inequality. Graph the solution.
4 − 6𝑥 ≥ −32
Solution_________________
23
When you exercise, your pulse rate rises. Recommended pulse rates vary with age and
physical condition. For vigorous exercise, such as jogging, the inequality
𝑅
0.7 ≤ (220−𝑎) ≤ 0.85 gives a target range for pulse rate R (in beats per minute), based on
age 𝑎 (in years).
a. What is the target range for pulse rates for a person 35 years old? Round to the
nearest whole number and write your answer as a compound inequality.
b. Your cousin’s target pulse rate is in the range between 140 and 170 beats per minute.
What is your cousin’s age?
24
Solve the system of equations.
2𝑥 + 9𝑦 = −1
−𝑥 + 9𝑦 = 14
25
Name 5 ordered pairs that satisfy the equation y = x – 9.
26
Two groups of students order burritos and tacos at a local restaurant. One order of 3
burritos and 4 tacos costs $11.33.The other order of 9 burritos and 5 tacos costs $23.56.
3
4
a. Write a system of equations that describes this situation.
b. Solve by elimination to find the cost of a burrito and the cost of a taco.
27
Find a solution to the following system of equations
−5𝑥 + 𝑦 = −5
−4𝑥 + 2𝑦 = 2
28
You have saved $800 from your babysitting job. You decide to invest your money in an
account that has a semi-annual interest rate of 4%. Write an expression to show how
much money will be in your account when you graduate from high school in 5.5 years.
How much money will you have?
29
Sunshine Summer Camp requires a $15.00 registration fee in addition to $9.00 per day of
attendance. The points on the graph show the total cost, y , of attending the camp for x
days. The line that is drawn connecting these points represents the function relating these
two quantities.
Which equation describes the line shown in the graph?
A
B
30
C
D
𝑦 = 9𝑥 + 15
𝑦 = 15𝑥 + 9
9𝑥 + 15𝑦 = 0
15 = 9𝑥 + 𝑦
Mario is solving the system of equations below.
2𝑥 + 7𝑦 = −11
{
9𝑥 − 4𝑦 = 128
He wants to start by eliminating one of the variables.
•
•
Explain the mathematical steps Mario can take to eliminate one variable.
Solve the system for both variables.
Use words, numbers, and/or pictures to show your work. Write your answer(s) on the
paper provided.
31
Graph the inequality: 2y < x + 2
32
Describe each function as either a growth or decay. Explain why.
a)
33
1 𝑥
𝑓(𝑥) = 9 (4)
3
b) 𝑓(𝑥) = 4 (7)𝑥
Mr. Miller owns an apple orchard. He offers his workers two possible payment plans.
Option A is $1.50 per bushel of apples
Option B is 1₵ if you pick one bushel, 3₵ if you pick two bushels, 9₵ if you pick three
bushels and so on, tripling for each additional bushel you pick
If you only have enough time to pick 6 bushels, which plan should you choose? Why?
If you have enough time to pick 9 bushels, which plan should you choose? Why?
34
The expression (𝑥 3 𝑦 2 )−3 can be rewritten as
A
1
9
𝑥 𝑦6
C
𝑥9𝑦6
B
𝑥 0 𝑦 −1
D
𝑥9
𝑦6
35 In 2012 the population of Sterling Heights was 130,410. Its population is increasing
by 1.6% per year. Write an equation to model the population growth of Sterling
Heights since the year 2012.
36
Since 1990, the population of Virginia has grown at an average annual rate of about 1%.
In 1990, the population was about 6,284,000.
a. Write an equation to model the population growth in Virginia since 1990.
b. Suppose this rate of growth continues. Predict Virginia’s population in 2010.
37 Which graph BEST represents the equation
?
A
C
B
D
38
Suppose two mice live in a barn. If the number of mice Doubles every month, how many
mice will be in the barn after 6 months?
A) Create a table of values with (x) representing the number of months and (y)
representing the number of mice.
B) Create an equation that represents the relationship between the month (x) and the
number of mice (y).
39
Based on his records for his investments, Tom has determined that
the equation 𝐴 = 734(1.0512)𝑥 represents the amount of money in his
bank account x years after he invested $734.
Describe the rate of change of Tom’s account balance.
40
Function
below.
has the equation
, and function
is described by the table
How are these two functions alike?
A
Both are linear functions.
B
Both are exponential functions.
C
Both have graphs with the same y-intercept.
D
Both have graphs that approach
as
approaches
.
41
Which equation BEST describes the graph below?
A
𝑓 (𝑥 ) = 𝑥
B
𝑓 (𝑥 ) = 𝑥
42
2
C
𝑓 (𝑥 ) = 2𝑥
D
1 𝑥
𝑓 (𝑥 ) = ( )
2
An initial investment of $50 is expected to double in value every 10 years.
Draw a graph that models the investment’s value. Be sure to choose an appropriate scale,
label the axes, and give the graph a title.
43
Two functions are defined as follows: 𝑓(𝑥) = 100𝑥 and 𝑔(𝑥) = 2(3)𝑥
For which integers, 𝑥, does the value of 𝑔(𝑥) exceed the value of 𝑓(𝑥) ?
44
A
𝑥 ≥1
C
𝑥≥5
B
𝑥≥4
D
𝑥≥6
1
Given the expression𝑓(𝑥) = 8(2)𝑥 , what does 8 represent?
A
Growth Factor
C
Initial Value
B
Decay Factor
D
None of these
45
Graph the following absolute value function 𝑓(𝑥) = −2|𝑥 − 3| + 4
46
Solve the following absolute value inequality: 2|𝑥 + 3| ≤ 10
UCS Algebra 1 Midterm Review #2 Answer Key
1. E
B
G
F
A
C
B
D
2. a) Coef: 8, -14, 34,-1;
Const: 54
b) Coef: 5; Const: 0
3. Not a function, one
height matches more than
one shoe size.
4. C
5. a) {-300, -210, 0, 72}
b) D: # of cameras sold
R: amount of profit
6. (0, 50)
7.
{𝟖𝟎𝟎, 𝟗𝟎𝟎, 𝟏, 𝟎𝟎𝟎, 𝟏, 𝟏𝟎𝟎, 𝟏, 𝟐𝟎𝟎}
8.
9. $0.05 per dollar
10. -2 degrees per hour
11. B
12. The value of p increases
by 71.5 every hour
13. c = 0.50t + 2.75
14. $125
15. C
16. length=9 in; width=21 in
17. 8x + 3y = 15
19. y = 0.15x + 25;
Scale of 10
20.
𝒙=
𝑪−𝑩𝒚
𝑨
21. Steps 1 and 4; x = -9
22. 𝒙 ≤ 𝟔
23.
24.
25.
26.
a) 𝟏𝟑𝟎 ≤ 𝑹 ≤ 𝟏𝟓𝟕
(-5, 1)
32. a) Decay, growth
factor < one.
b) Growth, growth
factor < one.
33. 6 bushels option A
($9 > $2.43);
9 bushels option B
($65.61 > $13.50)
34. A
35. y = 130,410 (1.016)x
36. y = 6,284,000(1.01)x
37. D
38. a.
b. y = 2(2)x
b) 20 yrs.
Answers vary; (0, -9), (4, -6), etc
a) 𝟑𝒃 + 𝟒𝒕 = 𝟏𝟏. 𝟑𝟑
𝟗𝒃 + 𝟓𝒕 = 𝟐𝟑. 𝟓𝟔
b) Burrito =$1.79; Taco = $1.49
27. (2, 5)
28. 𝟖𝟎𝟎(𝟏. 𝟎𝟐)𝟏𝟏 = $944.70
29. A
30. Multiply both equations by a
constant that will make the
coefficients of either x or y equal
except for sign. Next, add the
equations to eliminate a variable.
Solve this equation for the noneliminated variable. Substitute
this value back into one of the
original equations to solve for the
eliminated variable.
Solution: (12, -5)
𝟏
31. y < 𝟐x + 1
39. Account grows at a
rate of 5.12% per year.
40. B
41. C
42.
43. D
44. C
45.
46. -8≤ x ≤ 2
18. Let c =hours in ice cream
shop; let b = hours
babysitting. 6c + 4b ≥ 60
c + b ≤ 12