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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 2017.

The following are questions from the past paper Regents High School Algebra 2, January 2017 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 2017 Regents - Questions and solutions 1 - 12

1 Relative to the graph of y = 3sin x, what is the shift of the graph of y = 3sin(x + π/3))?

2 A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If t represents the time, in weeks, and P(t)is the population of rabbits with respect to time, about how many rabbits will there be in 98 days?

3 When factored completely, m^{5} + m^{3} - 6m is equivalent to

4 If sin^{2}(32°) + cos^{2}(M) = 1, then M equals

5 What is the solution to the system of equations y = 3x - 2 and y = g(x) where g(x) is defined by the function below?

6 Which statement about statistical analysis is false?

(1) Experiments can suggest patterns and relationships in data.

(2) Experiments can determine cause and effect relationships.

(3) Observational studies can determine cause and effect relationships.

(4) Observational studies can suggest patterns and relationships in data.

7 The expression (m^{2}/m^{1/2})^{-1/2} is equivalent to

8 What is the inverse of the function y = log_{3}x?

9 Gabriel performed an experiment to see if planting 13 tomato plants in black plastic mulch leads to larger tomatoes than if 13 plants are planted without mulch. He observed that the average weight of the tomatoes from tomato plants grown in black plastic mulch was 5 ounces greater than those from the plants planted without mulch. To determine if the observed difference is statistically significant, he rerandomized the tomato groups 100 times to study these random differences in the mean weights. The output of his simulation is summarized in the dotplot below.

10 If p(x) = ab^{x} and r(x) = cd^{2}, then p(x) ˙ r(x) equals

11 The solution to the equation 18x^{2} - 24x + 87 = 0 is

12 When g(x) = 2/(x+2) and h(x) = log(x + 1) + 3 are graphed on the same set of axes, which coordinates best approximate their point of intersection?

Algebra 2 - January 2017 Regents - Questions and solutions 13 - 24

13 The price of a postage stamp in the years since the end of World War I is shown in the scatterplot below. The equation that best models the price, in cents, of a postage stamp based on these data is

14 The eighth and tenth terms of a sequence are 64 and 100. If the sequence is either arithmetic or geometric, the ninth term can not be

15 The loudness of sound is measured in units called decibels (dB). These units are measured by first assigning an intensity I_{0} to a very soft sound that is called the threshold sound. The sound to be measured is assigned an intensity, I, and the decibel rating, d, of this sound is found using d = 10 log I/I_{0}. The threshold sound audible to the average person is 1.0 × 10^{-12} W/m^{2} (watts per square meter). Consider the following sound level classifications:

16 Pedro and Bobby each own an ant farm. Pedro starts with 100 ants and says his farm is growing exponentially at a rate of 15% per month. Bobby starts with 350 ants and says his farm is steadily decreasing by 5 ants per month.

Assuming both boys are accurate in describing the population of their ant farms, after how many months will they both have approximately the same number of ants?

17 What is the solution, if any, of the equation

2/(x+3) - 3/(4-x) = (2x-2)/(x^{2} - x - 12)?

18 In 2013, approximately 1.6 million students took the Critical Reading portion of the SAT exam. The mean score, the modal score, and the standard deviation were calculated to be 496, 430, and 115, respectively. Which interval reflects 95% of the Critical Reading scores?

19 Which statement regarding the graphs of the functions below is untrue?

20 When g(x) is divided by x 4, the remainder is 0. Given g(x) = x^{4} + 3x^{3} - 6x^{2} - 6x + 8, which conclusion about g(x) is true?

21 Joelle has a credit card that has a 19.2% annual interest rate compounded monthly. She owes a total balance of B dollars after m months. Assuming she makes no payments on her account, the table below illustrates the balance she owes after m months. Over which interval of time is her average rate of change for the balance on her credit card account the greatest?

22 Which graph represents a cosine function with no horizontal shift, an amplitude of 2, and a period of 2π/3?

23 According to a pricing website, Indroid phones lose 58% of their cash value over 1.5 years. Which expression can be used to estimate the value of a $300 Indroid phone in 1.5 years?

24 A cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5 - x, and height by x - 1. The volume of the box is modeled by the function below.

Algebra 2 - January 2017 Regents - Questions and solutions 25 - 37

25 Express (1 - i)^{3} in a + bi form.

26 An orange-juice processing plant receives a truckload of oranges. The quality control team randomly chooses three pails of oranges, each containing 50 oranges, from the truckload. Identify the sample and the population in the given scenario. State one conclusion that the quality control team could make about the population if 5% of the sample was found to be unsatisfactory.

27 Using the unit circle below, explain why cscθ = 1/y.

28 The function M(t) represents the mass of radium over time, t, in years.

M(t) = 100e^{(ln1/2)t/1500}

Determine if the function M(t) represents growth or decay. Explain your reasoning.

29 On the grid below, sketch a cubic polynomial whose zeros are 1, 3, and -2.

30 Given the equal terms ^{3}√x^{5} and y^{5/6}, determine and state y, in terms of x.

31 The results of a survey of the student body at Central High School about television viewing preferences are shown below. Are the events “student is a male” and “student prefers reality series” independent of each other? Justify your answer.

32 Given f(x) = 3x^{2} + 7x - 20 and g(x) = x - 2, state the quotient and remainder of f(x)/g(x), in the form q(x) + r(x)/g(x)

33 Algebraically determine the values of h and k to correctly complete the identity stated below.

2x^{3} - 10x^{2} + 11x - 7 = (x - 4)(2x^{2} + hx + 3) + k

34 Elaina has decided to run the Buffalo half-marathon in May. She researched training plans on the Internet and is looking at two possible plans: Jillian’s 12-week plan and Josh’s 14-week plan. The number of miles run per week for each plan is plotted below. Which one of the plans follows an arithmetic pattern? Explain how you arrived at your answer. Write a recursive definition to represent the number of miles run each week for the duration of the plan you chose. Jillian’s plan has an alternative if Elaina wanted to train instead for a full 26-mile marathon. Week one would start at 13 miles and follow the same pattern for the half-marathon, but it would continue for 14 weeks. Write an explicit formula, in simplest form, to represent the number of miles run each week for the full-marathon training plan.

35 The guidance department has reported that of the senior class, 2.3% are members of key club, K, 8.6% are enrolled in AP Physics, P, and 1.9% are in both. Determine the probability of P given K, to the nearest tenth of a percent. The principal would like a basic interpretation of these results. Write a statement relating your calculated probabilities to student enrollment in the given situation.

36 Using the formula below, determine the monthly payment on a 5-year car loan with a monthly percentage rate of 0.625% for a car with an original cost of $21,000 and a $1000 down payment, to the nearest cent.

37 The speed of a tidal wave, s, in hundreds of miles per hour, can be modeled by the equation s = √t - 2t + 6, where t represents the time from its origin in hours. Algebraically determine the time when s = 0. How much faster was the tidal wave traveling after 1 hour than 3 hours, to the nearest mile per hour? Justify your answer.

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