High School Math based on the topics required for the Regents
Exam conducted by NYSED. The following are the worked solutions
for the Algebra 1 (Common Core) Regents High School Examination
More Lessons for the Regents High School Exam
More Lessons for Algebra
Algebra I Common Core Regents New York State Exam - June 2015
The following are questions from the past paper Regents High School Algebra 1 June 2015 Exam (pdf)
Scroll down the page for the step by step solutions.
Algebra 1 - June 2015 Regents - Q #1 - 12
1. The cost of airing a commercial on television is modeled by the computations.
function C(n) = 110n + 900, where n is the number of times the
commercial is aired. Based on this model, which statement is true?
(1) The commercial costs $0 to produce and $110 per airing up to
(2) The commercial costs $110 to produce and $900 each time it is
(3) The commercial costs $900 to produce and $110 each time it is
(4) The commercial costs $1010 to produce and can air an unlimited
number of times.
2. The graph below represents a jogger’s speed during her 20-minute
jog around her neighborhood.
Which statement best describes what the jogger was doing during
the 9–12 minute interval of her jog?
3. If the area of a rectangle is expressed as x4
, then the product computations.
of the length and the width of the rectangle could be expressed as
4. Which table represents a function?
5. Which inequality is represented in the graph below?
6. Mo’s farm stand sold a total of 165 pounds of apples and peaches. computations.
She sold apples for $1.75 per pound and peaches for $2.50 per
pound. If she made $337.50, how many pounds of peaches did she
7. Morgan can start wrestling at age 5 in Division 1. He remains in that
division until his next odd birthday when he is required to move up
to the next division level. Which graph correctly represents this
8. Which statement is not always true?
(1) The sum of two rational numbers is rational.
(2) The product of two irrational numbers is rational.
(3) The sum of a rational number and an irrational number is irrational.
(4) The product of a nonzero rational number and an irrational
number is irrational.
9. The graph of the function is shown below.
The domain of the function is
10. What are the zeros of the function f(x) = x2
- 13x - 30?
11. Joey enlarged a 3-inch by 5-inch photograph on a copy machine.
He enlarged it four times. The table below shows the area of the
photograph after each enlargement.
What is the average rate of change of the area from the original
photograph to the fourth enlargement, to the nearest tenth?
12. Which equation(s) represent the graph below?
Algebra 1 - June 2015 Regents - Q #13 - 24
13. A laboratory technician studied the population growth of a colony of computations.
bacteria. He recorded the number of bacteria every other day, as
shown in the partial table below.
Which function would accurately model the technician’s data?
14. Which quadratic function has the largest maximum?
15. If f(x) = 3x
and g(x) = 2x + 5, at which value of x is f(x) < g(x)?
16. Beverly did a study this past spring using data she collected from a
cafeteria. She recorded data weekly for ice cream sales and soda sales.
Beverly found the line of best fit and the correlation coefficient,
as shown in the diagram below.
Given this information, which statement(s) can correctly be concluded?
I. Eating more ice cream causes a person to become thirsty.
II. Drinking more soda causes a person to become hungry.
III. There is a strong correlation between ice cream sales and soda sales.
17. The function V(t) = 1350(1.017)t
represents the value V(t), in dollars,
of a comic book t years after its purchase. The yearly rate of
appreciation of the comic book is
18. When directed to solve a quadratic equation by completing the computations.
square, Sam arrived at the given equation. Which equation
could have been the original equation given to Sam?
19. The distance a free falling object has traveled can be modeled by the
equation d = 1/2 at2
, where a is acceleration due to gravity and t is
the amount of time the object has fallen. What is t in terms of a and d?
20. The table below shows the annual salaries for the 24 members of a
professional sports team in terms of millions of dollars.
The team signs an additional player to a contract worth 10 million
dollars per year. Which statement about the median and mean is
21. A student is asked to solve the equation 4(3x - 1)2
- 17 = 83.
The student’s solution to the problem starts as
22. A pattern of blocks is shown below.
If the pattern of blocks continues, which formula(s) could be used
to determine the number of blocks in the nth term?
23. What are the solutions to the equation x2
- 8x = 24?
24. Natasha is planning a school celebration and wants to have live music
and food for everyone who attends. She has found a band that will
charge her $750 and a caterer who will provide snacks and drinks for
$2.25 per person. If her goal is to keep the average cost per person
between $2.75 and $3.25, how many people, p, must attend?
25 Graph the function y = |x - 3| on the set of axes below.
Explain how the graph of y = |x - 3| has changed from the related graph y = |x|.
26 Alex is selling tickets to a school play. An adult ticket costs $6.50 and a student ticket costs $4.00.
Alex sells x adult tickets and 12 student tickets. Write a function, f(x), to represent how much
money Alex collected from selling tickets.
27 John and Sarah are each saving money for a car. The total amount of money John will save is given
by the function f(x) = 60 + 5x. The total amount of money Sarah will save is given by the
function g(x) = x2
+ 46. After how many weeks, x, will they have the same amount of money
saved? Explain how you arrived at your answer.
28 If the difference (3x2
- 2x + 5) - (x2
+ 3x - 2) is multiplied by 1/2 x2
, what is the result, written in standard form?
29 Dylan invested $600 in a savings account at a 1.6% annual interest rate. He made no deposits or
withdrawals on the account for 2 years. The interest was compounded annually. Find, to the
nearest cent, the balance in the account after 2 years.
30 Determine the smallest integer that makes -3x + 7 - 5x < 15 true.
31 The residual plots from two different sets of bivariate data are graphed below.
Explain, using evidence from graph A and graph B, which graph indicates that the model for the
data is a good fit.
32 A landscaper is creating a rectangular flower bed such that the width is half of the length.
The area of the flower bed is 34 square feet. Write and solve an equation to determine the width
of the flower bed, to the nearest tenth of a foot.
33 Albert says that the two systems of equations shown below have the same solutions.
Determine and state whether you agree with Albert. Justify your answer.
34 The equation to determine the weekly earnings of an employee at The Hamburger Shack is given
by w(x), where x is the number of hours worked.
Determine the difference in salary, in dollars, for an employee who works 52 hours versus one
who works 38 hours.
Determine the number of hours an employee must work in order to earn $445. Explain how you
arrived at this answer.
35 An on-line electronics store must sell at least $2500 worth of printers and computers per day.
Each printer costs $50 and each computer costs $500. The store can ship a maximum of 15 items
On the set of axes below, graph a system of inequalities that models these constraints.
Determine a combination of printers and computers that would allow the electronics store to
meet all of the constraints. Explain how you obtained your answer
36 An application developer released a new app to be downloaded. The table below gives the number
of downloads for the first four weeks after the launch of the app.
Write an exponential equation that models these data.
Use this model to predict how many downloads the developer would expect in the 26th week if
this trend continues. Round your answer to the nearest download.
Would it be reasonable to use this model to predict the number of downloads past one year?
Explain your reasoning.
37 A football player attempts to kick a football over a goal post. The path of the football can be
modeled by the function h(x) = - 1/225 x2
+ 2/3 x, where x is the horizontal distance from the kick,
and h(x) is the height of the football above the ground, when both are measured in feet.
On the set of axes below, graph the function y = h(x) over the interval 0 ≤ x ≤ 150.
Determine the vertex of y = h(x). Interpret the meaning of this vertex in the context of the problem.
The goal post is 10 feet high and 45 yards away from the kick. Will the ball be high enough to pass over the goal post? Justify your answer.
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