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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 January 2018.

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

- The operator of the local mall wants to find out how many of the computations. mall’s employees make purchases in the food court when they are working. She hopes to use these data to increase the rent and attract new food vendors. In total, there are 1023 employees who work at the mall. The best method to obtain a random sample of the employees would be to survey

(1) all 170 employees at each of the larger stores

(2) 50% of the 90 employees of the food court

(3) every employee

(4) every 30th employee entering each mall entrance for one week - What is the solution set for x in the equation below?

√(x + 1) - 1 = x - For the system shown below, what is the value of z?

y = -2x + 14

3x - 4z = 2

3x - y = 16 - The hours of daylight, y, in Utica in days, x, from January 1, 2013 can be modeled by the equation y = 3.06sin(0.017x - 1.40) + 12.23.

How many hours of daylight, to the nearest tenth, does this model predict for February 14, 2013? - A certain pain reliever is taken in 220 mg dosages and has a half-life of 12 hours. The function A 220(1/2)
^{t/12}can be used to model this situation, where A is the amount of pain reliever in milligrams remaining in the body after t hours.

According to this function, which statement is true? - The expression (x + a)(x + b) can not be written as
- There are 440 students at Thomas Paine High School enrolled in U.S. History. On the April report card, the students’ grades are approximately normally distributed with a mean of 79 and a standard deviation of 7. Students who earn a grade less than or equal to 64.9 must attend summer school. The number of students who must attend summer school for U.S. History is closest to
- For a given time, x, in seconds, an electric current, y, can be represented by y = 2.5(1 - 2.7
^{-.10x}). Which equation is not equivalent? - What is the quotient when 10x
^{3}- 3x^{2}- 7x + 3 is divided by 2x - 1? - Judith puts $5000 into an investment account with interest compounded continuously. Which approximate annual rate is needed for the account to grow to $9110 after 30 years?
- If n = √a
^{5}and m = a, where a > 0, an expression for n/m could be - The solutions to x + 3 - 4/(x - 1) = 5 are

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

13. If ae^{bt} = c, where a, b, and c are positive, then t equals

14. For which values of x, rounded to the nearest hundredth, will |x^{2} - 9| - 3 = log_{3} x?

15. The terminal side of θ, an angle in standard position, intersects the unit circle at P(-1/3 , -√8/3). What is the value of sec θ?

16. What is the equation of the directrix for the parabola -8(y - 3) = (x + 4)^{2}?

17. The function below models the average price of gas in a small town computations. since January 1st.

G(t) = -0.0049t^{4} + 0.0923t^{3} - 0.56t^{2} + 1.166t + 3.23, where 0 ≤ t ≤ 10.

If G(t) is the average price of gas in dollars and t represents the number of months since January 1st, the absolute maximum G(t) reaches over the given domain is about

18. Written in simplest form, (c^{2} - d^{2})/(d^{2} + cd - 2c^{2}), where c ≠ d, is equivalent to

19. If p(x) = 2x^{3} - 3x + 5, what is the remainder of p(x) ÷ (x - 5)?

20. The results of simulating tossing a coin 10 times, recording the number of heads, and repeating this 50 times are shown in the graph below.

21. What is the inverse of f(x) = -6(x - 2)?

22. Brian deposited 1 cent into an empty non-interest bearing bank account on the first day of the month. He then additionally deposited 3 cents on the second day, 9 cents on the third day, and 27 cents on the fourth day. What would be the total amount of money in the account at the end of the 20th day if the pattern continued?

23. If the function g(x) = ab^{x} represents exponential growth, which statement about g(x) is false?

24. At her job, Pat earns $25,000 the first year and receives a raise of $1000 each year. The explicit formula for the nth term of this sequence is a_{n} = 25,000 + (n - 1)1000. Which rule best represents the equivalent recursive formula?

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

25. Elizabeth tried to find the product of (2 + 4i) and (3 - i), and her work is shown below.

(2 + 4i)(3 - i)

= 6 - 2i + 12i - 4i^{2}

= 6 - 10i - 4i^{2}

= 6 + 10i - 4(1)

= 6 + 10i - 4

= 2 + 10i

Identify the error in the process shown and determine the correct product of (2 + 4i) and (3 - i).

26. A runner is using a nine-week training app to prepare for a “fun run.” The table below represents the amount of the program completed, A, and the distance covered in a session, D, in miles.

Based on these data, write an exponential regression equation, rounded to the nearest thousandth, to model the distance the runner is able to complete in a session as she continues through the nine-week program.

27. A formula for work problems involving two people is shown below.

1/t_{1} + 1/t_{2} = 1/t_{b}

t_{1} = the time taken by the first person to complete the job

t_{2} = the time taken by the second person to complete the job

t_{b} = the time it takes for them working together to complete the job

Fred and Barney are carpenters who build the same model desk. It takes Fred eight hours to build the desk while it only takes Barney six hours. Write an equation that can be used to find the time it would take both carpenters working together to build a desk.

Determine, to the nearest tenth of an hour, how long it would take Fred and Barney working together to build a desk.

28. Completely factor the following expression:

x^{2} + 3xy + 3x^{3} + y

29. Researchers in a local area found that the population of rabbits with an initial population of 20 grew continuously at the rate of 5% per month. The fox population had an initial value of 30 and grew continuously at the rate of 3% per month.

Find, to the nearest tenth of a month, how long it takes for these populations to be equal.

30. Consider the function h(x) = 2sin (3x) + 1 and the function q represented in the table below.

Determine which function has the smaller minimum value for the domain [2,2]. Justify your answer.

31. The zeros of a quartic polynomial function h are -1, ±2, and 3.

Sketch a graph of y = h(x) on the grid below.

32. Explain why 81^{3/4} equals 27.

33. Given: f(x) = 2x^{2} + x - 3 and g(x) = x - 1

Express f(x) • g(x) - [f(x) + g(x)] as a polynomial in standard form.

34. A student is chosen at random from the student body at a given high school. The probability that the student selects Math as the favorite subject is 1/4. The probability that the student chosen is a junior is 116/459. If the probability that the student selected is a junior or that the student chooses Math as the favorite subject is 47/108, what is the exact probability that the student selected is a junior whose favorite subject is Math?

Are the events “the student is a junior” and “the student’s favorite subject is Math” independent of each other? Explain your answer.

35. In a random sample of 250 men in the United States, age 21 or older, 139 are married. The graph below simulated samples of 250 men, 200 times, assuming that 139 of the men are married.

a) Based on the simulation, create an interval in which the middle 95% of the number of married men may fall. Round your answer to the nearest integer.

b) A study claims “50% of men 21 and older in the United States are married.” Do your results from part a contradict this claim? Explain.

36. The graph of y = f(x) is shown below. The function has a leading coefficient of 1.

Write an equation for f(x).

The function g is formed by translating function f left 2 units. Write an equation for g(x).

37. The resting blood pressure of an adult patient can be modeled by the function P below, where

P(t) is the pressure in millimeters of mercury after time t in seconds.

P(t) = 24cos(3πt) + 120

On the set of axes below, graph y = P(t) over the domain 0 ≤ t ≤ 2.

Determine the period of P. Explain what this value represents in the given context.

Normal resting blood pressure for an adult is 120 over 80. This means that the blood pressure oscillates between a maximum of 120 and a minimum of 80. Adults with high blood pressure (above 140 over 90) and adults with low blood pressure (below 90 over 60) may be at risk for health disorders. Classify the given patient’s blood pressure as low, normal, or high and explain your reasoning.

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