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 2023.

**Related Pages**

Regents Exam Past Papers

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

Solutions for Questions 1 - 24

- When the expression 2x(x - 4) - 3(x + 5) is written in simplest form, the result is
- The point (3,w) is on the graph of y = 2x + 7. What is the value of w?
- Students were asked to write 2x
^{3}+ 3x + 4x^{2}+ 1 in standard form. - Given f(x) = -3x
^{2}+ 10, what is the value of f(-2)? - Which relation is a function?
- What is the value of the third quartile in the box plot shown below?
- What is the solution to 2 + 3(2a - 1) = 3(a + 2)?
- One Saturday afternoon, three friends decided to keep track of the number of text messages they received each hour from 8 a.m. to noon. The results are shown below. Emily said that the number of messages she received increased by 8 each hour. Jessica said that the number of messages she received doubled every hour. Chris said that he received 3 messages the first hour, 10 the second hour, none the third hour, and 15 the last hour. Which of the friends’ responses best classifies the number of messages they received each hour as a linear function?
- Which expression is equivalent to (x + 4)
^{2}(x + 4)^{3}? - Caitlin graphs the function f(x) = ax
^{2}, where a is a positive integer. If Caitlin multiplies a by -2, when compared to f(x), the new graph will become - Sunny purchases a new car for $29,873. The car depreciates 20% annually.
- If f(x) = x
^{2}+ 2x + 1 and g(x) = 7x - 5, for which values of x is f(x) = g(x)? - Skyler mows lawns in the summer. The function f(x) is used to model the amount of money earned, where x is the number of lawns completely mowed. A reasonable domain for this function would be
- Which expression is equivalent to 2x
^{2}+ 8x - 10? - Ian throws a ball up in the air and lets it fall to the ground.
The height of the ball, h(t), is modeled by the equation
h(t) = -16t
^{2}+ 6t + 3, with h(t) measured in feet, and time, t, measured in seconds. The number 3 in h(t) represents - Thirty-two teams are participating in a basketball tournament. Only the winning teams in each round advance to the next round, as shown in the table below.
- In a geometric sequence, the first term is 4 and the common ratio is 3. The fifth term of this sequence is
- The amount of energy, Q, in joules, needed to raise the temperature of m grams of a substance is given by the formula Q = mC(Tf - Ti), where C is the specific heat capacity of the substance. If its initial temperature is Ti, an equation to find its final temperature, Tf , is
- When using the method of completing the square, which equation is
equivalent to x
^{2}- 12x - 10 = 0? - Which quadratic function has the smallest minimum value?
- Which representation yields the same outcome as the sequence defined recursively below?
- If the zeros of the function g(x) are {-3,0,4}, which function could represent g(x)?
- Morgan read that a snail moves about 72 feet per day.
- During summer vacation, Ben decides to sell hot dogs and pretzels on a food cart in Manhattan. It costs Ben $0.50 for each hot dog and $0.40 for each pretzel. He has only $100 to spend each day on hot dogs and pretzels. He wants to sell at least 200 items each day. If h is the number of hot dogs and p is the number of pretzels, which inequality would be part of a system of inequalities used to determine the total number of hot dogs and pretzels Ben can sell? 25.Graph the function g(x) = √(x + 3) on the set of axes below.
- The function f(x) is graphed on the set of axes below.
- Solve the inequality
- Determine the common difference of the arithmetic sequence in which a1 = 3 and a4 = 15.
- Given: A = √363 and B = √27. Explain why A B is irrational.
- Use the quadratic formula to solve x
^{2}- 4x + 1 = 0 for x. Round the solutions to the nearest hundredth - Factor completely: 4x
^{3}- 49x - The function g is defined as
- Anessa is studying the changes in population in a town. The graph below shows the population over 50 years.
- The table below shows the number of math classes missed during a school year for nine students, and their final exam scores.
- A fence was installed around the edge of a rectangular garden. The length, l, of the fence was 5 feet less than 3 times its width, w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation. Determine algebraically the dimensions, in feet, of the garden.
- Graph the system of inequalities on the set of axes below
- Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line

Let y represent the distance from the starting line and x represent the time elapsed, in seconds.

Write an equation to model the distance Aidan traveled.

Write an equation to model the distance Ella traveled.

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