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More Lessons for the Regents High School Exam

More Lessons for Algebra

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 August 2016.

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

The following are questions from the past paper

Regents High School Algebra I August 2016 Exam (pdf).

Scroll down the page for the step by step solutions.

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

1. The graph below shows the distance in miles, m, hiked from a camp in h hours.

2. The solution of an equation with two variables, x and y, is

(1) the set of all x values that make y = 0

(2) the set of all y values that make x = 0

(3) the set of all ordered pairs, (x,y), that make the equation true

(4) the set of all ordered pairs, (x,y), where the graph of the equation crosses the y-axis

3. Which statistic can not be determined from a box plot representing the scores on a math test in Mrs. DeRidder’s algebra class?

4. Which chart could represent the function f(x) = -2x + 6?

5. If f(n) = (n - 1)^{2} + 3n, which statement is true?

6. The table below shows 6 students' overall averages and their averages in their math class.

If a linear model is applied to these data, which statement best describes the correlation coefficient?

7. What is the solution to 2h + 8 > 3h - 6?

8. Which expression is equivalent to 36x^{2} - 100?

9. Patricia is trying to compare the average rainfall of New York to that of Arizona. A comparison between these two states for the months of July through September would be best measured in

10. Which function defines the sequence -6, -10, -14, -18, …, where f(6) = -26?

11. Which function has the greatest y-intercept?

12. What is the product of 2x + 3 and 4x^{2} - 5x + 6?

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

13. The height of a rocket, at selected times, is shown in the table below.

Based on these data, which statement is not a valid conclusion?

14. A parking garage charges a base rate of $3.50 for up to 2 hours, and an hourly rate for each additional hour. The sign below gives the prices for up to 5 hours of parking.

Which linear equation can be used to find x, the additional hourly parking rate?

15. Which function has a constant rate of change equal to -3?

16. Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. She brings 60 cookies to the party. Which equation can be used to find the number of boxes, x, Kendal bought?

17. The table below shows the temperature, T(m), of a cup of hot chocolate that is allowed to chill over several minutes, m.

Which expression best fits the data for T(m)?

18. As x increases beyond 25, which function will have the largest value?

19. What are the solutions to the equation 3x^{2} + 10x = 8?

20. An online company lets you download songs for $0.99 each after you have paid a $5 membership fee. Which domain would be most appropriate to calculate the cost to download songs?

21. The function f(x) = 3x^{2} + 12x + 11 can be written in vertex form as

22. A system of equations is given below.

x + 2y = 5

2x + y = 4

Which system of equations does not have the same solution?

23. Based on the graph below, which expression is a possible factorization of p(x)?

24. Milton has his money invested in a stock portfolio. The value, v(x), of his portfolio can be modeled with the function v(x) = 30,000(0.78)^{x},
where x is the number of years since he made his investment. Which
statement describes the rate of change of the value of his portfolio?

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

25. Graph the function \(y = - \sqrt {x + 3} \) on the set of axes below.

26. Richard is asked to transform the graph of b(x) below

The graph of b(x) is transformed using the equation h(x) = b(x - 2) - 3. Describe how the graph of b(x) changed to form the graph of h(x).

27. Consider the pattern of squares shown below:

Which type of model, linear or exponential, should be used to determine how many squares are in the nth pattern? Explain your answer.

28. When multiplying polynomials for a math assignment, Pat found the product to be -4x + 8x^{2} - 2x^{3} + 5. He then had to state the leading coefficient of this polynomial. Pat wrote
down -4. Do you agree with Pat’s answer? Explain your reasoning.

29. Is the sum of \(3\sqrt 2 \) and \(4\sqrt 2 \) rational or irrational? Explain your answer.

30. The graph below shows two functions, f(x) and g(x). State all the values of x for which f(x) = g(x)

31. Find the zeros of f(x) = (x - 3)^{2} - 49, algebraically.

32. Solve the equation below for x in terms of a.

4(ax + 3) - 3ax = 25 + 3a

33. The data table below shows the median diameter of grains of sand and the slope of the beach for 9 naturally occurring ocean beaches.

Write the linear regression equation for this set of data, rounding all values to the nearest thousandth.

Using this equation, predict the slope of a beach, to the nearest tenth of a degree, on a beach with grains of sand having a median diameter of 0.65 mm.

34. Shawn incorrectly graphed the inequality -x - 2y ≥ 8 as shown below.

Explain Shawn’s mistake.

Graph the inequality correctly on the set of axes below.

35. A drama club is selling tickets to the spring musical. The auditorium holds 200 people. Tickets cost $12 at the door and $8.50 if purchased in advance. The drama club has a goal of selling at least $1000 worth of tickets to Saturday’s show.

Write a system of inequalities that can be used to model this scenario.

If 50 tickets are sold in advance, what is the minimum number of tickets that must be sold at the door so that the club meets its goal? Justify your answer.

36. Janice is asked to solve 0 = 64x^{2} + 16x - 3. She begins the problem by writing the following
steps:

Line 1: 0 = 64x^{2} + 16x - 3

Line 2: 0 = B^{2} + 2B - 3

Line 3: 0 = (B + 3)(B - 1)

Use Janice's procedure to solve the equation for x.

Explain the method Janice used to solve the quadratic equation.

37. For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92. The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76.

Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w.

Kara said that the juice boxes might have cost 52 cents each and that the bottles of water might have cost 33 cents each. Use your system of equations to justify that Kara’s prices are not possible.

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.

More Lessons for the Regents High School Exam

More Lessons for Algebra

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 August 2016.

Regents High School Algebra I August 2016 Exam (pdf).

Scroll down the page for the step by step solutions.

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

1. The graph below shows the distance in miles, m, hiked from a camp in h hours.

2. The solution of an equation with two variables, x and y, is

(1) the set of all x values that make y = 0

(2) the set of all y values that make x = 0

(3) the set of all ordered pairs, (x,y), that make the equation true

(4) the set of all ordered pairs, (x,y), where the graph of the equation crosses the y-axis

3. Which statistic can not be determined from a box plot representing the scores on a math test in Mrs. DeRidder’s algebra class?

4. Which chart could represent the function f(x) = -2x + 6?

5. If f(n) = (n - 1)

6. The table below shows 6 students' overall averages and their averages in their math class.

If a linear model is applied to these data, which statement best describes the correlation coefficient?

7. What is the solution to 2h + 8 > 3h - 6?

8. Which expression is equivalent to 36x

9. Patricia is trying to compare the average rainfall of New York to that of Arizona. A comparison between these two states for the months of July through September would be best measured in

10. Which function defines the sequence -6, -10, -14, -18, …, where f(6) = -26?

11. Which function has the greatest y-intercept?

12. What is the product of 2x + 3 and 4x

13. The height of a rocket, at selected times, is shown in the table below.

Based on these data, which statement is not a valid conclusion?

14. A parking garage charges a base rate of $3.50 for up to 2 hours, and an hourly rate for each additional hour. The sign below gives the prices for up to 5 hours of parking.

Which linear equation can be used to find x, the additional hourly parking rate?

15. Which function has a constant rate of change equal to -3?

16. Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. She brings 60 cookies to the party. Which equation can be used to find the number of boxes, x, Kendal bought?

17. The table below shows the temperature, T(m), of a cup of hot chocolate that is allowed to chill over several minutes, m.

Which expression best fits the data for T(m)?

18. As x increases beyond 25, which function will have the largest value?

19. What are the solutions to the equation 3x

20. An online company lets you download songs for $0.99 each after you have paid a $5 membership fee. Which domain would be most appropriate to calculate the cost to download songs?

21. The function f(x) = 3x

22. A system of equations is given below.

x + 2y = 5

2x + y = 4

Which system of equations does not have the same solution?

23. Based on the graph below, which expression is a possible factorization of p(x)?

24. Milton has his money invested in a stock portfolio. The value, v(x), of his portfolio can be modeled with the function v(x) = 30,000(0.78)

25. Graph the function \(y = - \sqrt {x + 3} \) on the set of axes below.

26. Richard is asked to transform the graph of b(x) below

The graph of b(x) is transformed using the equation h(x) = b(x - 2) - 3. Describe how the graph of b(x) changed to form the graph of h(x).

27. Consider the pattern of squares shown below:

Which type of model, linear or exponential, should be used to determine how many squares are in the nth pattern? Explain your answer.

28. When multiplying polynomials for a math assignment, Pat found the product to be -4x + 8x

29. Is the sum of \(3\sqrt 2 \) and \(4\sqrt 2 \) rational or irrational? Explain your answer.

30. The graph below shows two functions, f(x) and g(x). State all the values of x for which f(x) = g(x)

31. Find the zeros of f(x) = (x - 3)

32. Solve the equation below for x in terms of a.

4(ax + 3) - 3ax = 25 + 3a

33. The data table below shows the median diameter of grains of sand and the slope of the beach for 9 naturally occurring ocean beaches.

Write the linear regression equation for this set of data, rounding all values to the nearest thousandth.

Using this equation, predict the slope of a beach, to the nearest tenth of a degree, on a beach with grains of sand having a median diameter of 0.65 mm.

34. Shawn incorrectly graphed the inequality -x - 2y ≥ 8 as shown below.

Explain Shawn’s mistake.

Graph the inequality correctly on the set of axes below.

35. A drama club is selling tickets to the spring musical. The auditorium holds 200 people. Tickets cost $12 at the door and $8.50 if purchased in advance. The drama club has a goal of selling at least $1000 worth of tickets to Saturday’s show.

Write a system of inequalities that can be used to model this scenario.

If 50 tickets are sold in advance, what is the minimum number of tickets that must be sold at the door so that the club meets its goal? Justify your answer.

36. Janice is asked to solve 0 = 64x

Line 1: 0 = 64x

Line 2: 0 = B

Line 3: 0 = (B + 3)(B - 1)

Use Janice's procedure to solve the equation for x.

Explain the method Janice used to solve the quadratic equation.

37. For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92. The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76.

Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w.

Kara said that the juice boxes might have cost 52 cents each and that the bottles of water might have cost 33 cents each. Use your system of equations to justify that Kara’s prices are not possible.

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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