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 June 2019.

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The following are questions from the past paper Regents High School Algebra I June 2019 Exam (pdf). Scroll down the page for the step by step solutions.

Algebra 1 - June 2019 Regents - Questions and solutions 1 - 12

- The expression w
^{4}- 36 is equivalent to - If f(x) = 4x + 5, what is the value of f(-3)?
- Which relation is not a function?
- Given: f(x) = (x - 2)
^{2}+ 4

g(x) = (x - 5)^{2}+ 4

When compared to the graph of f(x), the graph of g(x) is - Students were asked to write 6x
^{5}+ 8x - 3x^{3}+ 7x^{7}in standard form. - The function f is shown in the table below
- Which expression results in a rational number?
- A polynomial function is graphed below
- When solving p
^{2}+ 5 = 8p - 7, Kate wrote p^{2}+ 12 = 8p. The property she used is - David wanted to go on an amusement park ride. A sign posted at the entrance read “You must be greater than 42 inches tall and no more than 57 inches tall for this ride.” Which inequality would model the height, x, required for this amusement park ride?
- Which situation can be modeled by a linear function?
- Jenna took a survey of her senior class to see whether they preferred pizza or burgers. The results are summarized in the table below.

Algebra 1 - June 2019 Regents - Questions and solutions 13 - 24

- When 3a + 7b > 2a - 8b is solved for a, the result is
- Three functions are shown below.
- Nicci’s sister is 7 years less than twice Nicci’s age, a. The sum of Nicci’s age and her sister’s age is 41. Which equation represents this relationship?
- The population of a small town over four years is recorded in the chart below, where 2013 is represented by x = 0. [Population is rounded to the nearest person]
- When written in factored form, 4w
^{2}- 11w - 3 is equivalent to - Which ordered pair does not represent a point on the graph of y = 3x
^{2}- x + 7? - Given the following three sequences:

Which ones are arithmetic sequences? - A grocery store sells packages of beef. The function C(w) represents the cost, in dollars, of a package of beef weighing w pounds. The most appropriate domain for this function would be
- The roots of x
^{2}- 5x - 4 = 0 are - The following table shows the heights, in inches, of the players on the opening-night roster of the 2015-2016 New York Knicks.
- A population of bacteria can be modeled by the function f(t) = 1000(0.98)
^{t}, where t represents the time since the population started decaying, and f(t) represents the population of the remaining bacteria at time t. What is the rate of decay for this population? - Bamboo plants can grow 91 centimeters per day. What is the approximate growth of the plant, in inches per hour?

Algebra 1 - June 2019 Regents - Questions and solutions 25 - 37

- Solve algebraically for x:
- If C = G - 3F, find the trinomial that represents C when F = 2x
^{2}+ 6x - 5 and G = 3x^{2}+ 4. - Graph the following piecewise function on the set of axes below.
- Solve 5x
^{2}= 180 algebraically. - A blizzard occurred on the East Coast during January, 2016. Snowfall totals from the storm were recorded for Washington, D.C. and are shown in the table below.

Which interval, 1 a.m. to 12 noon or 6 a.m. to 3 p.m., has the greatest rate of snowfall, in inches per hour? Justify your answer. - The formula for the volume of a cone is V = 1/3πr
^{2}h. Solve the equation for h in terms of V, r, and π. - Given the recursive formula:

a_{1}= 3

a_{n}= 2(a_{n - 1}+ 1)

State the values of a_{2}, a_{3}, and a_{4}for the given recursive formula. - Determine and state the vertex of f(x) = x
^{2}- 2x - 8 using the method of completing the square. - A school plans to have a fundraiser before basketball games selling shirts with their school logo. The school contacted two companies to find out how much it would cost to have the shirts made. Company A charges a $50 set-up fee and $5 per shirt. Company B charges a $25 set-up fee and $6 per shirt.

Write an equation for Company A that could be used to determine the total cost, A, when x shirts are ordered. Write a second equation for Company B that could be used to determine the total cost, B, when x shirts are ordered.

Determine algebraically and state the minimum number of shirts that must be ordered for it to be cheaper to use Company A. - Graph y = f(x) and y = g(x) on the set of axes below.

f(x) = 2x^{2}- 8x + 3

g(x) = -2x + 3

Determine and state all values of x for which f(x) = g(x). - The table below shows the number of hours ten students spent studying for a test and their scores.

Write the linear regression equation for this data set. Round all values to the nearest hundredth.

State the correlation coefficient of this line, to the nearest hundredth.

Explain what the correlation coefficient suggests in the context of the problem. - A system of inequalities is graphed on the set of axes below.

State the system of inequalities represented by the graph.

State what region A represents.

State what the entire gray region represents - When visiting friends in a state that has no sales tax, two families went to a fast-food restaurant for lunch. The Browns bought 4 cheeseburgers and 3 medium fries for $16.53. The Greens bought 5 cheeseburgers and 4 medium fries for $21.11.

Using c for the cost of a cheeseburger and f for the cost of medium fries, write a system of equations that models this situation.

The Greens said that since their bill was $21.11, each cheeseburger must cost $2.49 and each order of medium fries must cost $2.87 each. Are they correct? Justify your answer.

Using your equations, algebraically determine both the cost of one cheeseburger and the cost of one order of medium fries.

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