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Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial
credit will be allowed. For each statement or question, choose the word or expression that, of those
given, best completes the statement or answers the question. Record your answers on your
separate answer sheet. [48]

1. 1 The owner of a small computer repair business has one employee,
who is paid an hourly rate of $22. The owner estimates his weekly
profit using the function P(x) = 8600  22x. In this function, x
represents the number of
(1) computers repaired per week
(2) hours worked per week
(3) customers served per week
(4) days worked per week Answer: 2
2. 2 Peyton is a sprinter who can run the 40yard dash in 4.5 seconds.
He converts his speed into miles per hour, as shown below.
Answer: 2
3. 3 Which equation has the same solutions as 2x^{2} + x  3 = 0?
(1) (2x  1)(x + 3) = 0 (3) (2x  3)(x + 1) = 0
(2) (2x + 1)(x  3) = 0 (4) (2x + 3)(x  1) = 0 Answer: 4
4. 4 Krystal was given $3000 when she turned 2 years old. Her parents
invested it at a 2% interest rate compounded annually. No deposits or
withdrawals were made. Which expression can be used to determine
how much money Krystal had in the account when she turned 18?
(1) 3000(1 + 0.02)^{16} (3) 3000(1 + 0.02)^{18}
(2) 3000(1  0.02)^{16} (4) 3000(1  0.02)^{18} Answer: 1
5. 5 Which table of values represents a linear relationship?
x f(x) x f(x)
−1 −3 −1 −3
0 −2 0 −1
1 1 1 1
2 6 2 3
3 13 3 5
(1) (3)
x f(x) x f(x )
−1 ½ −1 −1
0 1 0 0
1 2 1 1
2 4 2 8
3 8 3 27
(2) (4) Answer: 3
6. 6 Which domain would be the most appropriate set to use for a
function that predicts the number of household onlinedevices in
terms of the number of people in the household?
(1) integers (3) irrational numbers
(2) whole numbers (4) rational numbers Answer: 2
7.
Answer: 1
8. 8 The value in dollars, v(x), of a certain car after x years is represented
by the equation v(x) = 25,000(0.86)^{x}. To the nearest dollar,
how much more is the car worth after 2 years than after 3 years?
(1) 2589 (3) 15,901
(2) 6510 (4) 18,490 Answer: 1
9. 9 Which function has the same yintercept as the graph below?
Answer: 4
10. 10 Fred is given a rectangular piece of paper. If the length of Fred’s
piece of paper is represented by 2x  6 and the width is represented
by 3x  5, then the paper has a total area represented by
(1) 5x  11 (3) 10x  22
(2) 6x^{2}  28x + 30 (4) 6x^{2}  6x  11 Answer: 2
11. 11 The graph of a linear equation contains the points (3,11) and (2,1).
Which point also lies on the graph?
(1) (2,1) (3) (2,6)
(2) (2,4) (4) (2,9) Answer: 4
12. 12 How does the graph of f(x) = 3(x  2)^{2} + 1 compare to the graph
of g(x) = x^{2}?
(1) The graph of f(x) is wider than the graph of g(x), and its vertex
is moved to the left 2 units and up 1 unit.
(2) The graph of f(x) is narrower than the graph of g(x), and its vertex
is moved to the right 2 units and up 1 unit.
(3) The graph of f(x) is narrower than the graph of g(x), and its vertex
is moved to the left 2 units and up 1 unit.
(4) The graph of f(x) is wider than the graph of g(x), and its vertex is
moved to the right 2 units and up 1 unit. Answer: 2
13. 13 Connor wants to attend the town carnival. The price of admission to
the carnival is $4.50, and each ride costs an additional 79 cents.
If he can spend at most $16.00 at the carnival, which inequality can
be used to solve for r, the number of rides Connor can go on, and
what is the maximum number of rides he can go on?
(1) 0.79 + 4.50r ≤ 16.00; 3 rides
(2) 0.79 + 4.50r ≤ 16.00; 4 rides
(3) 4.50 + 0.79r ≤ 16.00; 14 rides
(4) 4.50 + 0.79r ≤ 16.00; 15 rides Answer: 3
14. 14 Corinne is planning a beach vacation in July and is analyzing the
daily high temperatures for her potential destination. She would like
to choose a destination with a high median temperature and a small
interquartile range. She constructed box plots shown in the diagram
below.
Which destination has a median temperature above 80 degrees and
the smallest interquartile range?
(1) Ocean Beach (3) Serene Shores
(2) Whispering Palms (4) Pelican Beach Answer: 4
15. What is the yintercept of this equation and what does it represent?
(1) 0.98, the percent of money in the account initially
(2) 0.98, the percent of money in the account after x years
(3) 5000, the amount of money in the account initially
(4) 5000, the amount of money in the account after x years
15 Some banks charge a fee on savings accounts that are left inactive
for an extended period of time. The equation y = 5000(0.98)^{x}
represents the value, y, of one account that was left inactive for a
period of x years. Answer: 3
16.
16 The equation for the volume of a cylinder is V = πr^{2}h. The positive
value of r, in terms of h and V, is Answer: 1
17. 17 Which equation has the same solutions as x^{2} + 6x  7 = 0?
(1) (x + 3)^{2} = 2 (3) (x  3)^{2} = 16
(2) (x  3)^{2} = 2 (4) (x + 3)^{2} = 16 Answer: 4
18. 18 Two functions, y = x  3 and 3x + 3y = 27, are graphed on the
same set of axes. Which statement is true about the solution to the
system of equations?
(1) (3,0) is the solution to the system because it satisfies the equation
y = x  3.
(2) (9,0) is the solution to the system because it satisfies the equation
3x + 3y = 27.
(3) (6,3) is the solution to the system because it satisfies both equations.
(4) (3,0), (9,0), and (6,3) are the solutions to the system of equations
because they all satisfy at least one of the equations. Answer: 3
19.
Answer: 4
20.
Answer: 3
21. 21 An astronaut drops a rock off the edge of a cliff on the Moon.
The distance, d(t), in meters, the rock travels after t seconds can be
modeled by the function d(t) = 0.8t^{2}. What is the average speed,
in meters per second, of the rock between 5 and 10 seconds after
it was dropped?
(1) 12 (3) 60
(2) 20 (4) 80 Answer: 1
22. 22 When factored completely, the expression p^{4}  81 is equivalent to
(1) (p^{2} + 9)(p^{2}  9)
(2) (p^{2}  9)(p^{2}  9)
(3) (p^{2} + 9)(p + 3)(p  3)
(4) (p + 3)(p  3)(p + 3)(p  3) Answer: 3
23. 23 In 2013, the United States Postal Service charged $0.46 to mail a
letter weighing up to 1 oz. and $0.20 per ounce for each additional
ounce. Which function would determine the cost, in dollars, c(z), of
mailing a letter weighing z ounces where z is an integer greater
than 1?
(1) c(z) = 0.46z + 0.20 (3) c(z) = 0.46(z  1) + 0.20
(2) c(z) = 0.20z + 0.46 (4) c(z) = 0.20(z  1) + 0.46 Answer: 4
24. 24 A polynomial function contains the factors x, x  2, and x + 5.
Which graph(s) below could represent the graph of this function?
(1) I, only (3) I and III
(2) II, only (4) I, II, and III Answer: 1
Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only 1 credit. All answers should be written in pen, except for graphs and drawings,
which should be done in pencil. [16]

25. 25 Ms. Fox asked her class “Is the sum of 4.2 and √2 rational or irrational?” Patrick answered that
the sum would be irrational.
State whether Patrick is correct or incorrect. Justify your reasoning. Answer: (25) [2] Correct is stated and a correct justification is given.
26. 26 The school newspaper surveyed the student body for an article about club membership. The table
below shows the number of students in each grade level who belong to one or more clubs.
1 Club 2 Clubs 3 or More Clubs
9th 90 33 12
10th 125 12 15
11th 87 22 18
12th 75 27 23
If there are 180 students in ninth grade, what percentage of the ninth grade students belong to
more than one club? Answer: (26) [2] 25, and correct work is shown.
27. 27 A function is shown in the table below.
x f(x)
–4 2
–1 –4
0 –2
3 16
If included in the table, which ordered pair, (4,1) or (1,4), would result in a relation that is
no longer a function? Explain your answer. Answer: (27) [2] (4,1), and a correct explanation is given.
28. 28 Subtract 5x^{2} + 2x  11 from 3x^{2} + 8x  7. Express the result as a trinomial. Answer: (28) [2] 2x^{2} + 6x + 4 or equivalent trinomial, and correct work is shown.
29. 29 Solve the equation 4x^{2}  12x = 7 algebraically for x. Answer:
30. 30 Graph the following function on the set of axes below.
f(x) = x, 3 ≤ x < 1
4, 1 ≤ x ≤ 8
Answer: (30) [2] A correct graph is drawn.
31. 31 A gardener is planting two types of trees:
Type A is three feet tall and grows at a rate of 15 inches per year.
Type B is four feet tall and grows at a rate of 10 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height. Answer:
32. 32 Write an exponential equation for the graph shown below.
Explain how you determined the equation. Answer: (32) [2] y = 0.25(2)^{x} or an equivalent equation is written, and a correct explanation is
given.
Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only 1 credit. All answers should be written in pen, except for graphs and drawings,
which should be done in pencil. [16]

33. 33 Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob
spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50
for four bags of popcorn and two drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and the price
of one drink.
Using these equations, determine and state the price of a bag of popcorn and the price of a drink,
to the nearest cent. Answer: (33) [4] A correct system of equations is written, popcorn = 5.75, drink = 2.25 and
correct work is shown.
34. 34 The graph of an inequality is shown below.
a) Write the inequality represented by the graph.
b) On the same set of axes, graph the inequality x + 2y < 4.
c) The two inequalities graphed on the set of axes form a system. Oscar thinks that the point (2,1)
is in the solution set for this system of inequalities. Determine and state whether you agree
with Oscar. Explain your reasoning. Answer: (34) [4] y ≥ 2x  3, a correct graph, and disagree, and a correct explanation is written.
35. 35 A nutritionist collected information about different brands of beef hot dogs. She made a table
showing the number of Calories and the amount of sodium in each hot dog.
Calories per Milligrams of Sodium
Beef Hot Dog per Beef Hot Dog
186 495
181 477
176 425
149 322
184 482
190 587
158 370
139 322
a) Write the correlation coefficient for the line of best fit. Round your answer to the nearest
hundredth.
b) Explain what the correlation coefficient suggests in the context of this problem. Answer: (35) [4] 0.94 and a correct explanation is written.
36. 36 a) Given the function f(x) = x^{2} + 8x + 9, state whether the vertex represents a maximum or
minimum point for the function. Explain your answer.
b) Rewrite f(x) in vertex form by completing the square. Answer: (36) [4] Maximum is stated, a correct explanation is written, and f(x) = (x  4)^{2} + 25,
and correct work is shown using completing the square.
Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate
the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.
A correct numerical answer with no work shown will receive only 1 credit. All answers should
be written in pen, except for graphs and drawings, which should be written in pencil. [6]

37. 37 New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a
square is being adjusted so that one side is doubled in length, while the other side is decreased
by three meters.
The new rectangular garden will have an area that is 25% more than the original square garden.
Write an equation that could be used to determine the length of a side of the original square
garden.
Explain how your equation models the situation.
Determine the area, in square meters, of the new rectangular garden. Answer: (37) [6] (x  3)(2x) = 1.25x^{2} or an equivalent quadratic in one variable is written, a cor
rect explanation is written, 80, and correct work is shown.
38. High School Math Reference Sheet
1 inch = 2.54 centimeters 1 kilometer = 0.62 mile 1 cup = 8 fluid ounces
1 meter = 39.37 inches 1 pound = 16 ounces 1 pint = 2 cups
1 mile = 5280 feet 1 pound = 0.454 kilogram 1 quart = 2 pints
1 mile = 1760 yards 1 kilogram = 2.2 pounds 1 gallon = 4 quarts
1 mile = 1.609 kilometers 1 ton = 2000 pounds 1 gallon = 3.785 liters
1 liter = 0.264 gallon
1 liter = 1000 cubic centimeters
Answer:
Try the Quiz : Algebra I (Common Core)  New York Regents January 2015 Exam
