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 2023.

**Related Pages**

Regents Exam Past Papers

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

Solutions for Questions 1 - 24

- The expression 9m
^{2}- 100 is equivalent to - Which expression represents an irrational number?
- Which linear equation represents a line that passes through the point (-3,-8)?
- The expression (5x
^{2}- x + 4) - 3(x^{2}- x - 2) is equivalent to - The 24th term of the sequence 25, 211, 217, 223, … is
- When completing the square for x
^{2}- 18x + 77 = 0, which equation is a correct step in this process? - Which function will have the greatest value when x > 1?
- Mike uses the equation b = 1300(2.65)
^{x}to determine the growth of bacteria in a laboratory setting. The exponent represents - A company ships an average of 30,000 items each week. The approximate number of items shipped each minute is calculated using the conversion
- A function is graphed below.
- If g(x) = -x
^{2}- x + 5, then g(24) is equal to - A movie theater’s popcorn box is a rectangular prism with a base that measures 6 inches by 4 inches and has a height of 8 inches. To create a larger box, both the length and the width will be increased by x inches. The height will remain the same. Which function represents the volume, V(x), of the larger box?
- The expression 300(4)
^{x + 3}is equivalent to - Ashley only has 7 quarters and some dimes in her purse. She needs at least $3.00 to pay for lunch. Which inequality could be used to determine the number of dimes, d, she needs in her purse to be able to pay for lunch?
- The formula for the area of a trapezoid is A = 1/2(b1 + b2)h. The height, h, of the trapezoid may be expressed as
- The function f(x) = |x| is multiplied by k to create the new function g(x) = k|x|. Which statement is true about the graphs of f(x) and g(x) if k = 1/2?
- Some adults were surveyed to find out if they would prefer to buy a sports utility vehicle (SUV) or a sports car. The results of the survey are summarized in the table below
- The solution to 2x
^{2}= 72 is - Three quadratic functions are given below
- The domain of the function f(x) = x
^{2}1 x 2 12 is - A father makes a deal with his son regarding his weekly allowance. The first year, he agrees to pay his son a weekly allowance of $10. Every subsequent year, the allowance is recalculated by doubling the previous year’s weekly allowance and then subtracting 8. Which recursive formula could be used to calculate the son’s weekly allowance in future years?
- What is the solution to the inequality below?
- Which statement is correct about the polynomial 3x
^{2}+ 5x - 2? - A store manager is trying to determine if they should continue to sell a particular brand of nails. To model their profit, they use the function p(n), where n is the number of boxes of these nails sold in a day. A reasonable domain for this function would be
- Solve the equation algebraically for x:
- The function f(x) is graphed on the set of axes below.
- Breanna creates the pattern of blocks below in her art class.
- The data set 20, 36, 52, 56, 24, 16, 40, 4, 28 represents the number of books purchased by nine book club members in a year.
- Given: A = x + 5, B = x
^{2}- 18. Express A^{2}+ B in standard form. - The two relations shown below are not functions.
- Factor 2x
^{2}+ 16x - 18 completely - Solve 3d
^{2}- 8d + 3 = 0 algebraically for all values of d, rounding to the nearest tenth. - Graph f(x) = |x| + 1 and g(x) = -x
^{2}+ 6x + 1 on the set of axes below. - Jean recorded temperatures over a 24-hour period one day in August in Syracuse, NY. Her results are shown in the table below.
- Solve the following system of inequalities graphically on the set of axes below.
- Suzanna collected information about a group of ponies and horses. She made a table showing the height, measured in hands (hh), and the weight, measured in pounds (lbs), of each pony and horse.
- Dana went shopping for plants to put in her garden. She bought three roses and two daisies
for $31.88. Later that day, she went back and bought two roses and one daisy for $18.92.
If r represents the cost of one rose and d represents the cost of one daisy, write a system of
equations that models this situation.
Use your system of equations to algebraically determine both the cost of one rose and the cost of
one daisy.

If Dana had waited until the plants were on sale, she would have paid $4.50 for each rose and $6.50 for each daisy. Determine the total amount of money she would have saved by buying all of her flowers during the sale.

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