january-2016-nys-algebra-1-common-core-regents-part-4-16-to-20-new-york-examination-solutions

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In the function f(x) (x 2)2 4, the minimum value occurs computations.

when x is

(1) 2 (3)4

(2) 2 (4) 4

2 The graph below was created by an employee at a gas station.

Which statement can be justified by using the graph?

(1) If 10 gallons of gas was purchased, $35 was paid.

(2) For every gallon of gas purchased, $3.75 was paid.

(3) For every 2 gallons of gas purchased, $5.00 was paid.

(4) If zero gallons of gas were purchased, zero miles were driven.

45

40

35

30

25

20

15

10

5

0

2 4 6 8 10 12 14 16 18 20

50

Algebra I (Common Core) – Jan. ’16 [3] [OVER]

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3 For a recently released movie, the function y 119.67(0.61)x models computations.

the revenue earned, y, in millions of dollars each week, x, for several

weeks after its release.

Based on the equation, how much more money, in millions of dollars,

was earned in revenue for week 3 than for week 5?

(1) 37.27 (3) 17.06

(2) 27.16 (4) 10.11

4 Given the following expressions:

I. III.

II. IV.

Which expression(s) result in an irrational number?

(1) II, only (3) I, III, IV

(2) III, only (4) II, III, IV

5 Which inequality is represented by the graph below?

(1) y ≤ 2x 3 (3) y ≤ 3x 2

(2) y ≥ 2x 3 (4) y ≥ 3x 2

3 49 • ( ) 12

2

5 ( 5) • ( 5)

8

35

y

x

Algebra I (Common Core) – Jan. ’16 [4]

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6 Michael borrows money from his uncle, who is charging him simple computations.

interest using the formula I Prt. To figure out what the interest

rate, r, is, Michael rearranges the formula to find r. His new formula

is r equals

(1) (3)

(2) (4)

7 Which equation is equivalent to y 34 x(x 12)?

(1) y (x 17)(x 2) (3) y (x 6)2 2

(2) y (x 17)(x 2) (4) y (x 6)2 2

8 The equation A 1300(1.02)7 is being used to calculate the amount

of money in a savings account. What does 1.02 represent in this

equation?

(1) 0.02% decay (3) 2% decay

(2) 0.02% growth (4) 2% growth

9 The zeros of the function f(x) 2x2 4x 6 are

(1) 3 and 1 (3) 3 and 1

(2) 3 and 1 (4) 3 and 1

10 When (2x 3)2 is subtracted from 5x2, the result is

–

Algebra I (Common Core) – Jan. ’16 [5] [OVER]

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11 Joe has a rectangular patio that measures 10 feet by 12 feet. He wants computations.

to increase the area by 50% and plans to increase each dimension by

equal lengths, x. Which equation could be used to determine x?

(1) (10 x)(12 x) 120 (3) (15 x)(18 x) 180

(2) (10 x)(12 x) 180 (4) (15)(18) 120 x2

12 When factored completely, x3 13x2 30x is

13 The table below shows the cost of mailing a postcard in different years.

During which time interval did the cost increase at the greatest

average rate?

(1) 1898–1971 (3) 1985–2006

(2) 1971–1985 (4) 2006–2012

14 When solving the equation x28x7 0 by completing the square,

which equation is a step in the process?

(1) (x 4)2 9 (3) (x 8)2 9

(2) (x 4)2 23 (4) (x 8)2 23

15 A construction company uses the function f(p), where p is the number

of people working on a project, to model the amount of money it spends

to complete a project. A reasonable domain for this function would be

(1) positive integers

(2) positive real numbers

(3) both positive and negative integers

(4) both positive and negative real numbers

Year 1898 1971 1985 2006 2012

Cost (¢) 1 6 14 24 35

Algebra I (Common Core) – Jan. ’16 [6]

16 Which function is shown in the table below?

(1) f(x) 3x (3) f(x) x3

(2) f(x) x 3 (4) f(x) 3x

17 Given the functions h(x) x 3 and j(x) |x|, which value of x

makes h(x) j(x)?

(1) 2 (3) 3

(2) 2 (4) 6

18 Which recursively defined function represents the sequence

3, 7, 15, 31, …?

19 The range of the function defined as y 5x is

Use this space for

computations.

Algebra I (Common Core) – Jan. ’16 [7] [OVER]

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20 The graph of y f(x) is shown below. computations.

What is the graph of y f(x 1) 2?

Algebra I (Common Core) – Jan. ’16 [8]

21 Which pair of equations could not be used to solve the following

equations for x and y?

22 The graph representing a function is shown below.

Which function has a minimum that is less than the one shown in the

graph?

y

x

Use this space for

computations.

Algebra I (Common Core) – Jan. ’16 [9] [OVER]

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23 Grisham is considering the three situations below. computations.

I. For the first 28 days, a sunflower grows at a rate of 3.5 cm per day.

II. The value of a car depreciates at a rate of 15% per year after it

is purchased.

III. The amount of bacteria in a culture triples every two days during

an experiment.

Which of the statements describes a situation with an equal difference

over an equal interval?

(1) I, only (3) I and III

(2) II, only (4) II and III

24 After performing analyses on a set of data, Jackie examined the scatter

plot of the residual values for each analysis. Which scatter plot

indicates the best linear fit for the data?

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