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Algebra I (Common Core) - New York Regents Fall 2013 Exam Sample

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1   Which ordered pair is not in the solution set of
(1)   (5,3)
(2)   (4,3)
(3)   (3,4)
(4)   (4,4)


2   If the quadratic formula is used to find the roots of the equation x2 − 6x − 19 = 0, the
    correct roots are
    (1) 3 ± 2 √7                              (3)     3 ± 4 √14
    (2) −3 ± 2 √7                             (4)     −3 ± 4 √14


3   Which statistic would indicate that a linear function would not be a good fit to model a data set?
(1) r = -0.93                                (2) r = 1


4   On the set of axes below, graph the function represented by y = 3√(x − 2) for the domain
    −6 ≤ x ≤ 10.


5   Solve 8m2 + 20m = 12 for m by factoring.


6   Ryker is given the graph of the function y = ½ x2 – 4. He wants to find the zeros of the function,
    but is unable to read them exactly from the graph.
Find the zeros in simplest radical form.


7   Emma recently purchased a new car. She decided to keep track of how many gallons of gas
    she used on five of her business trips. The results are shown in the table below.
                                Miles Driven      Number of
                                                  Gallons Used
                                     150                7
                                     200               10
                                     400               19
                                     600               29
                                    1000               51
    Write the linear regression equation for these data where miles driven is the independent
    variable. (Round all values to the nearest hundredth.)


8   Max purchased a box of green tea mints. The nutrition label on the box stated that a serving of
    three mints contains a total of 10 Calories.
    On the axes below, graph the function, C, where C (x) represents the number of Calories in x mints.
Write an equation that represents C (x).
A full box of mints contains 180 Calories. Use the equation to determine the total number of
mints in the box.


9   David has two jobs. He earns $8 per hour babysitting his neighbor’s children and he earns
    $11 per hour working at the coffee shop.
    Write an inequality to represent the number of hours, x, babysitting and the number of hours, y,
    working at the coffee shop that David will need to work to earn a minimum of $200.
David worked 15 hours at the coffee shop. Use the inequality to find the number of full hours he
must babysit to reach his goal of $200.


10 On the set of axes below, graph the function y = |x + 1| .
State the range of the function.
State the domain over which the function is increasing.


11 The table below lists the total cost for parking for a period of time on a street in Albany, N.Y. The
   total cost is for any length of time up to and including the hours parked. For example, parking for
   up to and including 1 hour would cost $1.25; parking for 3.5 hours would cost $5.75.
                                      Hours           Total
                                      Parked          Cost
                                         1            1.25
                                         2            2.50
                                         3            4.00
                                         4            5.75
                                         5            7.75
                                         6            10.00
    Graph the step function that represents the cost for the number of hours parked.
Explain how the cost per hour to park changes over the six-hour period.


12 At an office supply store, if a customer purchases fewer than 10 pencils, the cost of each pencil is
   $1.75. If a customer purchases 10 or more pencils, the cost of each pencil is $1.25.
    Let c be a function for which c (x) is the cost of purchasing x pencils, where x is a whole number.
              ⎧1.75x, if 0 ≤ x ≤ 9
     c ( x) = ⎨
              ⎩1.25x, if x ≥ 10
    Create a graph of c on the axes below.
A customer brings 8 pencils to the cashier. The cashier suggests that the total cost to purchase
10 pencils would be less expensive. State whether the cashier is correct or incorrect. Justify your


13 About a year ago, Joey watched an online video of a band and noticed that it had been viewed
   only 843 times. One month later, Joey noticed that the band’s video had 1708 views. Joey made
   the table below to keep track of the cumulative number of views the video was getting online.
                 Months Since First Viewing               Total Views
                               0                               843
                               1                              1708
                               2                         forgot to record
                               3                              7124
                               4                             14,684
                               5                             29,787
                               6                             62,381
    a) Write a regression equation that best models these data. Round all values to the nearest
       hundredth. Justify your choice of regression equation.
b) As shown in the table, Joey forgot to record the number of views after the second month.
   Use the equation from part a to estimate the number of full views of the online video that
   Joey forgot to record.


14 Use the data below to write the regression equation (y = ax + b) for the raw test score based on
   the hours tutored. Round all values to the nearest hundredth.
                          Tutor       Raw Test           Residual
                         Hours, x      Score        (Actual – Predicted)
                             1            30                 1.3
                             2            37                 1.9
                             3            35                –6.4
                             4            47                –0.7
                             5            56                 2.0
                             6            67                 6.6
                             7            62                –4.7
    Equation: _______
    Create a residual plot on the axes below, using the residual scores in the table above.
Based on the residual plot, state whether the equation is a good fit for the data. Justify your


15 A local business was looking to hire a landscaper to work on their property. They narrowed
   their choices to two companies. Flourish Landscaping Company charges a flat rate of $120
   per hour. Green Thumb Landscapers charges $70 per hour plus a $1600 equipment fee.
    Write a system of equations representing how much each company charges.
    Determine and state the number of hours that must be worked for the cost of each company to
    be the same. [The use of the grid below is optional.]
    If it is estimated to take at least 35 hours to complete the job, which company will be less
    expensive? Justify your answer.

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