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
January 2016.

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More Lessons for the Regents High School Exam

More Lessons for Algebra

### Algebra I Common Core Regents New York State Exam - January 2016

The following are questions from the past paper Regents High School Algebra 1 January 2016 Exam (pdf).

Scroll down the page for the step by step solutions.

Algebra 1 - January 2016 Regents - Questions and solutions 1 - 12

1. In the function computations. f(x) = (x - 2)^{2} + 4, the minimum value occurs
when x is

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.

3. For a recently released movie, the function y = 119.67(0.61)^{x} models
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?

4. Given the following expressions:

Which expression(s) result in an irrational number?

5. Which inequality is represented by the graph below?

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

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

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?

9. The zeros of the function f(x) = 2x^{2} - 4x - 6 are

10 When (2x - 3)^{2} is subtracted from 5x^{2}, the result is

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?

12. When factored completely, x^{3} - 13x^{2} - 30x is

Algebra 1 - January 2016 Regents - Questions and solutions 13 - 24

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?

14. When solving the equation x^{2} - 8x - 7 = 0 by completing the square,
which equation is a step in the process?

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

16. Which function is shown in the table below?

17. Given the functions h(x) = \(\frac{1}{2}\)x + 3 and j(x) = |x|, which value of x makes h(x) = j(x)?

18. Which recursively defined function represents the sequence 3, 7, 15, 31, …?

19. The range of the function defined as y = 5^{x} is

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

What is the graph of y = f(x + 1) - 2? 21. Which pair of equations could not be used to solve the following equations for x and y?

4x + 2y = 22

-2x + 2y = -8

22. The graph representing a function is shown below.

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

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?

Algebra 1 - January 2016 Regents - Questions and solutions 25 - 37

25. The function, t(x), is shown in the table below.

Determine whether t(x) is linear or exponential. Explain your answer.

26. Marcel claims that the graph below represents a function.

State whether Marcel is correct. Justify your answer

27. Solve the equation for y

(y - 3)^{2} = 4y - 12

28. The graph below shows the variation in the average temperature of Earth’s surface from 1950–2000, according to one source.

During which years did the temperature variation change the most per unit time? Explain how you determined your answer.

29. The cost of belonging to a gym can be modeled by C(m) = 50m + 79.50, where C(m) is the total cost for m months of membership.

State the meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership.

30. A statistics class surveyed some students during one lunch period to obtain opinions about television programming preferences. The results of the survey are summarized in the table below. Based on the sample, predict how many of the school’s 351 males would prefer comedy. Justify your answer.

31. Given that a > b, solve for x in terms of a and b:

b(x - 3) ≥ ax + 7b

32. Jacob and Jessica are studying the spread of dandelions. Jacob discovers that the growth over t weeks can be defined by the function f(t) = (8) • 2^{t}. Jessica finds that the growth function over
t weeks is g(t) = 2^{t + 3}.

Calculate the number of dandelions that Jacob and Jessica will each have after 5 weeks. Based on the growth from both functions, explain the relationship between f(t) and g(t).

33. Let h(t) = 16t^{2} + 64t + 80 represent the height of an object above the ground after t seconds.
Determine the number of seconds it takes to achieve its maximum height. Justify your answer.

State the time interval, in seconds, during which the height of the object decreases. Explain your reasoning.

34. Fred’s teacher gave the class the quadratic function f(x) = 4x^{2} + 16x + 9.

a) State two different methods Fred could use to solve the equation f(x) = 0.

b) Using one of the methods stated in part a, solve f(x) = 0 for x, to the nearest tenth.

35. Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue from coffee sales. Data from nine days this past fall are shown in the table below.

State the linear regression function, f(t), that estimates the day’s coffee sales with a high temperature of t. Round all values to the nearest integer.

State the correlation coefficient, r, of the data to the nearest hundredth. Does r indicate a strong linear relationship between the variables? Explain your reasoning.

36. A contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular garden. The length of one side of the garden is represented by x, and the area of the garden is 108 square meters.

Determine, algebraically, the dimensions of the garden in meters.

37. The Reel Good Cinema is conducting a mathematical study. In its theater, there are 200 seats. Adult tickets cost $12.50 and child tickets cost $6.25. The cinema’s goal is to sell at least $1500 worth of tickets for the theater.

Write a system of linear inequalities that can be used to find the possible combinations of adult tickets, x, and child tickets, y, that would satisfy the cinema’s goal.

Graph the solution to this system of inequalities on the set of axes on the next page. Label the solution with an S.

Marta claims that selling 30 adult tickets and 80 child tickets will result in meeting the cinema’s goal. Explain whether she is correct or incorrect, based on the graph drawn.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics:

More Lessons for the Regents High School Exam

More Lessons for Algebra

Scroll down the page for the step by step solutions.

Algebra 1 - January 2016 Regents - Questions and solutions 1 - 12

1. In the function computations. f(x) = (x - 2)

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.

3. For a recently released movie, the function y = 119.67(0.61)

Based on the equation, how much more money, in millions of dollars, was earned in revenue for week 3 than for week 5?

4. Given the following expressions:

Which expression(s) result in an irrational number?

5. Which inequality is represented by the graph below?

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

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

8. The equation A = 1300(1.02)

9. The zeros of the function f(x) = 2x

10 When (2x - 3)

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?

12. When factored completely, x

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?

14. When solving the equation x

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

16. Which function is shown in the table below?

17. Given the functions h(x) = \(\frac{1}{2}\)x + 3 and j(x) = |x|, which value of x makes h(x) = j(x)?

18. Which recursively defined function represents the sequence 3, 7, 15, 31, …?

19. The range of the function defined as y = 5

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

What is the graph of y = f(x + 1) - 2? 21. Which pair of equations could not be used to solve the following equations for x and y?

4x + 2y = 22

-2x + 2y = -8

22. The graph representing a function is shown below.

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

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?

Algebra 1 - January 2016 Regents - Questions and solutions 25 - 37

25. The function, t(x), is shown in the table below.

Determine whether t(x) is linear or exponential. Explain your answer.

26. Marcel claims that the graph below represents a function.

State whether Marcel is correct. Justify your answer

27. Solve the equation for y

(y - 3)

28. The graph below shows the variation in the average temperature of Earth’s surface from 1950–2000, according to one source.

During which years did the temperature variation change the most per unit time? Explain how you determined your answer.

29. The cost of belonging to a gym can be modeled by C(m) = 50m + 79.50, where C(m) is the total cost for m months of membership.

State the meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership.

30. A statistics class surveyed some students during one lunch period to obtain opinions about television programming preferences. The results of the survey are summarized in the table below. Based on the sample, predict how many of the school’s 351 males would prefer comedy. Justify your answer.

31. Given that a > b, solve for x in terms of a and b:

b(x - 3) ≥ ax + 7b

32. Jacob and Jessica are studying the spread of dandelions. Jacob discovers that the growth over t weeks can be defined by the function f(t) = (8) • 2

Calculate the number of dandelions that Jacob and Jessica will each have after 5 weeks. Based on the growth from both functions, explain the relationship between f(t) and g(t).

33. Let h(t) = 16t

State the time interval, in seconds, during which the height of the object decreases. Explain your reasoning.

34. Fred’s teacher gave the class the quadratic function f(x) = 4x

a) State two different methods Fred could use to solve the equation f(x) = 0.

b) Using one of the methods stated in part a, solve f(x) = 0 for x, to the nearest tenth.

35. Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue from coffee sales. Data from nine days this past fall are shown in the table below.

State the linear regression function, f(t), that estimates the day’s coffee sales with a high temperature of t. Round all values to the nearest integer.

State the correlation coefficient, r, of the data to the nearest hundredth. Does r indicate a strong linear relationship between the variables? Explain your reasoning.

36. A contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular garden. The length of one side of the garden is represented by x, and the area of the garden is 108 square meters.

Determine, algebraically, the dimensions of the garden in meters.

37. The Reel Good Cinema is conducting a mathematical study. In its theater, there are 200 seats. Adult tickets cost $12.50 and child tickets cost $6.25. The cinema’s goal is to sell at least $1500 worth of tickets for the theater.

Write a system of linear inequalities that can be used to find the possible combinations of adult tickets, x, and child tickets, y, that would satisfy the cinema’s goal.

Graph the solution to this system of inequalities on the set of axes on the next page. Label the solution with an S.

Marta claims that selling 30 adult tickets and 80 child tickets will result in meeting the cinema’s goal. Explain whether she is correct or incorrect, based on the graph drawn.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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