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 2023.

**Related Pages**

Regents Exam Past Papers

Algebra I Regents New York State Exam Questions August 2023 (pdf)

Solutions for Questions 1 - 24

Solutions for Questions 25 - 37

- A café owner tracks the number of customers during business hours. The graph below models the data.
- The expression (3x
^{2}+ 4x - 8) + 2(11 - 5x) is equivalent to - Which point is a solution to y = x
^{3}- 2x? - What is the value of x in the equation
- The graph of y 5 f (x) is shown below. Which graph represents y = f(x - 2) + 1?
- The length of a rectangular flat-screen television is six inches less than twice its width, x. If the area of the television screen is 1100 square inches, which equation can be used to determine the width, in inches?
- A box plot is shown below. Which number represents the third quartile?
- What is the product of (2x + 7) and (x - 3)?
- What is the degree of the polynomial 2x + x
^{3}+ 5x^{2}? - What is the solution to -3(x - 6) > 2x - 2?
- Three expressions are shown below
- Jim uses the equation A = P(1 + 0.05)
^{t}to find the amount of money in an account, A, of an investment, P, after t years. For this equation, which phrase describes the yearly rate of change? - What are the zeros of m(x) = x(x
^{2}- 16)? - For which function is the value of the y-intercept the smallest?
- The function f is graphed on the set of axes below.
- The range of f (x) = x
^{2}+ 2x - 5 is the set of all real numbers - Tables of values for four functions are shown below.
- If f(x) = x
^{2}+ 3x, then which statement is true? - Jack started a new fitness program. The first day he did 10 pushups. The program required him to increase the number of push-ups
each day by doing 9 less than twice the number from the previous
day. Which recursive formula correctly models Jack’s new program,
where n is the number of days and a
_{n}is the number of push-ups on the nth day? - Which equation is equivalent to x
^{2}- 6x + 4 = 0? - What is the equation of the line that passes through the point (6,-3) and has a slope of -4/3?
- The function G(m) represents the amount of gasoline consumed by a car traveling m miles. An appropriate domain for this function would be
- The table below shows the number of reported polio cases in Nigeria from 2006 to 2015.
- Joe compared gas prices in England and New York State one day. In England, gas sold for 1.35 euros per liter, and one dollar equaled 0.622 euros. A correct way to figure out this cost, in dollars per gallon, is
- Classify the expression
- Julia surveyed 150 of her classmates at City Middle School to determine their favorite animals. Of the 150 students, 46% were male. Forty-two students said their favorite animal was a horse, and 1/3 of those students were female. Of the 60 students who said dolphins were their favorite animal, 30% were male. Using this information, complete the two-way frequency table below
- Bryan said that the piecewise function graphed below has a domain of all real numbers. State two reasons why Bryan is incorrect.
- The formula
- Solve x
^{2}- 9x = 36 algebraically for all values of x. - Determine the common difference of the arithmetic sequence in which a
_{1}= 5 and a_{5}= 17. Determine the 21^{st}term of this sequence. - Factor 18x
^{2}- 2 completely. - Solve x
^{2}+ 3x - 9 = 0 algebraically for all values of x. Round your answer to the nearest hundredth. - The senior class at Hills High School is purchasing sports drinks and bottled water to sell at the school field day. At the local discount store, a case of sports drinks costs $15.79, and a case of bottled water costs $5.69. The senior class has $125 to spend on the drinks. If x represents the number of cases of sports drinks and y represents the number of cases of bottled water purchased, write an inequality that models this situation. Nine cases of bottled water are purchased for this year’s field day. Use your inequality to determine algebraically the maximum number of full cases of sports drinks that can be purchased. Explain your answer.
- The path of a rocket is modeled by the function h(t) = 24.9
^{t}+ 49t, where h is the height, in meters, above the ground and t is the time, in seconds, after the rocket is launched.

Sketch the graph on the set of axes below.

State the vertex of this function.

Explain what the vertex means in the context of this situation. - A software company kept a record of their annual budget for advertising and their profit for each
of the last eight years. These data are shown in the table below. Write the linear regression equation for this set of data.

State, to the nearest hundredth, the correlation coefficient of these linear data.

State what this correlation coefficient indicates about the linear fit of the data. - Graph the following system of inequalities on the set of axes below:
- Lydia wants to take art classes. She compares the cost at two art centers. Center A charges
$25 per hour and a registration fee of $25. Center B charges $15 per hour and a registration
fee of $75. Lydia plans to take x hours of classes.

Write an equation that models this situation, where A represents the total cost of Center A.

Write an equation that models this situation, where B represents the total cost of Center B.

If Lydia wants to take 10 hours of classes, use your equations to determine which center will cost less.

Graph your equations for Center A and Center B on the set of axes below.

State the number of hours of classes when the centers will cost the same.

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