Algebra 1 STAAR Review
Name:
Date:
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1. Which graph does not represent y as a function of x?
I.
II.
III.
A) I only
B) II only
C) III only
D) I and III
E) I and II
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2. Which expression is equivalent to
12𝑥 6 𝑦 −4 𝑧 2
3𝑥 2 𝑦 −6 𝑧 3
?
3. Which expression represents the nth term
of this arithmetic sequence? −9, −5, −1, 3, 7, …
A.
9𝑥 8 𝑧 5
𝑦 −10
9𝑥 4 𝑦 2
B.
4𝑥 8 𝑧 5
A. −9 + (n – 1)4
𝑦 −10
4𝑥 4 𝑦 2
B. −9 + (n – 1)(−4)
C.
D.
C. 7 + (n – 1)4
D. 7 + (n – 1)(−4)
𝑧
𝑧
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4. A family will travel 350 miles from their house in order to reach Dallas, TX. Which inequality can be used to find all
possible values of t, the time it will take this family to reach Dallas in hours, if they travel at an average speed of at least r
miles per hour? (𝑑 = 𝑟𝑡)
𝑟
350
A. 𝑡 ≤ 350𝑟
B. 𝑡 >
C. 𝑡 ≤
D. 𝑡 > 350𝑟 2
350
𝑟
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5. A print shop charges a fixed amount per photocopy and gives a 10% discount off the total cost of the photocopies.
The total cost is a function of the number of photocopies made. What is the dependent quantity in this situation?
A. The total number of photocopies made
B. The price per photocopy
C. The amount of the discount
D. The total cost of the photocopies
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6. A dentist made the scatterplot below to show the number of cavities her patients had as it relates to the number of
times they flossed their teeth each week.
Which of the following best describes the correlation for the data?
A. Positive correlation
B. Nonlinear correlation
C. Negative correlation
D. No correlation
7. A table of values for the exponential function f is shown below.
Which situation could describe this function?
x
1
2
3
4
5
f(x)
140,000
143,850
147,806
151,871
156,047
3
A. The value of a house increases by approximately 2 4 % per year.
B. The value of a house increases by $3,850 per year.
3
C. The value of a house decreases by approximately 2 4 % per year.
D. The value of a house decreases by $3,850 per year.
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8. Which graph shows a function with a domain of all real numbers greater than 7?
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9. The population of a town is currently 9,000. The function 𝑝 = 9,000 + 8𝑡 2 can be used to estimate p, the population
of the town t years from now. Based on this function, which statement is true?
A. The population of the town is increasing at a constant rate.
B. The population of the town will reach 10,000 between 11 and 12 years from now.
C. The population of the town will increase by 256 people two years from now.
D. The population of the town will increase and then decrease.
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10. The cost, C, of getting your car repaired is given by 𝐶 = 75ℎ + 90, where h is the number of hours in labor the
mechanic works on your car, 75 is the cost per hour the mechanic charges, and 90 is the cost for the parts needed to
repair your car. Identify the independent variable.
A) 90
B) C
C) h
D) 75
2
11. The dishwasher at a restaurant is loaded with the same number of dishes every time it is used. The table below
shows the total number of dishes washed as a function of the number of times the dishwasher is used.
Based on the data in the table, what is the total number of dishes that will have been washed when the dishwasher is
used 9 times? Record your answer and fill in the bubbles on the grid.
Restaurant Dishwasher
Number of
Times Total Number of Dishes
Used
Washed
2
52
4
104
6
156
8
208
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12. The set of ordered pairs below represents some points on the graph of function f.
{(3, 11), (−1, 3), (5, 15), (−4, −3), (−7, −9)}
What is the parent function of f?
A. 𝑦 = 𝑥
B. 𝑦 = 2𝑥
C. 𝑦 = 𝑥 2
D. 𝑦 = √𝑥
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13. What is the range of the function shown below?
A. {-7, -2, 0, 5}
B. {-9, -4, -1}
C. {-9, -7, -4, -2, -1, 0, 5}
D. {-1}
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14. A storm is headed through North Texas. The duration of the storm is measured in hours while the rainfall is
measured in inches as seen in the table below. a) What is the independent part of this situation?
b) What would the domain be for this scenario?
c) What would the range be for this scenario?
Duration of the storm(hrs), x
1
2
3
Amount of rain(inches), y
0.5
1
1.5
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15. The time, t, it takes to travel a certain distance varies
16. The length of one edge of a square is given
inversely as the rate, r. If t = 10h when r = 80km/h,
by 3𝑥 2 𝑦 3. Which answer represents the area
which equation represents this situation?
of the square?
A. 𝑡 = 800𝑟
B. 𝑡 =
800
𝑟
𝑟
C. 𝑡 = 800
A. 12𝑥 2 𝑦 3
B. 9𝑥 4 𝑦 9
C. 9𝑥 4 𝑦 6
D. 12𝑥 8 𝑦12
3
18. Katie rented a moving truck. The total
rental cost included a one-time fee of
$40.00 and $0.75 for each mile driven.
Which equation represents, t, the total cost
in dollars of renting a truck that was driven
m miles?
17. Which inequality can be represented by the graph below?
A. 𝑦 ≥ 𝑥 + 𝑏
B. 𝑥 − 𝑦 ≥ −𝑏
C. 𝑥 + 𝑦 ≤ 𝑏
0.75
𝑚
A. 𝑡 = 0.75 + 40𝑚
B. 𝑡 = 40 +
C. 𝑡 = 40 + 0.75𝑚
D. 𝑡 = 0.75 +
D. −𝑦 ≤ 𝑥 + 𝑏
40
𝑚
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19. Determine which table of values represents a quadratic function? How do you know?
A.
B.
C.
x
y
x
y
x
y
−1
8
−3
−1
−2
8
0
5
0
0
0
4
1
2
3
1
2
8
2
−1
6
2
4
13
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20. Tickets for a school play cost $4 for adults and $2 for students. At the end of the play, the school sold a total of 105
tickets and collected $360. Write a linear system of equations letting x represent the number of adult tickets sold and y
represent the number of student tickets sold.
Write the system below.
Graph the linear system.
Find the number of adult tickets and
student tickets sold.
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21. On Monday, the office staff at your school paid $8.77 for 4 cups of coffee and 7 bagels. On Wednesday, they paid
$15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel? Explain.
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22. The dimensions of a rectangle are (𝑥 + 5) and (2𝑥– 3). Which expression best represents the perimeter of the
rectangle in simplest form?
A. 2𝑥 2 + 7𝑥 − 15
B. 6𝑥 + 4
C. 2𝑥 2 − 15
D. 3𝑥 + 2
4
23. The graph of the quadratic function h passes through the points (−4, 32), (3, 4), (5, 14), and (7, 32).
Which of the following shows the same relationship as h?
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24. What is the domain for the function graphed below?
25. What is the vertex of the graph of the
quadratic function 𝑓(𝑥) = 𝑥 2 + 6𝑥 + 10?
What is the range for the function graphed below?
A. 0 < 𝑦 ≤ 5
B. 2 < 𝑥 ≤ 5
C. 0 < 𝑥 ≤ 5
D. 0 < 𝑦 < 2
E. 0 ≤ 𝑦 ≤ 4
A. (−3, 1)
B. (−3, −1)
C. (3, −1)
D. (3, 1)
F. 0 < 𝑥 ≤ 4
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26. Simplify the polynomial: −3𝑥(7𝑥 − 4) + 6𝑥 − (13 − 24𝑥 2 )
27. If (−7, y) is a solution to the equation
2𝑥 − 7𝑦 − 42 = 0, what is the value of y?
2
2
A. 3𝑥 + 18𝑥 − 13
B. −24𝑥 − 15𝑥 − 17
A. −4
B. −8
C. −24𝑥 2 + 10𝑥 − 17
D. 3𝑥 2 + 18𝑥 + 13
C. −3.5
D. −6.7
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28. Ms. Barton determined that the total cost of her wedding, c, could be represented by the equation 𝑐 = 75𝑛 + 1500
where n is the number of people attending the wedding. If Ms. Barton’s wedding cost $8625, would it be reasonable
that 135 people attended the wedding? Explain.
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29. What is the standard form of the equation of the line passing through points (−2, 7) 𝑎𝑛𝑑 (2, 5).
A. 𝑥 + 2𝑦 = 12
B. 𝑥 − 2𝑦 = 12
C. 𝑥 − 2𝑦 = −12
D.
1
𝑥
2
+ 2𝑦 = 6
5
30. Anna makes hand-painted plates. Her overhead costs are
$750 per week and she pays an additional $10 per plate in
material costs. If Anna sells the plates for $25 each, how many
plates does she have to sell each week before she can make a
profit?
31. What are the x-intercepts of the graph of
quadratic function 𝑓(𝑥) = 5𝑥 2 + 4𝑥 − 1?
A.
1
5
and − 1
C. 0 and −1
1
5
B. − and 1
2
2
D. − 5 and 1 5
A. 20
B. 30
C. 50
D. 75
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32. Trini’s car breaks down on a highway. Trini estimates that she is 20 to 30 miles from the nearest car repair shop.
She calls a towing company that charges a fee of $80 plus $3 per mile to tow a car. If Trini uses this towing company,
which is the best estimate for the amount of money, m, she will pay for the company to tow her car?
A. 103 ≤ 𝑚 ≤ 113
B. 140 ≤ 𝑚 ≤ 150
C. 160 ≤ 𝑚 ≤ 170
D. 140 ≤ 𝑚 ≤ 170
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33. Which of the following graphs represents the function 𝑦 = −𝑥 2 + 2𝑥 + 8?
A.
B.
C.
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34. Which shows 6𝑥 3 − 3𝑥 2 − 3𝑥 factored completely?
A. 3x ( 2x + 1 ) ( x – 1 )
35. If (x, −4) is a solution to the equation
4𝑥 − 5𝑦 = 8, what is the value of x?
B. 3x ( 2x – 1 ) ( x + 1 )
A. −4.8
B. −3
C. 3 ( 2x + 1 ) ( x – 1 )
D. 3x ( 2x + 1 ) ( x – 1 )
C. 1.6
D. 7
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36. Which table shows the same relationship as
37. A table of values for the quadratic function f
2
𝑦 = −𝑥 + 3𝑥?
is shown below.
2
A
If 3 is one solution
to f(x) = 0, what is
the value of the
other solution?
B
C
D
...
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.
38. What is the slope of a line that passes through the points (2, −4) and (6, 4)?
A. 0
B. −2
C. 2
D. undefined
6
5
39. The graph of the linear equation 𝑦 = − 2 𝑥 + 7 is shown
below. Which coordinate pair is in the solution set of
5
𝑦 < −2𝑥 + 7 ?
A. (4, −3)
B. (1, 2)
40. Auto-Check Motors charged Mr. Jones
$84.00 for an automotive part plus $68
per hour for the mechanic’s labor to
install the part. The total charge was
$353.00. For about how long did the
mechanic work to install the part on Mr.
Jones’ car?
C. (5, 6)
A. 6 h
B. 5 h
D. (0, 7)
C. 4 h
D. 3 h
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41. To solve 𝑥 2 − 15𝑥 + 54 = 0, Anita made this table for the related function 𝑦 = 𝑥 2 − 15𝑥 + 54.
x
y
Which shows the solutions for this quadratic equation?
5
4
6
0
A. x = 0 only
B. x = 0 and x = 6
7
−2
1
1
1
1
C. x = 7 2 and x = −2 4
D. x = 6 and x = 9
7
−2
2
4
8
−2
9
0
10
4
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42. The graph of 𝑦 = 3𝑥 2 − 2 is shown below.
If the coefficient of 𝑥 2 is changed from 3 to another positive number to
create a new function, how will the graph of the new function compare with
the graph of the original function?
A. The x-intercepts of the new graph will be the same as the x-intercepts of
the original graph.
B. The vertex of the new graph will be different from the vertex of the
original graph.
C. The new graph will be wider or narrower than the original graph.
D. The new graph will open in the opposite direction as the original graph.
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43. George works in a restaurant cleaning tables and earns $15 per night plus $0.75 for each table he cleans. George’s
boss told him that because George was doing such a good job, she was going to double the amount George earned
for each night. Which of the following equations could George use to calculate his new earnings, e, for cleaning t tables?
A. 𝑒 = 15 + .75𝑡
B. 𝑒 = 15 + 1.50𝑡
C. 𝑒 = 30 + .75𝑡
D. 𝑒 = 30 + 1.50𝑡
7
44. What are the effects of changing c in a quadratic function?
45. What is the parent linear function?
What is the parent quadratic function?
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9
46. The equation 𝐹 = 5 𝐶 + 32 represents the relationship
between F, the temperature in degrees Fahrenheit, and C, the
temperature in degrees Celsius. If the temperature is 104⁰F,
what is the temperature in degrees Celsius?
Record your answer and fill in the bubbles on the grid.
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47. Nyesha earns $1,000 per month plus a commission of 5% of the total dollar amount of each sale she makes. Her
total monthly earnings, P, are represented by the equation 𝑃 = 1,000 + 0.05𝑡, where t represents the total dollar
amount of her sales for the month. Which equation will represent her total monthly earnings in dollars if her
commission increases an additional 2%?
A. 𝑃 = 1,200 + 0.05𝑡
B. 𝑃 = 1,000 + 0.02𝑡
C. 𝑃 = 1,200 + 0.07𝑡
D. 𝑃 = 1,000 + 0.07𝑡
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48. Charles and Jenna took turns driving while on vacation. By the end of their vacation, they had driven about 900
miles, with Jenna driving about half as many miles as Charles. Which statement is reasonable, based on this
information?
A. Jenna drove 295 miles and Charles drove 610 miles
B. Jenna drove 610 miles and Charles drove 295 miles
C. Jenna drove 590 miles and Charles drove 305 miles
D. Jenna drove 600 miles and Charles drove 280 miles
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49. The graph below shows the relationship between the number of miles driven and the number of hours driven.
What does the slope of the graph represent?
A. The number of hours to travel 100 miles
Miles
B. The amount of miles traveled per hour
C. The amount of miles for 6 hours of driving
D. The number of miles driven per hour traveled
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50. What is the domain of the function f(x) = −x + 5 when
51. What is the range of the function
the range is {−1, 10, 7}?
f(x) = −x + 15 when the domain is {−3, −1, 11}?
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52. Kate earned $120 for 12 cars she washed. If the amount Kate earns varies directly with the number of cars she
washed, how much will she earn for 5 cars?
8
5
53. What is the domain of the function shown in the graph?
54. What is the zero of the function y = 6 x + 5?
A. −4 < 𝑦 ≤ 2
B. −1 ≤ 𝑥 < 2
C. −1 < 𝑥 ≤ 2
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55. a) If the graph of y = 9x + 4 is translated 4 units up, which equation below describes the new graph?
A. y = 9x + 8
B. y = 13x + 4
C. y = 13x + 8
D. y = 4x + 4
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b) Describe the change(s) that occur(s) when the graph of y = 4x + 2 is transformed to y = −x – 5.
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56. 2 roommates, Kevin, K, and Jose, J, together have $50. From his portion of the money, Kevin pays Jose the $10 he
owes his roommate, bringing Jose’s share of the money to $25. Which system of equations will determine the original
amounts of money that Kevin and Jose had?
A. 𝐾 + 𝐽 = 50
𝐾 + 𝐽 − 10 = 25
B. 𝐾 + 𝐽 = 50
𝐾 + 10 = 25
C. 𝐾 + 𝐽 = 50
𝐽 + 10 = 25
D. 𝐾 + 𝐽 = 25
E. 𝐾 + 𝐽 = 50 − 10
𝐾 − 10 = 50
𝐽 = 25
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57. The graph below shows the water level in a tank being drained at a constant rate.
If the rate at which the tank is drained is changed to 3 inches per hour and
the initial water level stays the same, how would the time it takes to
empty the tank be affected?
A. It would take 4 fewer hours
C. It would take 2 fewer hours
B. It would take 1.5 more hours
D. It would take 2 more hours
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58. Find the point where the graph of −2𝑥 + 2𝑦 = 4
59. Which of the following has a y-intercept of 8
crosses the y-axis.
and an x-intercept of −4?
A. (1, 0)
B. (0, 2)
A. 2x – y = −8
B. 2x – y = 8
C. (2, 0)
D. (0, −1)
C. 8x – y = 4
D. 4x – y = 8
9
60. A craft store has 12 identical sacks of loose buttons. Each button is perfectly circular and is either solid black, b, or
solid white, w. Each sack contains 9 more black buttons than white ones. The total number of buttons in all of the sacks
is 372. The number of buttons of each color in 1 sack can be found by using the following system of equations:
𝑏−𝑤 =9
12(𝑏 + 𝑤) = 372
Which ordered pair, (b, w), is a reasonable solution for the number of buttons of each color in 1 sack?
A. (11, 2)
B. (20, 11)
C. (29, 20)
D. (15, 6)
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61.
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62. A table of values for a linear function is shown below.
63. The function y = 7x + 3 shows a relationship
What is the x-intercept?
between x and y. If the value of x increases by 1,
what happens to the value of y?
x
y
A. 3
B. 2
−2
3
0
2
2
1
B. The value of y increases by 7
4
0
C. The value of y increases by 10
C. 4
D. 1
A. The value of y increases by 3
D. The value of y increases by 21
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64. Compare the two equations and decide which description best compares the differences.
Equation a: 𝒚 = 𝟐𝒙 + 𝟏
Equation b: 𝒚 = −𝟑𝒙 − 𝟑
A. Equation a is shifted down 4 units from equation b
B. Equation b is shifted down 5 units from equation a
C. Equation a is steeper than equation b
D. None of the above
10
65. Peter placed an order with an online nursery for 6 apple
trees and 5 azaleas. The order totaled $147. The next order
for 3 apple trees and 4 azaleas came to $96. What was the
cost for each azalea? Record your answer and fill in the
bubbles on the grid.
66. How does adding a constant c to x in the
parent function y = x affect the graph?
A. The graph shifts upward or downward.
B. The graph shifts to the left or to the right.
C. The graph becomes steeper or less steep.
D. The graph is not affected by adding c.
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67. Three trains (A, B, and C) leave a train station at the same time. The graph shows the relationship between time and
distance for Train A.
Train B
𝑦 = 45𝑥
a) What is the slope of the graph?
b) What does this slope represent?
c) The relationship between time and distance for Train B is given by the equation above, where x represents hours
and y represents miles. Find the slope m.
d) Which train is moving faster, Train A or Train B? How do you know?
e) The time-distance relationship for Train C is shown in the table above. What is the ratio of distance to time?
f) Compare the speed of Train C to the speeds of Train A and Train B.
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68. Given that y is a function of x, which of the following tables best represents a function?
A.
B.
C.
D.
11
69. Juan tells Ella that one of the solutions to the equation 𝑎2 − 8𝑎 − 20 = 0 represents his age. How old is Juan?
A. 8
B. 10
C. 12
D. 20
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70. Which of the following provides the correct interpretation of the x-intercept for the graph below.
A. A brand new truck is worth almost $70,000.
B. The truck decreases in value over time.
C. A five year old truck is worth $0.
D. The truck increases in value over time.
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71.
Which statement is not true of the quadratic function graphed?
A. It has a vertex at (−2, 0).
B. Its vertex is also its x-intercept.
C. It has exactly one zero.
D. It has an x-intercept at (0, −4).
E. (−2, 0) is the only solution.
F. (−2, 0) is a root.
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72. Which of the following equations are represented
73. If (2, k) and (5, −3) are two points of the graph
by the graph?
of a line with the slope of 4, what is the value of k?
1
I. 𝑦 = − 2 𝑥 + 3
II. 2𝑦 = −𝑥 − 6
1
III. 𝑦 + 5 = − 2 (𝑥 − 4)
IV. 𝑦 = −2𝑥 − 3
A.
B.
C.
D.
II and IV
I and III
II and III
I and IV
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74. What is the solution set for the quadratic equation
75. What is the slope of the line that has equation
2
𝑥 − 16 = 0?
3𝑥 + 2𝑦 = −10?
A. {4}
B. {−4, 4}
3
B. − 2
A. 3
2
C. {256}
D. {−256, 256}
C. −
D. −5
3
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3
76. What is the equation of the line with slope of 5 that passes through the point (10, −3)?
A. 𝑦 =
3
𝑥
5
−3
B. 𝑦 =
3
𝑥
5
+ 10
C. 𝑦 =
3
𝑥
5
−6
D. 𝑦 =
3
𝑥
5
−9
12
77. If the graph of 𝑦 = −2𝑥 + 5 is translated down 3 units, which equation describes the new graph?
A. 𝑦 = −5𝑥 + 5
B. 𝑦 = −𝑥 + 5
C. 𝑦 = −2𝑥 − 3
D. 𝑦 = −2𝑥 + 2
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1
78. Which statement correctly compares the graphs of 𝑦 = 5𝑥 − 2 𝑎𝑛𝑑 𝑦 = 5 𝑥 − 2 ?
A. Both lines pass through (−2, 0), but 𝑦 =
1
𝑥
5
− 2 is not as steep as 𝑦 = 5 𝑥 − 2.
B. Both lines pass through (0, −2), but 𝑦 =
1
𝑥
5
− 2 is not as steep as 𝑦 = 5 𝑥 − 2.
C. Both lines pass through (−2, 0), but 𝑦 = 5 𝑥 − 2 is not as steep as 𝑦 =
1
𝑥
5
− 2.
1
D. Both lines pass through (0, −2), but 𝑦 = 5 𝑥 − 2 is not as steep as 𝑦 = 5 𝑥 − 2.
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79. Which graph shows the result of multiplying the slope of 𝑦 = 3𝑥 + 2 by −1?
A.
B.
C.
D.
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80. What is the slope of the linear function 81. The area of a rectangle is 2𝑥 2 − 7𝑥 − 15. Which of the following
represented by the table below?
shows possible dimensions of the rectangle?
x
−3
0
6
9
y
1
2
4
5
A. (2x + 3) and (x – 5)
B. (2x – 3) and (x + 5)
C. (2x + 3) and (2x – 10)
D. (2x – 3) and (2x + 10)
13
82. The graph below represents the parent function 𝑦 = 𝑥.
1
If the slope of the equation were changed to , which graph below would illustrate this change?
3
A.
B.
C.
D.
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83. The equation y = 461.19x + 3,492 represents the
84. Which of the following is equivalent to
value of a work of art from 1964 to 2005. What does
16𝑎2 − 49?
the number 461.19 represent?
A. (4a – 7)(4a + 7)
B. (4a – 7)(4a – 7)
A. Value of the work of art in 1964
B. Value of the work of art in 2005
C. (8a – 7)(8a + 7)
D. (8a – 7)(8a – 7)
C. Yearly decrease in value
D. Yearly increase in value
_________________________________________________________________________________________
85. Which equation describes the function below?
x
−2
5
4
7
y
6
27
18
51
A. 𝑦 = −3𝑥
B. 𝑦 = 5𝑥 + 16
C. 𝑦 = 2𝑥 2 − 2
D. 𝑦 = 𝑥 2 + 2
86. For f(x) = 24 – 2x, find f(2) and find x such that f(x) = 10.
A. 28; 12
B. 22; 4
C. 20; 7
D. 22; 7
14
87. Stan’s solution to an equation is shown below.
Given:
n + 8(n + 20) = 110
Step 1:
n + 8n + 20 = 110
Step 2:
9n + 20 = 110
Step 3:
9n = 110 – 20
Step 4:
9n = 90
Step 5:
9𝑛
9
=
Which statement about Stan’s solution is true?
A.
B.
C.
D.
Stan’s solution is correct
Stan made a mistake in Step 1
Stan made a mistake in Step 3
Stan made a mistake in Step 5
90
9
Step 6:
n = 10
_________________________________________________________________________________________________
88. The perimeter of a rectangle is 42 centimeters. The
89. Which best describes the effect on the graph of
1
length of the rectangle can be represented by (x + 4), and
𝑦 = 3 𝑥 2 when the equation is changed to 𝑦 = −4𝑥 2 ?
its width can be represented by (2x – 7). What is the
length of the rectangle? Record your answer on the grid.
A. The graph is congruent but opens down
B. The graph is narrower and opens down
C. The graph is translated left and opens down
D. The graph is wider and opens down
__________________________________________________________________________________________________
90. Match the function to its graph and its equation.
Equation
Graph
Quadratic:
_______
_______
Exponential Growth
_______
_______
A. y = 3x
E.
F.
Equation
Graph
Exponential Decay:
_______
_______
Linear:
_______
_______
G.
H.
B. y = −5x + 6
C. y = −x2 + 3
1 𝑥
D. y = (2)
15