Download December 2013 Edition - North Thurston Public Schools

NORTH THURSTON PUBLIC SCHOOLS
ALGEBRA I
END OF COURSE
PRACTICE TEST
Updated – December 2013
Name: _________________________________________________
Period: _________________________________________________
Page 1 of 22
1.
The chart shows the amount of total salary (commission plus base salary) paid to employees of a store that
specializes in big screen televisions.
Which equation best represents the total salary (T) that an employee makes for selling any number of
television sets (n)?
2.
3.
O A.
T = 50n + 100
O B.
T = 100(n + 50)
O C.
T = 100n + 50
O D.
T = 50(n + 100)
A 1,500-gallon tank contains 200 gallons of water. Water begins to run into the tank at the rate of 75 gallons
per hour. After 2 hours, the rate increases to 80 gallons per hour. How long can the water flow at a rate of
80 per hour before the tank is full, but not overflowing?
O A.
14 hours, 22.5 minutes
O B.
16 hours, 15 minutes
O C.
17 hours, 20 minutes
O D.
18 hours, 45 minutes
Which statement best describes the difference(s) between the graphs of :
𝑓(𝑥) = −5𝑥 +
3
4
and
𝑔(𝑥) = −10𝑥 +
3
4
O A.
The graph of 𝑓(𝑥) is twice as steep as the graph of 𝑔(𝑥)
O B.
The graph of 𝑓(𝑥) is half as steep as the graph of 𝑔(𝑥)
O C.
The graph of 𝑓(𝑥) has a y-intercept of –5 while 𝑔(𝑥) has a y-intercept of –10.
O D.
The graph of 𝑓(𝑥) has a lower y-intercept than the graph of 𝑔(𝑥)
Page 2 of 22
4.
5.
According to the graph, which statement best describes the slope?
O A.
The amount of gas in the tank decreases by 3, as the distance traveled increases by 20.
O B.
The amount of gas in the tank increases by 20, as the distance traveled decreases by 3.
O C.
The amount of gas in the tank increases by 2, as the distance traveled increases by 30.
O D.
The amount of gas in the tank decreases by 3, as the distance traveled decreases by 20.
Mr. Shindler begins traveling east on Interstate 90 from Spokane with a full tank of gasoline. His car has a
15-gallon gas tank and gets 30 miles per gallon during highway travel.
Let m = the number of miles Mr. Shindler has driven
Let g = the number of gallons of gas remaining in his tank
Select which equation describes the relationship between the number of miles Mr. Shindler has traveled
and the number of gallons remaining in his gas tank:
O A.
g = 15 − 30m
O B.
m = 30g − 15
O C.
g = 15 −
O D.
m=
30
g
m
30
− 15
Justify your choice in the answer box below. Support your answer using words, numbers, &/or diagrams.
Page 3 of 22
6.
This graph shows the relationship between the age of a planet in millions of years and the number of moons
the planet has.
Which of these statements is true about the graph?
O A.
The dependent variable is the number of moons.
O B.
The independent variable is the number of moons.
O C.
Since the number of moons is staying the same, there is no dependent variable.
O D.
Since the number of moons is staying the same, there is no independent variable.
7.
Which table represents the recursive formula: 𝑎𝑛 = 𝑎𝑛−1 − 6
8.
Find the 21st term of the arithmetic sequence: 18, 23, 28, 33, …
Page 4 of 22
9.
Determine whether the sequence appears to be an arithmetic sequence. If so, write the explicit formula and
the recursive formula.
–5, –11, –17, –23, –29
recursive:
explicit:
10. Solve the equation for x.
7 − 3(2𝑥 − 4) = 5𝑥 − 2
11. Solve:
22
𝑥−3
O A.
+4=7
31
𝑥=
3
O B.
𝑥=
47
O C.
𝑥=
55
O D.
𝑥=
29
7
3
7
12. Choose the correct solution to the equation
O A.
𝑥=2
O B.
𝑥=−
O C.
𝑥 = −4
O D.
𝑥=
3𝑥−1
2
= 4𝑥 + 3
7
5
5
7
Page 5 of 22
13. Look at the system of linear equations.
{
3𝑥 + 𝑦 = 13
𝑥 + 6𝑦 = −7
Solve the system of linear equations.
O A.
(-5, 28)
O B.
(-2, 19)
O C.
(7, 2)
O D.
(5, -2)
14. After solving the following system of equations Sarah claimed that the system has no solution.
𝑦 = 2𝑥 − 5
{
4𝑥 − 2𝑦 = 10
Carl disagreed and said that the system actually has an infinite number of solutions.
Who is correct and why?
Who is correct? __________
Why is that person correct? Show all work to justify your conclusion.
Page 6 of 22
15. Only chocolate and vanilla ice cream cones are sold at an ice cream store. One day, the number of
chocolate cones sold was 1 more than 4 times the number of vanilla cones sold. A total of 121 cones were
sold that day.
Let c = the number of chocolate cones sold.
Let v = the number of vanilla cones sold.



Write equations to determine the number of chocolate cones sold that day.
Use the equations to determine the number of chocolate cones sold that day.
Show your work using words, numbers, and/or diagrams.
16. A master pizza maker and his assistant need to make 106 pizzas, total. The assistant can make 8 pizzas per
hour. The master pizza maker can make 10 pizzas per hour, but starts 2 hours later than his assistant.
How many hours will the assistant make pizzas before there are 106 pizzas done?
Support your answer using words, numbers, and/or pictures.
How many hours will the assistant make pizzas? __________
Page 7 of 22
17. Write an equation of the line that passes through the pair of points:
1
11
8
O A.
𝑦 = 8𝑥 −
O B.
𝑦 = −8𝑥 −
O C.
𝑦 = −8𝑥 −
O D.
𝑦 = 8𝑥 − 8
3
31
8
1
21
8
3
(-5, -2) and (3, -1)
1
18. Write the equation of the line that goes through the points (-4, 5) and (-2,-3) without graphing.
19. Which of the following lines is parallel to the line represented by the equation 𝑥 − 3𝑦 = 10
O A.
1
𝑦=− 𝑥+4
3
1
O B.
𝑦= 𝑥+6
O C.
𝑦 = 3𝑥 − 7
O D.
𝑦 = −3𝑥 + 1
3
1
20. Write an equation of the line that is perpendicular to 𝑦 = 𝑥 + 8 and goes through (-4, 5).
2
1
O A.
𝑦=− 𝑥+3
O B.
𝑦=− 𝑥+7
O C.
𝑦 = −2𝑥 + 8
O D.
𝑦 = −2𝑥 − 3
2
1
2
21. Write the equation in slope intercept form:
O A.
y = −3x − 6
O B.
y = 3x − 6
O C.
y = 3x − 12
O D.
y = 3x + 9
𝑦 + 9 = 3(𝑥 − 1)
Page 8 of 22
22. Find the slope of the line described by 𝑥 − 3𝑦 = −6 .
O A.
1
3
O B. −
O C.
1
3
3
O D. −3
23. Which equation is y 
O A.

O B.
1
x  5 in standard form?
3
1
− 𝑥 + 𝑦 = −5
3
1
3
𝑥−𝑦=5
O C.
𝑥 − 3𝑦 = 15
O D.
𝑥 + 3𝑦 = 15
24. Solve the equation for a :
O A.
O B.

O C.

O D.
1
d  vt  at 2
2
2d
vt3
d  vt
a 2
t
a
2d  vt
t2
2d  vt
a
t2
a

25. Solve for 𝑥:


−4 < 3𝑥 + 2 ≤ 12 .
Represent the set of solutions on the number line below.
Page 9 of 22
26. Tara’s cell phone plan costs $39.00 a month, which includes 100 text messages. After she uses all of her
text messages, it will cost her $.15 per text message.


Write an equation or inequality that could be used to determine the total cost of her cell phone bill
after her first 100 text messages.
Be sure to define your variables.
If Tara only wants to spend $43 on her cell phone bill, how many text messages can she send? Support
your answer with words, numbers, and/or diagrams.
Explain what your answer means:
27. Fred, Thomas, and Zachary worked at the ice cream store in the mall. Last week, Fred earned more money
than Thomas, but less than Zachary. The graph shows the money earned by Zachary and Thomas.
Which area of the graph represents Fred’s possible weekly pay and why?
O A.
P because that represents more than Thomas.
O B.
T because that represents more than Zachary and less than Thomas.
O C.
P because that represents more than both Zachary and Thomas.
O D.
T because that represents more than Thomas and less than Zachary.
Page 10 of 22
28. Which is the graph of the solution set of the system of inequalities?
x  2y  10
2x  y  0

29. Look at the system of linear inequalities.
{
𝑦 > −𝑥 − 3
𝑦 < −𝑥 + 8
Which graph represents the solutions to the system of linear inequalities?
O A.
O B.
O C.
O D.
Page 11 of 22
30. Solve the equation for x:
−3|2𝑥 + 1| + 6 = −12
31. The equation 13 − 2|𝑥 + 3| = 5 has two real solutions.

Determine the negative solution of the equation.

Write your answer on the line.
What is the negative solution of the equation? ________________
32. If 𝑦 = |𝑥| + 3 , then when is y a positive number?
O A.
always
O B.
when x > -3
O C.
when x > 3
O D.
never
33. Graph A is the graph of 𝑦 = |𝑥| + 2 and graph B is the graph of 𝑦 = |2𝑥| + 8 .
Which statement about the two graphs is true?
O A.
Graph A and B have the same vertex.
O B.
Graph A is less steep than graph B.
O C.
Graph B has a y-intercept that is 8 units above the y-intercept of Graph A.
O D.
Graph B has a vertex that is 8 units above the vertex of Graph A.
34. Which equation or inequality has exactly ONE real solution?
O A.
|x − 7| ≥ 10
O B.
0=
O C.
4 ≤ 2x + 10 < 7
O D.
2(x − 4) = 6x + 8
10
x
Page 12 of 22
3
√−27
35. Evaluate the expression:
Write your answer on the line.
What is the cube root of -27? __________________
36. Look at the list of numbers.
−
3𝜋
1
1
, 7.5 × 10−1 , 2 , √10 , −
4
2
3
Which number line represents the list of numbers?
O A.
-2
-1
0
1
2
3
-2
-1
0
1
2
3
-2
-1
0
1
2
3
-2
-1
0
1
2
3
O B.
O C.
O D.
37. Order the following numbers from least to greatest: 3𝜋, √62 , 8.7 × 100 ,
O A.
O B.
19
, 3, 8.7  100,
2
62, 8.7  100, 3,

O C.
8.7  100, 3,
O D.
3,



62,
19
,
2
19
2
62
19
2
62
19
, 8.7  100
2
Page 13 of 22
38. For what values of a is 𝑎 > 𝑎2 ?
O A.
𝑎<0
O B.
−1 < 𝑎 < 1
O C.
0<𝑎<1
O D.
𝑎>0
39. Simplify √20𝑥 3 𝑦 2
O A.
10𝑦√𝑥 3
O B.
4𝑦√5𝑥 3
O C.
2𝑥𝑦√5𝑥
O D.
5𝑥𝑦√2𝑥
40. Look at the expression.
−16𝑚10
8𝑚5
Simplify the expression and write it without negative exponents.
O A.
−8𝑚5
O B.
−2𝑚5
O C.
O D.
1
2
𝑚15
−2𝑚15
41. Simplify the expression
(𝑥 3 )
−2
−3
( 𝑥 2 ∙𝑥 3 )
Write your answer on the line.
What is the simplified version of the expression? __________________
Page 14 of 22
3𝑥 −2 𝑦 3 𝑧
42. Simplify:
9𝑥 3 𝑦 −5 𝑧 2
O A.
O B.
O C.
O D.
y8
3x5 z
𝑥𝑦 2 𝑧
3
𝑥𝑧
3𝑦 2
𝑦 15
3𝑥 6 𝑧 2
43. Given the expression


5  x , state the values of 𝑥 for which the expression is defined.
Express your answer with an inequality.
Write your answer on the line.

What are the defined values of x? _____________________
44. You are a full time employee at a marketing firm. In order to maintain fulltime status you must work a
minimum of 25 hours a week, and you cannot work more than 45 hours in a week. You make $20 per hour.


Define the domain and range variables in the context of the problem.
Express the domain and range as inequalities.
Define domain
variable:
Define range
variable:
Express domain: _________________
Express range: ________________
Page 15 of 22
45. Given that 𝑓(𝑥) = 3𝑥 − 2, find x when 𝑓(𝑥) = 14.
46. Look at the function:
𝒇(𝒙) = 𝟐𝒙𝟐 − 𝟒𝒙 + 𝟓
Evaluate 𝑓(−3).
Write your answer on the line.
What is (−𝟑) ? ___________________________________
47. Look at the function.
What is the domain and range?
O A.
Domain: −6 ≤ x ≤ 4, Range: −3 ≤ y ≤ 3
O B.
Domain: −3 ≤ x ≤ 3, Range: −6 ≤ y ≤ 4
O C.
Domain: −2 ≤ x ≤ 4, Range: 0 ≤ y ≤ 3
O D.
Domain: −2 ≤ x ≤ 3, Range: −6 ≤ y ≤ 3
y
48. Give the domain and range of the relation. Then state whether the relation is a function.
5
O A.
Domain: −3 ≤ 𝑥 ≤ 3
Range: −2 ≤ 𝑦 ≤ 2
The relation is not a function.
O B.
Domain: −3 ≤ 𝑥 ≤ 3
The relation is a function.
O C.
Domain: −2 ≤ 𝑥 ≤ 2
Range: −3 ≤ 𝑦 ≤ 3
The relation is not a function.
4
3
2
Range: −2 ≤ 𝑦 ≤ 2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
–2
–3
O D.
Domain: −2 ≤ 𝑥 ≤ 2
The relation is a function.
Range: −3 ≤ 𝑦 ≤ 3
–4
–5
Page 16 of 22
x
49. Which of the following is not a function?
O A.
O B.
{(4,1), (7, -2), (-2,4), (1, 2)}
y
y

O C.

O D.






x








x
















50. Which function best represents the values in the table?
O A.
𝑓(𝑥) = 𝑥 3
x
-3
f(x)
-27
O B.
𝑓(𝑥) = √𝑥
O C.
𝑓(𝑥) = 𝑥
-1
0
2
5
-1
0
8
125
O D.
𝑓(𝑥) = |𝑥|
1
51. Brad and Tom are comparing their classes' scores on a math test. Both of their classes had mean scores of
80 on the test, but Brad's class had a range of 6 while Tom's class had a range of 30. If the highest possible
score was 100, which class had the LOWEST score in it?
O A.
Brad's class had the lowest score in it, because it has the smallest range.
O B.
Tom's class had the lowest score in it, because it has the greatest range.
O C.
The lowest score occurred in both classes, because the mean is the same.
O D.
Brad’s class had the lowest range because their range is a factor of the range of Tom’s class.
Page 17 of 22
52. At a particular company, every employee receives a 4% cost-of-living increase to their salary.
What impact does this increase have on the mean and on the range of employee salaries at the company?
O A.
The mean increases but the range does not change.
O B.
The mean does not change but the range increases.
O C.
The mean and range both increase.
O D.
The mean and range do not change.
53. A company decides to give every one of its employees a $1000 raise. What happens to the mean and
median of the salaries as a result?
O A.
Mean stays the same, median increases by $1000
O B.
Mean increases by $1000, median stays the same
O C.
Mean and median stay the same
O D.
Mean and median both increase by $1000.
The graph shows the stock value for a technology company.
54. Choose the equation of a line that fits the data.
𝑦 = 4𝑥 + 23
O B.
𝑦 = 𝑥 + 25
O C.
𝑦 = 𝑥 + 20
O D.
𝑦 = 9𝑥 + 18
5
2
1
2
Value (dollars)
O A.
Stock Value
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9 10 11 12
years since 1999
55. What is the most likely value of the stock in year 1?
O A.
$0
O B.
$20
O C.
$40
O D.
$60
Page 18 of 22
56. Lucy did a study on the number of hours students spend on the internet each day and their grades in math
class. She found that there was a strong negative correlation between the two.
Which scatterplot shows the strong, negative correlation of her data?
O A.
O B.
O C.
O D.
57. Vance graphed the relation between fund-raising profits for the chess club and the number of members.
Which equation represents a line that fits the data?
O A.
y = 30n + 180
O B.
y = 50n + 180
O C.
y = n + 180
O D.
y=
3
5
200
3
n + 180
Page 19 of 22
58. Samantha surveyed a group of adults to gather data on their height and weight. She put her results into this
graph:
Which of the following statements is a generalization of the slope of the line that fits the data?
O A. For every inch a person grows, he will gain one pound
O B. For every inch a person grows, his weight will not change
O C. For every inch a person grows, he will gain 8 pounds
O D. For every inch a person grows, he will gain 20 pounds
59. In 2000, there were 5500 people who attended the state basketball tournament. The enrollment has been
increasing 2% annually since then.
Select the equation that would determine the total number of people who will attend after x years. (Let
𝑥 = 0 represent the year 2000.)
O A.
𝑦 = 5500(0.02) 𝑥
O B.
𝑦 = 5500(0.2) 𝑥
O C.
y = 5500(1.02)x
O D.
y = 5500(1.2)x
60. Graph A is the graph of
𝑦 = 2(3) 𝑥
and graph B is the graph of 𝑦 = 3(2) 𝑥 .
Which statement about the two graphs is true?
O A.
Both graphs A and B rise at the same rate.
O B.
Graph B rises at a faster rate than graph A.
O C.
Graph A rises at a faster rate than graph B.
O D.
The y-intercept of graph A is above the y-intercept of graph B.
Page 20 of 22
61. Solve the equation 3  729 .
x
O A.
𝑥=5
O B.
x=6
O C.
x = 243
O D.
x = 726

62. Graph A is the graph of 𝑦 = −2(3)−𝑥 and graph B is the graph of 𝑦 = 2(3)x .
Which statement about the two graphs is true?
O A.
Both graphs A and B rise at the same rate.
O B.
Graph B rises at a faster rate than Graph A.
O C.
Graph A rises at a faster rate than graph B.
O D.
The y-intercept of Graph A is above the y-intercept of graph B.
63. Look at the exponential equation:
𝑦 = 200(1.08) 𝑥
Determine the approximate value when 𝑥 = 6.
Round any decimals to two places.
O A.
222
O B.
317.37
O C.
1,296
O D.
6,802.44
64. In the laboratory, a bacteria population doubles in size every hour. A new bacteria culture is started with
10 bacteria cells.
Which equation models the size of the bacteria population, p, at the end of t hours?
O A.
𝑝 = 2(10)𝑡
O B.
𝑝 = 10(2)𝑡
O C.
𝑝 = 10(2 + 15)𝑡
O D.
𝑝 = 2(10)𝑡−15
Page 21 of 22
65. Which graph represents the function: 𝑓(𝑥) = 3(2) 𝑥
y
O A.
–5
–4
–3
–2
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
5 x
4
–5
y
O C.
–5
–4
–3
–2
y
O B.
9
–4
–3
–2
–1
–1
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
1
2
3
4
5
x
2
3
4
5 x
1
2
3
4
5 x
y
O D.
9
–1
–1
1
–5
–4
–3
–2
–1
–1
66. Two quantities, 𝑥 and 𝑦, vary directly. Given that 𝑦 = 5 when 𝑥 = −10, choose the equation that
represents the relationship between the quantities. Then, find 𝑦 when 𝑥 = 1.
1
O A.
𝑦 = − 𝑥 and
−
O B.
𝑦 = 𝑥 and
O C.
𝑦 = − 𝑥 and −
O D.
𝑦=−
2
1
1
2
2
1
1
2
2
7
10
𝑥 and −
3
5
7
10
67. Translate this sentence into an equation: The sum of one-fifth p and 38 is as much as twice p
O A.
O B.
O C.
O D.
1
5
1
5
1
5
1
5
𝑝 + 38 = 2𝑝
(𝑝 + 38) = 2𝑝
𝑝(2𝑝 + 38) = 2𝑝
+ 𝑝 + 38 = 2𝑝
Page 22 of 22