         Mathematics
Unit 1




                                          Unit 1

         Directions:
         Today, you will take Unit 1 of the Algebra I Practice Test. Unit 1 has two sections.
         In the first section, you may not use a calculator. In the second section, you may
         use a calculator. You will not be allowed to return to the first section of the
         test after you start the calculator section. You must complete both the
         non-calculator and calculator sections of Unit 1 within the time allowed.
         Read each question. Then, follow the directions to answer each question. Mark
         your answers by completely filling in the circles in your answer document. Do not
         make any pencil marks outside of the circles. If you need to change an answer, be
         sure to erase your first answer completely. If a question asks you to show or
         explain your work, you must do so to receive full credit. Only responses written
         within the provided space will be scored.
         If you do not know the answer to a question, you may go on to the next question.
         When you finish the first section, you may review your answers and any questions
         you did not answer in this section ONLY. Once you have reviewed your answers,
         continue to the calculator section. When you are ready to go on to the calculator
         section, raise your hand to receive your calculator.




                                                  2


         Mathematics
Unit 1




                GO ON TO NEXT PAGE




                        4


                                                                          Mathematics




                                                                                         Unit 1
                Unit 1 - Section 1
                (Non-Calculator)


This unit has two sections: a non-calculator section and a calculator section.
You will now take the non-calculator section of this unit in which you may not use
a calculator. You will not be allowed to return to the first section of the test after
you start the calculator section. You must complete both sections within the time
allowed for this unit.
Once you finish the non-calculator section, read the directions in your test booklet
on how to continue.




                                           5


         Mathematics


         1.   Several points are plotted on the graph.
Unit 1




                                                   y


                                                       G
                                                  8


                                                  6


                                                  4


                                                       F
                                                  2

                                   E    D                  A           B
                                                                                   x
                              -8   -6   -4   -2    0           2   4       6   8


                                                  -2


                                                  -4


                                                  -6

                                                       C
                                                  -8




              Which of the plotted points on the graph represent the zeros of the function
              f(x) = (x 2 + 2x − 8)(x − 6)? Select all that apply.

              A.   (2, 0)

              B.   (6, 0)

              C.   (0, −8)

              D.   (− 4, 0)

              E.   (−6, 0)

              F.   (0, 2)

              G.   (0, 8)


                                                       6


                                                                       Mathematics


Use the information provided to answer Part A and Part B for question 2.




                                                                                       Unit 1
Let a represent a non-zero rational number and let b represent an irrational
number.

2.   Part A

     Which expression could represent a rational number?

     A.   −b

     B.   a+ b

     C.   ab

     D.   b2

     Part B

     Consider a quadratic equation with integer coefficients and two distinct zeros.
     If one zero is irrational, which statement is true about the other zero?

     A. The other zero must be rational.

     B. The other zero must be irrational.

     C. The other zero can be either rational or irrational.

     D. The other zero must be non-real.




                                         7


         Mathematics


         3.   Which graph best represents the solution to this system of inequalities?
Unit 1




                                                   x + y ≤ 6
                                                   x + 2y ≤ 8


              A.                 y                           B.                 y

                               8                                               8
                               6                                               6
                               4                                               4
                               2                                               2
                                               x                                                  x
                    -8 -6 -4 -2 0    2 4 6 8                        -8 -6 -4 -2 0       2 4 6 8
                              -2                                              -2
                              -4                                              -4
                              -6                                              -6
                              -8                                              -8



              C.                 y                           D.                 y

                               8                                               8
                               6                                               6
                               4                                               4
                               2                                               2
                                               x                                                  x
                    -8 -6 -4 -2 0    2 4 6 8                        -8 -6 -4 -2 0       2 4 6 8
                              -2                                              -2
                              -4                                              -4
                              -6                                              -6
                              -8                                              -8




         4.                                          (            ) (
              Which expression is equivalent to 3x 5 + 8x 3 − 7x 2 − 6x 3 ?         )
              A.   − 4x 3 + 14

              B.   − 4x 5 + 14x 3

              C.   3x 5 + 14x 3 − 7x 2

              D.   3x 5 + 2x 3 − 7x 2



                                                         8


                                                                       Mathematics


5.   Which points are on the graph of the equation −3x + 6y + 5 = −7?




                                                                                     Unit 1
     Select all that apply.

     A.   (−3, 6)

     B.   (−2,0)

     C.   (0, −2)

     D.   (6, −3)

     E.   (8, 2)




6.   Which factorization can be used to reveal the zeros of the function
     f(n) = −12n 2 − 11n + 15 ?

     A.   f(n) = − n(12n + 11) + 15

     B.   f(n) = (− 4n + 3)(3n + 5)

     C.   f(n) = −(4n + 3)(3n + 5)

     D.   f(n) = (4n + 3)(−3n + 5)




                                         9


         Mathematics


         Use the information provided to answer Part A and Part B for question 7.
Unit 1




                                   2
         The function f(x) = 4x − x is graphed in the xy-coordinate plane as shown.




         7.   Part A

              Based on the graph of the function, which statements are true?

              Select all that apply.

              A. f is increasing on the interval x < 0 .

              B. f is decreasing on the interval x < 0 .

              C. f is increasing on the interval 0 < x < 2 .

              D. f is decreasing on the interval 0 < x < 2 .

              E. f is increasing on the interval 2 < x < 4 .

              F. f is decreasing on the interval 2 < x < 4 .

              G. f is increasing on the interval x > 4 .

              H. f is decreasing on the interval x > 4 .




                                                  10


                                                                 Mathematics


Part B




                                                                               Unit 1
Based on the graph of the function, which statements are true?

Select all that apply.

A.   f(x) < 0 on the interval x < 0 .

B.   f(x) > 0 on the interval x < 0 .

C.   f(x) < 0 on the interval 0 < x < 2 .

D.   f(x) > 0 on the interval 0 < x < 2 .

E.   f(x) < 0 on the interval 2 < x < 4 .

F.   f(x) > 0 on the interval 2 < x < 4 .

G.   f(x) < 0 on the interval x > 4 .

H.   f(x) > 0 on the interval x > 4 .




                                    11                                 STOP


         Mathematics
Unit 1




                               STOP
         You have come to the end of the non-calculator section in Unit 1 of the
         test.


         • You may review your answers in the non-calculator section ONLY. You
           will not be allowed to return to the non-calculator section once you
           have received your calculator.
         • When you are ready to go on to the calculator section, raise your hand
           to receive your calculator.




                                            12                               STOP


                                                                 Mathematics




                                                                                Unit 1
               Unit 1 - Section 2
                 (Calculator)

Once you have received your calculator, continue into the calculator section.




                                        13


              Mathematics


         8.   The figure shows a graph of the function of f(x) in the xy-coordinate plane,
Unit 1




              with the vertex at (1, 9) and the zeros at −2 and 4.

                                                f(x)

                                                9
                                                8
                                                7
                                                6
                                                5
                                                4
                                                3
                                                2
                                                1
                                                                           x
                                    -4 -3 -2 -1 0      1 2 3 4 5 6 7 8 9
                                              -1
                                              -2
                                              -3
                                              -4




              The function g is defined by g(x) = −3x + 2 .

              Which statements are true? Select all that apply.

              A. f(−2) is greater than g(−2) .

              B.   f(−1) is less than g(−1) .

              C.   f(0) is greater than g(0) .

              D. f(1) is less than g(1) .

              E.   f(2) is greater than g(2) .




                                                          14


               Mathematics




                             Unit 1
GO ON TO NEXT PAGE




        15


              Mathematics


         Use the information provided to answer Part A through Part D for
Unit 1




         question 9.

         Leah would like to earn at least $120 per month. She babysits for $5 per hour and
         works at an ice cream shop for $8 per hour. Leah cannot work more than a total of
         20 hours per month. Let x represent the number of hours Leah babysits and let y
         represent the number of hours Leah works at the ice cream shop.

         9.   Part A

              Which graph shows the set of points that represents the number of hours that
              Leah can work in order to earn at least $120 and not work more than
              20 hours per month?

              A.                            y                            B.                            y
                   at Ice Cream Shop




                                                                              at Ice Cream Shop
                                       20                                                         20
                     Hours Working




                                                                                Hours Working
                                       15                                                         15

                                       10                                                         10

                                        5                                                          5

                                                                    x                                                          x
                                        0        5 10 15 20                                        0        5 10 15 20
                                                Hours Babysitting                                          Hours Babysitting

              C.                            y                            D.                            y
                   at Ice Cream Shop




                                                                              at Ice Cream Shop




                                       20                                                         20
                     Hours Working




                                                                                Hours Working




                                       15                                                         15

                                       10                                                         10

                                        5                                                          5

                                                                    x                                                          x
                                        0        5 10 15 20                                        0        5 10 15 20
                                                Hours Babysitting                                          Hours Babysitting




                                                                    16


                                                            Mathematics


Part B




                                                                               Unit 1
Which pairs (x, y) represent hours that Leah could work to meet the given
conditions?

Select all that apply.

A.   (4, 15)

B.   (5, 12)

C.   (10, 9)

D.   (15, 5)

E.   (19, 1)

Part C

If Leah babysits for 7 hours this month, what is the minimum number of
hours she would have to work at the ice cream shop to earn at least $120?

Give your answer to the nearest whole hour.

Enter your answer in the box.

Part D

Leah prefers babysitting over working at the ice cream shop. Out of 20 total
hours, what is the maximum number of hours she can babysit to be able to
earn at least $120 per month?

Give your answer to the nearest whole hour.

Enter your answer in the box.




                                   17


             Mathematics


         10. The figure shows the graphs of the functions y = f (x) and y = g(x). The four
Unit 1




             indicated points all have integer coordinates.

                                                       y

                                                      9
                                                      8
                                  y = f(x)            7       y = g(x)
                                                      6
                                                      5
                                                      4
                                                      3
                                                      2
                                                      1
                                                                                x
                            -9 -8 -7 -6 -5 -4 -3 -2 -1 0    1 2 3 4 5 6 7 8 9
                                                      -1
                                                     -2
                                                     -3
                                                     -4
                                                     -5
                                                     -6
                                                     -7
                                                     -8
                                                     -9




             If g(x) = k i f(x) , what is the value of k?

             Enter your answer in the box.




                                                       18


Let m be the number of cookies that Matt made. Let A represent the total amount of money earned.

Should Phill and Matt raise the price of the cookies?

                                                                    Mathematics


Use the information provided to answer Part A through Part C for




                                                                                    Unit 1
question 11.

Phil and Matt made cookies for a fundraiser at their high school.

• Phil made 25% more cookies than Matt.
• The cookies sold for $0.25 each.
• After the sale, 20% of the combined total of their cookies remained.


11. Part A

     Create an equation to represent the total amount of money Matt and Phil
     earned at the fundraiser based on the number of cookies Matt made. Explain
     how you determined your equation.

     Enter your equation and your explanation in the space provided.


     Part B

     Phil and Matt made a total of $72.00 selling the cookies. How many cookies
     did Phil make and how many cookies did Matt make? Show your work.

     Enter your answers and your work in the space provided.

     Part C

     Next year Phil and Matt may sell the cookies for $.50 each. They plan to
     make the same total number of cookies, but they predict that they will only
     sell 70% of them given the price increase. Based on their prediction, should
     Phil and Matt raise the price of the cookies? Justify your answer.

     Enter your answer and your justification in the space provided.




                                        19


             Mathematics


         12. A random sample of 200 teenagers participated in a taste test. Each teenager
Unit 1




             sampled four choices of fruit drink (labeled A, B, C, and D), and then were
             asked to pick a favorite. The table shows the results of this taste test.


                                        A      B        C    D    Total
                              Boys      45    25        30   20   120

                              Girls     25    10        30   15        80

                              Total     70    35        60   35   200


             Based on the information given, which of the given statements are true?

             Select all that apply.

             A. 40% of the participants were girls.


             B. 70% of the participants preferred A.


             C.    20   of the boys preferred D.
                  120


             D.   10 of the participants who preferred B were girls.
                  35


             E. The proportion of boys who preferred C is equal to the proportion of girls
                who preferred C.




                                                   20


                                                                    Mathematics


13. Let x + y = c where, c is a real number.




                                                                                  Unit 1
     Determine the number of points that would be on the graph of the equation
     for each given case:

     Case 1: c < 0

     Case 2: c = 0

     Case 3: c > 0

     Justify your answers.

     Enter your answers and justifications in the space provided.




14. The formula for finding the perimeter, P, of a rectangle with length l and
    width w is given.

                                    P = 2l + 2w

     Which formula shows how the length of a rectangle can be determined from
     the perimeter and the width?

     A.   l = P − 2w
              2


     B.   l = P − 2w
                  2


     C.   l = P +w
              2


     D.   l = P −2
              2w




                                        21


             Mathematics


         Use the information provided to answer Part A and Part B for question 15.
Unit 1




         Members of two cross-country teams ran an obstacle course. The table shows the
         times, in minutes and seconds, for the members of team R to complete the
         course.

                                  Team R Obstacle Course
                                          Times
                                  5:32    6:48    4:25       8:05   7:23
                                  5:37    5:12    6:26       5:31   4:43
                                  6:08    7:16    5:52       5:21   6:53
                                  4:49    5:02    6:33       5:54   6:20

         The obstacle course times, in minutes and seconds, for team S are summarized in
         the box plot shown.

                                         Team S Obstacle
                                          Course Times


                                     4    5   6    7     8    9 10




                                                  22


                                                                                            Mathematics


15. Part A




                                                                                                                   Unit 1
    Which histogram represents the times from Team R on the obstacle course?

    A.                               Team R                B.                               Team R
                     8                                                      7
                     7                                                      6




                                                                Frequency
                     6                                                      5
         Frequency




                     5                                                      4
                     4                                                      3
                     3                                                      2
                     2                                                      1
                     1                                                      0
                     0                                                          4   5   6     7   8     9     10
                         4   5   6     7   8     9   10                             Obstacle Course Times
                             Obstacle Course Times


    C.                               Team R                D.                               Team R

                     7                                                      8
                     6                                                      7
         Frequency




                     5                                                      6



                                                                Frequency
                     4                                                      5
                     3                                                      4
                     2                                                      3
                     1                                                      2
                     0                                                      1
                         4   5   6     7   8     9   10                     0
                             Obstacle Course Times                              4   5   6     7   8     9     10
                                                                                    Obstacle Course Times



    Part B

    Which statements are true about the data for team R and team S?

    Select all that apply.

    A. The median time of team R is less than the median time of team S.

    B. The median time of team R is greater than the median time of team S.

    C. The interquartile range of team R is less than the interquartile range of
       team S.

    D. The interquartile range of team R is equal to the interquartile range of
       team S.

    E. The data for team R is skewed to the left.

    F. The data for team S includes an outlier.


                                                      23                                                    STOP


             Mathematics
Unit 1




                                STOP
         You have come to the end of the calculator section in Unit 1 of the test.


         • Review your answers in the calculator section of Unit 1 only.
         • Then, close your test booklet and answer document and raise your
           hand to turn in your test materials.




                                              24                                STOP


       Mathematics




                     Unit 1
STOP



 25


         Mathematics
Unit 1




                                          Unit 1

         Directions:
         Today, you will take Unit 1 of the Algebra I Practice Test. Unit 1 has two sections.
         In the first section, you may not use a calculator. In the second section, you may
         use a calculator. You will not be allowed to return to the first section of the