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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 2019.

The following are questions from the past paper Regents High School Algebra 2, June 2019 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 2019 Regents - Questions and solutions 1 - 12

- A sociologist reviews randomly selected surveillance videos from a computations. public park over a period of several years and records the amount of time people spent on a smartphone. The statistical procedure the sociologist used is called
- Which statement(s) are true for all real numbers?

I (x - y)^{2}= x^{2}+ y^{2}

II (x + y)^{3}= x^{3}+ 3xy + y^{3} - What is the solution set of the following system of equations?

y = 3x + 6

y = (x + 4)^{2}- 10 - Irma initially ran one mile in over ten minutes. She then began a training program to reduce her one-mile time. She recorded her one-mile time once a week for twelve consecutive weeks, as modeled in the graph below
- A 7-year lease for office space states that the annual rent is $85,000 for the first year and will increase by 6% each additional year of the lease. What will the total rent expense be for the entire 7-year lease?
- The graph of y = f(x) is shown below

Which expression defines f(x)? - Given P(x) = x
^{3}- 3x^{3}- 2x + 4, which statement is true? - For x ≥ 0, which equation is false?
- What is the inverse of the function y = 4x + 5?
- Which situation could be modeled using a geometric sequence?
- The completely factored form of n
^{4}- 9n^{2}+ 4n^{3}- 36n + 12n^{2}+ 108 is - What is the solution when the equation wx
^{2}+ w = 0 is solved for x, where w is a positive integer?

Algebra 2 - June 2019 Regents - Questions and solutions 13 - 24

13. A group of students was trying to determine the proportion of candies in a bag that are blue. The company claims that 24% of candies in bags are blue. A simulation was run 100 times with a sample size of 50, based on the premise that 24% of the candies are blue. The approximately normal results of the simulation are shown in the dot plot below.

14. Selected values for the functions f and g are shown in the tables below.

15. The expression 6 - (3x - 2i)^{2} is equivalent to

16. A number, minus twenty times its reciprocal, equals eight. The number is

17. A savings account, S, has an initial value of $50. The account grows computations. at a 2% interest rate compounded n times per year, t, according to the function below.

18. There are 400 students in the senior class at Oak Creek High School. All of these students took the SAT. The distribution of their SAT scores is approximately normal. The number of students who scored within 2 standard deviations of the mean is approximately

19. The solution set for the equation

20. Which table best represents an exponential relationship?

21. A sketch of r(x) is shown below.

22. The temperature, in degrees Fahrenheit, in Times Square during computations. a day in August can be predicted by the function T(x) = 8sin(0.3x - 3) + 74, where x is the number of hours after midnight. According to this model, the predicted temperature, to the nearest degree Fahrenheit, at 7 P.M. is

23. Consider the system of equations below:

24. Camryn puts $400 into a savings account that earns 6% annually. The amount in her account can be modeled by C(t) = 400(1.06)^{t} where t is the time in years. Which expression best approximates the amount of money in her account using a weekly growth rate?

Algebra 2 - June 2019 Regents - Questions and solutions 25 - 37

25. The table below shows the number of hours of daylight on the first day of each month in Rochester, NY.

Given the data, what is the average rate of change in hours of daylight per month from January 1st to April 1st?

Interpret what this means in the context of the problem.

26. Algebraically solve for x:

27. Graph f(x) = log^{2}(x + 6) on the set of axes below.

28. Given tan θ = 7/24, and θ terminates in Quadrant III, determine the value of cos θ.

29. Kenzie believes that for x ≠ 0, the expression is equivalent to. Is she correct?

Justify your response algebraically.

30. When the function p(x) is divided by x - 1 the quotient is. State p(x) in standard form.

31. Write a recursive formula for the sequence 6, 9, 13.5, 20.25, . . .

32. Robin flips a coin 100 times. It lands heads up 43 times, and she wonders if the coin is unfair. She runs a computer simulation of 750 samples of 100 fair coin flips. The output of the proportion of heads is shown below.

Do the results of the simulation provide strong evidence that Robin’s coin is unfair? Explain your answer.

33. Factor completely over the set of integers: 16x^{4} - 81.

Sara graphed the polynomial y = 16x^{4} - 81 and stated “All the roots of y = 16x^{4} - 81 are real.”

Is Sara correct? Explain your reasoning.

34. The half-life of a radioactive substance is 15 years.

Write an equation that can be used to determine the amount, s(t), of 200 grams of this substance that remains after t years.

Determine algebraically, to the nearest year, how long it will take for 1/10 of this substance to remain.

35. Determine an equation for the parabola with focus (4,-1) and directrix y = -5.

(Use of the grid below is optional.)

36. 6 Juan and Filipe practice at the driving range before playing golf. The number of wins and corresponding practice times for each player are shown in the table below.

Given that the practice time was long, determine the exact probability that Filipe wins the next match.

Determine whether or not the two events “Filipe wins” and “long practice time” are independent. Justify your answer.

37. Griffin is riding his bike down the street in Churchville, N.Y. at a constant speed, when a nail gets caught in one of his tires. The height of the nail above the ground, in inches, can be represented by the trigonometric function f(t) = -13cos(0.8πt) + 13, where t represents the time (in seconds) since the nail first became caught in the tire.

Determine the period of f(t).

Interpret what the period represents in this context.

On the grid below, graph at least one cycle of f(t) that includes the y-intercept of the function.

Does the height of the nail ever reach 30 inches above the ground? Justify your answer.

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