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More Lessons for the Regents High School Exam

More Lessons for Algebra

High School Math based on the topics required for the Regents Exam conducted by NYSED.

The following are the worked solutions for the Algebra 2(Common Core) Regents High School Examination June 2022.

The following are questions from the past paper

Regents High School Algebra 2, June 2022 Exam (pdf).

Download the questions and try them, then scroll down the page to check your answers with the step by step solutions.

Algebra 2 - June 2022 Regents - Solutions for Questions 1 - 24

- For all positive values of x, which expression is equivalent to x
^{3/4} - Mrs. Favata’s statistics class wants to conduct a survey to see how students feel about changing the school mascot’s name. Which plan is the best process for gathering an appropriate sample?
- Given
- In a group of 40 people, 20 have brown hair, 22 have blue eyes, and 15 have both brown hair and blue eyes. How many people have neither brown hair nor blue eyes?
- Consider the function y = h(x), defined by the graph below.
- For the polynomial p(x), if p(3) = 0, it can be concluded that
- The solution to the equation 5e
^{x + 2}= 7 is - Consider the system of equations below
- Monthly mortgage payments can be found using the formula below, where M is the monthly payment, P is the amount borrowed, r is the annual interest rate, and n is the total number of monthly payments.
- For all real values of x, if f(x) = (x - 3)
^{2}and g(x) = (x + 3)^{2}, what is f(x) - g(x)? - If f(t)
- Consider the graph of g and the table representing t below
- A parabola has a directrix of y = 3 and a vertex at (2,1). Which ordered pair is the focus of the parabola?
- The heights of the 3300 students at Oceanview High School are approximately normally distributed with a mean of 65.5 inches and a standard deviation of 2.9 inches. The number of students at Oceanview who are between 64 and 68 inches tall is closest to
- Which statement below about the graph of f(x) = -log(x + 4) + 2 is true?
- A researcher wants to determine if room-darkening shades cause people to sleep longer. Which method of data collection is most appropriate?
- The inverse of f(x)
- The expression
- An angle, θ, is rotated counterclockwise on the unit circle, with its terminal side in the second quadrant, as shown in the diagram below
- The depth of the water, d(t), in feet, on a given day at Thunder Bay,
- A function is defined
- Which function has a maximum y-value of 4 and a midline of y = 1?
- Which expression is equivalent to
- The growth of a $500 investment can be modeled by the function
P(t) = 500(1.03)
^{t}, where t represents time in years. In terms of the monthly rate of growth, the value of the investment can be best approximated by

- Does the equation x
^{2}- 4x + 13 = 0 have imaginary solutions? Justify your answer - The initial push of a child on a swing causes the swing to travel a total of 6 feet. Each successive swing travels 80% of the distance of the previous swing. Determine the total distance, to the nearest hundredth of a foot, a child travels in the first five swings.
- Solve algebraically for n:
- Factor completely over the set of integers:
- The relative frequency table shows the proportion of a population who have a given eye color and the proportion of the same population who wear glasses.
- For x ≠ 0 and y ≠ 0
- Graph y =
- A cup of coffee is left out on a countertop to cool. The table below represents the temperature, F(t), in degrees Fahrenheit, of the coffee after it is left out for t minutes
- On the set of axes below, graph y = f(x) and y = g(x) for the given functions.
- A Foucault pendulum can be used to demonstrate that the Earth rotates. The time, t, in seconds, that it takes for one swing or period of the pendulum can be modeled by the equation t
- In order to decrease the percentage of its residents who drive to work, a large city launches a campaign to encourage people to use public transportation instead. Before starting the campaign, the city’s Department of Transportation uses census data to estimate that 65% of its residents drive to work. The Department of Transportation conducts a simulation, shown below, run 400 times based on this estimate. Each dot represents the proportion of 200 randomly selected residents who drive to work.
- Solve the system of equations algebraically:
- The population, in millions of people, of the United States can be represented by the recursive formula below, where a0 represents the population in 1910 and n represents the number of years since 1910.

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