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 2015.

### Algebra I Common Core Regents New York State Exam - January 2015

The following are questions from the past paper Regents High School Algebra 1 January 2015 Exam (pdf).

Scroll down the page for the step by step solutions.

Algebra 1 - January 2015 Regents - Q #1 - 12

1 The owner of a small computer repair business has one employee, computations. 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

2 Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds. He converts his speed into miles per hour, as shown below. Which ratio is incorrectly written to convert his speed?

3 Which equation has the same solutions as 2x^{2} + x - 3 = 0?

4 Krystal was given $3000 when she turned 2 years old. Her parents computations. 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?

5 Which table of values represents a linear relationship?

6 Which domain would be the most appropriate set to use for a function that predicts the number of household online-devices in terms of the number of people in the household?

7 The given inequality is equivalent to

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?

9 Which function has the same y-intercept as the graph below?

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

11 The graph of a linear equation contains the points (3,11) and (2,1). Which point also lies on the graph?

12 How does the graph of f(x) = 3(x - 2)^{2} + 1 compare to the graph
of g(x) = x^{2}?

Algebra 1 - January 2015 Regents - Q #13 - 24

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?

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?

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.
What is the y-intercept of this equation and what does it represent?

16 The equation for the volume of a cylinder is V = πr^{2}h. The positive computations.
value of r, in terms of h and V, is

17 Which equation has the same solutions as x^{2} + 6x - 7 = 0?

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?

19 Miriam and Jessica are growing bacteria in a laboratory. Miriam uses the growth function f(t) = n^{2t} while Jessica uses the function
g(t) = n^{4t}, where n represents the initial number of bacteria and
t is the time, in hours. If Miriam starts with 16 bacteria, how many
bacteria should Jessica start with to achieve the same growth over
time?

20 If a sequence is defined recursively by f(0) = 2 and f(n + 1) = -2f(n) + 3 for n ≥ 0, then f(2) is equal to

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?

22 When factored completely, the expression p^{4} - 81 is equivalent to

23 In 2013, the United States Postal Service charged $0.46 to mail a computations. 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?

24 A polynomial function contains the factors x, x - 2, and x + 5. Which graph(s) below could represent the graph of this function?

Algebra 1 - January 2015 Regents - Q #25 - 37

25. Ms. Fox asked her class “Is the sum of 4.2 and rational or irrational?” Patrick answered that the sum would be irrational. State whether Patrick is correct or incorrect. Justify your reasoning.

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. If there are 180 students in ninth grade, what percentage of the ninth grade students belong to more than one club?

27. A function is shown in the table below. 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.

28. Subtract 5x^{2} + 2x - 11 from 3x^{2} + 8x - 7. Express the result as a trinomial.

29. Solve the equation 4x^{2} - 12x - 7 algebraically for x.

30. Graph the following function on the set of axes below.

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

32. Write an exponential equation for the graph shown below. Explain how you determined the equation.

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.

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.

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.

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.

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.

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.

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.

Scroll down the page for the step by step solutions.

Algebra 1 - January 2015 Regents - Q #1 - 12

1 The owner of a small computer repair business has one employee, computations. 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

2 Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds. He converts his speed into miles per hour, as shown below. Which ratio is incorrectly written to convert his speed?

3 Which equation has the same solutions as 2x

4 Krystal was given $3000 when she turned 2 years old. Her parents computations. 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?

5 Which table of values represents a linear relationship?

6 Which domain would be the most appropriate set to use for a function that predicts the number of household online-devices in terms of the number of people in the household?

7 The given inequality is equivalent to

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)

9 Which function has the same y-intercept as the graph below?

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

11 The graph of a linear equation contains the points (3,11) and (2,1). Which point also lies on the graph?

12 How does the graph of f(x) = 3(x - 2)

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?

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?

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)

16 The equation for the volume of a cylinder is V = πr

17 Which equation has the same solutions as x

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?

19 Miriam and Jessica are growing bacteria in a laboratory. Miriam uses the growth function f(t) = n

20 If a sequence is defined recursively by f(0) = 2 and f(n + 1) = -2f(n) + 3 for n ≥ 0, then f(2) is equal to

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

22 When factored completely, the expression p

23 In 2013, the United States Postal Service charged $0.46 to mail a computations. 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?

24 A polynomial function contains the factors x, x - 2, and x + 5. Which graph(s) below could represent the graph of this function?

25. Ms. Fox asked her class “Is the sum of 4.2 and rational or irrational?” Patrick answered that the sum would be irrational. State whether Patrick is correct or incorrect. Justify your reasoning.

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. If there are 180 students in ninth grade, what percentage of the ninth grade students belong to more than one club?

27. A function is shown in the table below. 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.

28. Subtract 5x

29. Solve the equation 4x

30. Graph the following function on the set of axes below.

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

32. Write an exponential equation for the graph shown below. Explain how you determined the equation.

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.

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.

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.

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.

36. a) Given the function f(x) = -x

b) Rewrite f(x) in vertex form by completing the square.

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.

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