End Of Course Algebra I practice Test



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End Of Course
Algebra I
Practice Test


Name: _________________________________________________

Date: __________________________________________________





Day 1

  1. Order the following numbers from least to greatest:












  1. Solve the equation for a









  2. Determine what values of x the expression is defined for.

Express your answer with an inequality.

Write your answer on the line.


What are the defined values of x? _____________________



  1. Solve:









  2. Which equation is in standard form?










Day 2


  1. 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?

    1. P

    2. R

    3. S

    4. T




  1. Write an equation of the line that passes through the pair of points.

(-5, -2), (3, -1)















  1. Look at the list of numbers. 5-4., 0.75, 2,1-2., ,-10. , ,4-3.

Which number line represents the list of numbers?




  • A.


3

-2

-1

0

1

2


  • B.



  • C.

-2


-1

0

1

2

3



  • D.




-2


-1

0

1

2

3



  1. 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. When will the tank be full but not overflowing?

    1. 7 hours, 8 minutes

    2. 17 hours, 20 minutes

    3. 20 hours

    4. 22 hours, 40 minutes

  2. According to the graph, which statement best describes the slope?




    1. The amount of gas in the tank decreases by 3, as the distance traveled increases by 20.

    2. The amount of gas in the tank increases by 20, as the distance traveled decreases by 3.

    3. The amount of gas in the tank increases by 2, as the distance traveled increases by 30.

    4. The amount of gas in the tank decreases by 3, as the distance traveled decreases by 20.

Day 3

  1. 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?

    1. Brad's class had the lowest score in it.

    2. Tom's class had the lowest score in it.

    3. The lowest score occurred in both classes.

    4. It cannot be determined from the information.




  1. Only chocolate and vanilla ice cream cones are sold at an ice cream store. In 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.




  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)?




    1. T = 50n + 100

    2. T = 100(n + 50)

    3. T = 100n + 50

    4. T = 50(n + 100)




  1. 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 and justify in the answer box which equation describes the relationship between the number of miles Mr. Shindler has traveled and the number of gallons remaining in his gas tank.




  1. g=15−30m

  2. g=30m−15

  3. m=15−,-30g.

  4. m=,30-g.− 15

Show your work using words, numbers, and/or diagrams.





  1. 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 in the context of the problem.

  • Write your answer on the line.


Domain: ____________________ Range: ____________________

Day 4

  1. Look at the function:







  • Evaluate at .

  • Write your answer on the line.


What is = ___________________________________



  1. Which table represents the recursive formula:

an = an-1 - 6



  1. 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?




    1. The dependent variable is the number of moons.

    2. The independent variable is the number of moons.

    3. Since the number of moons is staying the same, there is no dependent variable.

    4. Since the number of moons is staying the same, there is no independent variable.


  1. Solve the equation for x.

4x + 14 = 7x + 5


  1. At a particular company, every employee receives a 4% cost-of-living increase to their salary.

What impact does this cost-of-living increase have on the mean and on the range of employee salaries at the company?





    1. The mean increases but the range does not change.

    2. The mean does not change but the range increases.

    3. The mean and range both increase.

    4. The mean and range do not change.


Day 5

  1. The graph shows the stock value for a technology company from 2002 to 2005. From this graph, draw a line that fits the data and determine what is the most likely value of the stock for the year 2000?




    1. $0

    2. $10

    3. $20

    4. $30



  1. Which of the following lines is parallel to the line represented by the equation? y=,1-2.x+10




    1. y=−,1-2.x+10

    2. y=,1-2.x+8

    3. y=2x+10

    4. y=−2x+8




  1. 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 negative correlation between the two.

Which scatterplot shows a strong, negative correlation of her data?




0 A.



0 B.



0 C.



0 D.





  1. Given the points (5, 9) and (-6, -13) find the graph of the equation of the line:




0 A.



0 C.




0 B.




0 D.




25. Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations


A) Write the equation of the line with y-intercept equal to 5 and a slope equal to 3.

B) Write the equation of the line with a slope of 2 that goes through the point (1,1).

C) Write the equation of the line that goes through the points (-3,5) and (-1,-3) without graphing.


Day 6


  1. Which of the following are functions (Mark all that apply)?


a.{(4,1),(7,1),(-2,4),(4,2)} b. c.





d. e.





  1. Which of these is the equation of a line with y-intercept (0, 2) and slope ?












  1. Look at the list of numbers.

Which list shows the numbers in order from least to greatest?




  • A.



  • B.




  • C.




  • D.

  1. Evaluate the expression for x = - 2.

What is the value of the expression?




  • A. 46

  • B. 22

  • C. -2

  • D. -26

30. Find the 21st term of the arithmetic sequence: 18, 23, 28, 33, . . .

Day 7

31. Write an equation of the line that is perpendicular to and goes through (-4, 5).










32. The assistant can make 8 pizzas in an hour. The master pizza maker can make 10 pizzas in an hour but starts baking 2 hours later than his assistant. Together, they must make 106 pizzas. How many hours will the assistant make pizzas before they are done making 106 pizzas?

Show your work using words, numbers, and/or pictures.




















How many hours will the assistant make pizzas? __________

33. Look at the function.




What is the domain and range?

  1. Domain: 6x4, Range: 2y3

  2. Domain: 3x3, Range: 6y4

  3. Domain: 2x4, Range: 0 y3

  4. Domain: 2x3, Range: 6y3

34. Solve the equation for x.

-3(x – 8) = -12
What is the value of x?


  • A. -4

  • B. 4

  • C. 12

  • D. 6

35. Look at the system of linear equations.
,, 3x+y = 13- x+6y = 7 ..

Solve the system of linear equations.




  • A. (-5, 28)

  • B. (-2, 19)

  • C. (7, 2)

  • D. (5, -2)

Day 8

36. After solving the following system of equations Sarah claimed that the system has no solution. Colton disagreed and said that the system actually has an infinite number of solutions. Who is correct and why? Show all work to justify your conclusion.



,, y=2x−5 -4x−2y=10..



















Who is correct? __________



  1. If , then when is y a positive number?

    1. always

    2. when x > -3

    3. when x > 3

    4. never




  1. Simplify

    1. 10







  2. The equation 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? ________________






  1. Solve for x: .

Display the set of solutions that makes the compound inequality true by graphing them on the number line below.







Day 9


  1. Which is the graph of the solution set of the system of inequalities?




  1. In 2000, 5500 people attended the State B basketball tournament. The enrollment has been increasing 2% annually. Select the equation that would determine the total number of people who attend t years after 2000.









  2. Which function best represents the values in the table below?



x

f(x)

-3

-27

-1

-1

0

0

2

8

5

125












  1. Which best describes the difference(s) between the graphs of and ?

    1. The graph of f(x) is twice as steep as the graph of g(x).

    2. The graph of f(x) is half as steep as the graph of g(x).

    3. The graph of f(x) has a y-intercept of 5 while g(x) has a y-intercept of 10.

    4. Both A and C are true.




  1. Graph A is the graph of and graph B is the graph of .

Which statement about the two graphs is true?



    1. Both graphs A and B rise at the same rate.

    2. Graph B rises at a faster rate than graph A.

    3. Graph A rises at a faster rate than graph B.

    4. The y-intercept of graph A is above the y-intercept of graph B.

Day 10

  1. Solve the equation .

    1. x = 5

    2. x = 6

    3. x = 243

    4. x = 726


  1. Evaluate the expression.

,.

Write your answer on the line.


What is the cube root of -27? __________________



  1. 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?




  • A. Graph A and B have the same vertex.

  • B. Graph A is less steep than graph B.

  • C. Graph B has a y-intercept that is 8 units above the y-intercept of Graph A.

  • D. Graph B has a vertex that is 8 units above the vertex of Graph A.



  1. Graph A is the graph of y=2,(3)-xxxxx.x and graph B is the graph of y=3,(2)x

Which statement about the two graphs is true?




  • A. Both graphs A and B rise at the same rate.

  • B. Graph B rises at a faster rate than graph A.

  • C. Graph A rises at a faster rate than graph B.

  • D. The y-intercept of graph A is above the y-intercept of graph B.




  1. Look at the exponential equation.

y=200,(1.08)-xx.x

Determine the approximate value for x = 6. Round any decimals to two places.



  • A. 222

  • B. 317.47

  • C. 1,296

  • D. 101,559,956,668,416

Day 11

  1. P and Q vary inversely. P is 10 when Q is 4. Find P, when Q is 8



  1. 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?














  1. 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?




    1. Mean stays the same, Median increases by $1000

    2. Mean increases by $1000, Median stays the same

    3. Mean and Median are the same

    4. Mean and Median both increase by $1000.




  1. Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.

If y=10 when x = -5, then find y when x=1.


    1. y=−,2.x; −,5.




    1. y=,2.x; ,2.




    1. y=−,-2.x; −,2.




    1. y=−,50x; −,50.




  1. Translate the sentence into an equation: The sum of one-fifth p and 38 is as much as twice p




    1. ,1/5p + 38 = 2p




    1. ,1-/5p + 38. = 2




    1. ,1-/5p +2p + 38. = 2p




    1. ,1-/5. + p + 38 = 2p


Day 12

  1. Write the equation in slope intercept form: y+3=3,x−1.




    1. y=−3x-4

    2. y=3x+2

    3. y=3x+4

    4. y=3x-4




  1. 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.

  • If Tara only wants to spend $43 on her cell phone bill, how many text messages can she send?



  1. A college professor at the University of Washington surveyed 150 students at the university. The students were asked if they prefer in class or take home tests. The professor drew the conclusion: “One out of four college students prefer take home tests.” Explain why this conclusion is misleading.

  1. The professor surveyed a small sample of the population at one university but made the conclusion about the entire population of college students.

  2. The survey question was biased toward in class tests.

  3. The students were not selected randomly.

  4. The sample size was too small.



  1. Give the domain and range of the relation. Tell whether the relation is a function.



0 a.

D: –3 x 3; R: –2 y 2

The relation is not a function.



0 c.

D: –3 x 3; R: –2 y 2

The relation is a function.



0 b.

D: –2 x 2; R: –3 y 3

The relation is not a function.



0 d.

D: –2 x 2; R: –3 y 3

The relation is a function.





  1. Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference, write the explicit formula, and the next three terms in the sequence.

–5, –11, –17, –23, –29




Day 13
61. Find the slope of the line described by x – 3y = –6.


0 a.



0 c.



0 b.



0 d.


62. Which of the following statements is a generalization of the slope of the line below?






0 A.

For every inch a person grows, he will gain one pound

0 B.

For every inch a person grows, his weight will not change

0 C.

For every inch a person grows, he will gain 8 pounds

0 D.

For every inch a person grows, he will gain 20 pounds


63. Write an equation or inequality for:
A) All numbers at least 3 units from 5
B) An equation with no real solutions

64. Solve the equation for x:


,2x+1 .+ 1= −12

65. Look at the system of linear inequalities.


, ,y > x3- y < x+8..

Which graph represents the solutions to the system of linear inequalities?






  1. c.









  1. d.

1. A.






2. C.
3. x ≤ 5

4. C.




5. C.
6. D. T




7. B.
8. B.

9. B. 17 hours, 20 minutes

10. A. The amount of gas in the tank decreases by 3, as the distance traveled increases by 20.

11. B. Tom's class had the lowest score in it.



  1. c= 4v + 1

c + v = 121

97 chocolate cones were sold

13. A. T = 50n + 100

14. C. m=15−,30g.

15. Domain: 25≤x≤45

Range: 500≤y≤900

16. f(−3).= 35

17.


18. B. The dependent variable is the number of moons.

19. X=3


20. C. The mean and range both increase.

21. B. $10

22. B. y=,1-2.x+8

23. D.



24. C.
25. A) y=3x+5

B) y=2x−1

C) y=−4x−7

Look at Student graphs.
26. a) Not a function (4 can’t map to both 1 and 2)


  1. Function

  2. Function

  3. Not a function

  4. Function


27. A.
28. B.

29. B. 22

30. The 21st term is 118



31. D.
32. 7 hours

Assistant: 8h

Master: 10(h−2)

8h+10h−2.= 106

8h+10h−20=106

18h=126

33. A. Domain: −6≤x≤4, Range: −2≤y≤3

34. C. 12

35. D. (5, -2)

36. Colton is correct, there are infinite solutions.

4x−2(,2x−5).=10

4x−4x+10=10

10=10

37. A. always



38. C.
39. x=−7 is the negative solution.
40.

41. Graph A



42. C.
43. A.

44. B. The graph of f(x) is half as steep as the graph of g(x).

45. C. Graph A rises at a faster rate than graph B.

46. B. x = 6

47. −3

48. B. Graph A is less steep than graph B.

49. C. Graph A rises at a faster rate than graph B.

50. B. 317.47

51. P=20

52. A.

53. D. Mean and Median both increase by $1000.

54. C. y=−,-2.x; −,-2.

55. A. ,1-/5.p+38=2p

56. D. y=3x-4

57. C=.15t+39


  1. xt (including the 100 included texts)

  2. Note….you can’t spend exactly $43 on this plan. You could spend $42.90 or $43.05.

58. A. The professor surveyed a small sample of the population at one university but made the conclusion about the entire population of college students.

59. A. D: –3 x 3; R: –2 y 2

The relation is not a function.

60. It appears to be an arithmetic sequence. The common difference is (-6)

Explicit formula: an= -6(n-1) -5

*assuming we define a1=-5

Next three terms: -35, -41, -47

61. A. ,1/-3.

62. C. For every inch a person grows, he will gain 8 pounds

63. Answers may vary; examples are given.

A. ,x−5.≥3

B. x+6=x−2

64. x = -7


65. A.


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