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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 August 2018.

The following are questions from the past paper Regents High School Algebra 2, August 2018 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 - August 2018 Regents - Questions and solutions 1 - 12

- The solution of 87e
^{0.3x}= 5918, to the nearest thousandth is - A researcher randomly divides 50 bean plants into two groups. He puts one group by a window to receive natural light and the second group under artificial light. He records the growth of the plants weekly. Which data collection method is described in this situation?
- If f(x) = x
^{2}+ 9 and g(x) = x + 3, which operation would not result in a polynomial expression? - Consider the function p(x) = 3x
^{3}+ x^{2}- 5x and the graph of y = m(x) below.

Which statement is true? - Which expression is equivalent to
- Given f(x) = 1/2 x + 8, which equation represents the inverse, g(x)?
- The value(s) of x that satisfy
- Stephanie found that the number of white-winged crossbills in an area can be represented by the formula C = 550(1.08)
^{t}, where t represents the number of years since 2010. Which equation correctly represents the number of white-winged crossbills in terms of the monthly rate of population growth? - The roots of the equation 3x
^{2}+ 2x - 7 are - The average depreciation rate of a new boat is approximately 8% per year. If a new boat is purchased at a price of $75,000, which model is a recursive formula representing the value of the boat n years after it was purchased?
- Given cos θ = 7/25, where θ is an angle in standard position terminating in quadrant IV, and sin
^{2}θ + cos^{2}θ = 1, what is the value of tan θ? - For x > 0, which expression is equivalent to

Algebra 2 - August 2018 Regents - Questions and solutions 13 - 24

13. Jake wants to buy a car and hopes to save at least $5000 for a down computations. payment. The table below summarizes the amount of money he plans to save each week.

Based on this plan, which expression should he use to determine how much he has saved in n weeks?

14. Which expression is equivalent to x^{6}y^{4}(x^{4} - 16) - 9(x^{4} - 16)

15. If A = -3 + 5i, B = 4 - 2i, and C = 1 + 6i, where i is the imaginary unit, then A - BC equals

16. Which sketch best represents the graph of x = 3^{y}?

17. The graph below represents national and New York State average gas prices.

If New York State’s gas prices are modeled by G(x) and C > 0, which expression best approximates the national average x months from August 2014?

18. Data for the students enrolled in a local high school are shown in the Venn diagram below.

If a student from the high school is selected at random, what is the probability that the student is a sophomore given that the student is enrolled in Algebra II?

19. If p(x) = 2 ln(x) - 1 and m(x) = ln(x + 6), then what is the solution for p(x) = m(x)?

20. Given c(m) = m^{3} - 2m^{2} + 4m - 8, the solution of c(m) = 0 is

21. Which equation represents a parabola with a focus of (2,5) and a directrix of y = 9?

22. The height above ground for a person riding a Ferris wheel after t seconds is modeled by h(t) = 150sin(π/45 t + 67.5) + 160 feet. How many seconds does it take to go from the bottom of the wheel to the top of the wheel?

23. The parabola described by the equation y = 1/12(x - 2)^{2} + 2 has the directrix at y = -1. The focus of the parabola is

24. A fast-food restaurant analyzes data to better serve its customers. After its analysis, it discovers that the events D, that a customer uses the drive-thru, and F, that a customer orders French fries, are independent. The following data are given in a report:

Algebra 2 - August 2018 Regents - Questions and solutions 25 - 37

25. Over the set of integers, factor the expression x^{4} - 4x^{2} - 12.

26. Express the fraction in simplest radical form.

27. The world population was 2560 million people in 1950 and 3040 million in 1960 and can be modeled by the function p(t) = 2560e^{0.017185t}, where t is time in years after 1950 and p(t) is the population in millions. Determine the average rate of change of p(t) in millions of people per year, from 4 ≤ t ≤ 8. Round your answer to the nearest hundredth.

28. The scores of a recent test taken by 1200 students had an approximately normal distribution with a mean of 225 and a standard deviation of 18. Determine the number of students who scored between 200 and 245.

29. Algebraically solve for x:.

30. Graph t(x) = 3sin(2x) + 2 over the domain [0,2π] on the set of axes below. 31. Solve the following system of equations algebraically. x^{2} + y^{2} = 400 y = x - 28

32. Some smart-phone applications contain “in-app” purchases, which allow users to purchase special content within the application. A random sample of 140 users found that 35 percent made in-app purchases. A simulation was conducted with 200 samples of 140 users assuming 35 percent of the samples make in-app purchases. The approximately normal results are shown below.

Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth, for the simulated results. In the given context, explain what this value represents.

33. Solve the following system of equations algebraically for all values of x, y, and z.

34. Evaluate j(1) given j(x) = 2x^{4} - x^{3} - 35x^{2} + 16x + 48. Explain what your answer tells you about x + 1 as a factor.

Algebraically find the remaining zeros of j(x).

35. Determine, to the nearest tenth of a year, how long it would take an investment to double at a 3 3/4% interest rate, compounded continuously.

36. To determine if the type of music played while taking a quiz has a relationship to results, 16 students were randomly assigned to either a room softly playing classical music or a room softly playing rap music. The results on the quiz were as follows:

John correctly rounded the difference of the means of his experimental groups as 7. How did John obtain this value and what does it represent in the given context? Justify your answer.

To determine if there is any significance in this value, John rerandomized the 16 scores into two groups of 8, calculated the difference of the means, and simulated this process 250 times as shown below.

Does the simulation support the theory that there may be a significant difference in quiz scores? Explain.

37. A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a fifteen-year period. The company represents its revenue and costs as a function of time, in years, x, using the given functions.

The company’s profits can be represented as the difference between its revenue and costs. Write the profit function, P(x), as a polynomial in standard form.

Graph y = P(x) on the set of axes below over the domain 2 ≤ x ≤ 16.

Over the given domain, state when the company was the least profitable and the most profitable, to the nearest year. Explain how you determined your answer.

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