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 2022.

**Related Pages**

Regents Exam Past Papers

Algebra I Regents New York State Exam Questions August 2022 (pdf)

Solutions for Questions 1 - 24

- If f(x) = (3x - 4)/2 ,then f(8) is
- If x ≠ 0, then the common ratio of the sequence x, 2x
^{2}, 4x^{3}, 8x^{4}, 16x^{5}, … is - The expression 36x
^{2}- 9 is equivalent to - Given the relation R = {(-4,2), (3,6), (x,8), (-1,4)} Which value of x would make this relation a function?
- If the point (K,-5) lies on the line whose equation is 3x + y = 7, then the value of K is
- The expression 1/3 x(6x
^{2}- 3x + 9) is equivalent to - The graphs below represent four polynomial functions. Which of these functions has zeros of 2 and -3?
- What is the constant term of the polynomial 4d + 6 + 3d
^{2}? - Emily was given $600 for her high school graduation. She invested it in an account that earns 2.4% interest per year. If she does not make any deposits or withdrawals, which expression can be used to determine the amount of money that will be in the account after 4 years?
- Different ways to represent data are shown below
- What would be the order of these quadratic functions when they are arranged from the narrowest graph to the widest graph?
- At Berkeley Central High School, a survey was conducted to see if students preferred cheeseburgers, pizza, or hot dogs for lunch. The results of this survey are shown in the table below.
- Which situation could be modeled by a linear function?
- Which function has the smallest y-intercept value?
- When solving x
^{2}- 10x - 13 = 0 by completing the square, which equation is a step in the process? - When 3x
^{2}+ 7x - 6 + 2x^{3}is written in standard form, the leading coefficient is - Which of the equations below have the same solution?
- In an organism, the number of cells, C(d), after d days can be
represented by the function C(d) = 120 • 2
^{3d}. This function can also be expressed as - In the process of solving the equation 10x
^{2}- 12x - 16x = 6, George wrote 2(5x^{2}- 14x) = 2(3), followed by 5x^{2}- 14x = 3. Which properties justify George’s process? - A sequence is defined recursively by
- A swimmer set a world record in the women’s 1500-meter freestyle, finishing the race in 15.42 minutes. If 1 meter is approximately 3.281 feet, which set of calculations could be used to convert her speed to miles per hour?
- The diagram below shows the graph of h(t), which models the height, in feet, of a rocket t seconds after it was shot into the air.
- The table below shows the time, in hours, spent by students on electronic devices and their math test scores. The data collected model a linear regression.
- The volume of a trapezoidal prism can be found using the formula V = 1/2 a(b + c)h. Which equation is correctly solved for b?
- Graph f(x) = |x + 1| on the set of axes below.
- The table below shows the value of a particular car over time.
- Is the product of
- The ages of the last 16 United States presidents on their first inauguration day are shown in the table below.
- The cost of one pound of grapes, g, is 15 cents more than one pound of apples, a. The cost of one pound of bananas, b, is twice as much as one pound of grapes. Write an equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples.
- A student is given the functions f(x) = (x + 1)
^{2}and g(x) = (x + 3)^{2}. Describe the transformation that maps f(x) onto g(x). - Solve 3x
^{2}- 5x - 7 = 0 algebraically for all values of x, rounding to the nearest tenth. - Factor completely: 3y
^{2}- 12y - 288 - Thomas took a 140-mile bus trip to visit his grandparents. His trip is outlined on the graph below Explain what might have happened in the interval between D and E. State the interval in which the bus traveled the fastest. State how many miles per hour the bus was traveling during this interval. What was the average rate of speed, in miles per hour, for Thomas’s entire bus trip?
- Graph f(x) and g(x) on the set of axes below.
- A store sells grapes for $1.99 per pound, strawberries for $2.50 per pound, and pineapples for $2.99 each. Jonathan has $25 to buy fruit. He plans to buy 2 more pounds of strawberries than grapes. He also plans to buy 2 pineapples. If x represents the number of pounds of grapes, write an inequality in one variable that models this scenario. Determine algebraically the maximum number of whole pounds of grapes he can buy.
- Solve the system of inequalities graphically on the set of axes below. Label the solution set S. Is the point (-5,0) in the solution set? Explain your answer.
- An ice cream shop sells small and large sundaes. One day, 30 small sundaes and 50 large sundaes were sold for $420. Another day, 15 small sundaes and 35 large sundaes were sold for $270. Sales tax is included in all prices. If x is the cost of a small sundae and y is the cost of a large sundae, write a system of equations to represent this situation. Peyton thinks that small sundaes cost $2.75 and large sundaes cost $6.75. Is Peyton correct? Justify your answer. Using your equations, determine algebraically the cost of one small sundae and the cost of one large sundae.

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