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More Lessons for the Regents High School Exam

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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 January 2023.

The following are questions from the past paper

Regents High School Algebra 2, January 2023 Exam (pdf).

Download the questions and try them, then look at the following videos to check your answers with the step by step solutions.

Algebra 2 - January 2023 Regents - Solutions for Questions 1 - 24

- Which expression is equivalent to (x + 2)
^{2}- 5(x + 2) + 6? - To the nearest tenth, the solution to the equation
4300e
^{0.07x}- 123 = 5000 is - The value of an automobile t years after it was purchased is given by
the function V = 38,000(0.84)
^{t}. Which statement is true? - Which function represents exponential decay?
- The expression
- The sum of the first 20 terms of the series -2 + 6 - 18 + 54 - … is
- If f(x) = 2x
^{4}- x^{3}- 16x + 8, then f(1/2) - If (6 - ki)
^{2}= 27 - 36i, the value of k is - What is the solution set of the equation
- How many real solutions exist for the system of equations below?
- Which equation represents a polynomial identity?
- Given x > 0, the expression
- A cyclist pedals a bike at a rate of 60 revolutions per minute. The height, h, of a pedal at time t, in seconds, is plotted below.
- Which statement about data collection is most accurate?
- If f(x) = 1/2 x + 2, then the inverse function is
- Given f(x) = x
^{4}- x^{3}- 6x^{2}, for what values of x will f(x) > 0? - For which approximate value(s) of x will log(x + 5) = |x - 1| - 3?
- Consider a cubic polynomial with the characteristics below
- Betty conducted a survey of her class to see if they like pizza. She gathered 200 responses and 65% of the voters said they did like pizza. Betty then ran a simulation of 400 more surveys, each with 200 responses, assuming that 65% of the voters would like pizza. The output of the simulation is shown below.
- If cos A =
- A tree farm initially has 150 trees. Each year, 20% of the trees are cut
down and 80 seedlings are planted. Which recursive formula models
the number of trees, a
_{n}, after n years? - Which equation represents a parabola with a focus of (4,-3) and directrix of y = 1?
- Mia has a student loan that is in deferment, meaning that she does
not need to make payments right now. The balance of her loan
account during her deferment can be represented by the function
f(x) = 35,000(1.0325)
^{x}, where x is the number of years since the deferment began. If the bank decides to calculate her balance showing a monthly growth rate, an approximately equivalent function would be - Which graph shows a quadratic function with two imaginary zeros?

- Algebraically determine the zeros of the function below.
- Given a > 0, solve the equation
- Given P(A) = 1/3 and P(B) = 5/12, where A and B are independent events, determine P(A ∩ B).
- The scores on a collegiate mathematics readiness assessment are approximately normally distributed with a mean of 680 and a standard deviation of 120. Determine the percentage of scores between 690 and 900, to the nearest percent.
- Consider the data in the table below.
- Write the expression A(x) • B(x) - 3C(x) as a polynomial in standard form.
- Over the set of integers, completely factor x
^{4}- 5x^{2}+ 4. - Natalia’s teacher has given her the following information about angle θ.
- Solve the equation
- Joette is playing a carnival game. To win a prize, one has to correctly guess which of five equally sized regions a spinner will land on, as shown in the diagram below.
- Graph c(x)
- The monthly high temperature (°F) in Buffalo, New York can be modeled by B(m) = 24.9sin(0.5m - 2.05) + 55.25, where m is the number of the month and January = 1. Find the average rate of change in the monthly high temperature between June and October, to the nearest hundredth.
- Objects cool at different rates based on the formula below.

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