# Algebra II (Common Core) 18 June 2018

Algebra II (Common Core) 18 June 2018 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Algebra II (Common Core)
Thursday, January 14, 2018 — 1:15 to 4:15 p.m., only
Student Name:____________________________________________________
School Name:_____________________________________________________

1. The graphs of the equations y = x² + 4x – 1 and y + 3 = x are drawn on the same set of axes. One solution of this system is

• (1) (-5,-2)
• (2) (-1,-4)
• (3) (1,4)
• (4) (-2,-1)
Answer: (2) (-1,-4)

2. Which statement is true about the graph of f(x) = (⅛)x ?

• (1) The graph is always increasing.
• (2) The graph is always decreasing.
• (3) The graph passes through (1,0).
• (4) The graph has an asymptote, x = 0.
Answer: (2) The graph is always decreasing. Answer: (3)

4. A scatterplot showing the weight, w, in grams, of each crystal after growing t hours is shown below. The relationship between weight, w, and time, t, is best modeled by

• (1) w = 4t + 5
• (2) w = (1.4)t+2
• (3) w = 5(2.1)t
• (4) w = 8(.75)t
Answer: (2) w = (1.4)t+2

5. Where i is the imaginary unit, the expression (x + 3i)² – (2x – 3i)² is equivalent to

• (1) -3x²
• (2) -3x² – 18
• (3) -3x² + 18xi
• (4) -3x² – 6xi – 18
Answer: (3) -3x² + 18xi

6. Which function is even?

• (1) f(x) = sin x
• (2) f(x) = x² – 4
• (3) f(x) = |x – 2| + 5
• (4) f(x) = x4 + 3x³ + 4
Answer: (2) f(x) = x² – 4

7. The function N(t) = 100e– 0.023t models the number of grams in a sample of cesium-137 that remain after t years. On which interval is the sample’s average rate of decay the fastest?

• (1) [1,10]
• (2) [10,20]
• (3) [15,25]
• (4) [1,30]
Answer: (1) [1,10]

8. Which expression can be rewritten as (x + 7)(x – 1)? Answer: (1) Answer: (4)

10. The depth of the water at a marker 20 feet from the shore in a bay is depicted in the graph below. If the depth, d, is measured in feet and time, t, is measured in hours since midnight, what is an equation for the depth of the water at the marker? Answer: (4)

11. On a given school day, the probability that Nick oversleeps is 48% and the probability he has a pop quiz is 25%. Assuming these two events are independent, what is the probability that Nick oversleeps and has a pop quiz on the same day?

• (1) 73%
• (2) 36%
• (3) 23%
• (4) 12%
Answer: (4) 12%

12. If x – 1 is a factor of x³ – kx² + 2x, what is the value of k?

• (1) 0
• (2) 2
• (3) 3
• (4) -3
Answer: (3) 3

13. The profit function, p(x), for a company is the cost function, c(x), subtracted from the revenue function, r(x). The profit function for
the Acme Corporation is p(x) = – 0.5x² + 250x – 300 and the revenue function is r(x) = – 0.3x² + 150x. The cost function for the Acme Corporation is

• (1) c(x) = 0.2x² – 100x + 300
• (2) c(x) = 0.2x² + 100x + 300
• (3) c(x) = – 0.2x² + 100x – 300
• (4) c(x) = – 0.8x² + 400x – 300
Answer: (1) c(x) = 0.2x² – 100x + 300

14. The populations of two small towns at the beginning of 2018 and their annual population growth rate are shown in the table below. Assuming the trend continues, approximately how many years after the beginning of 2018 will it take for the populations to be equal?

• (1) 7
• (2) 20
• (3) 68
• (4) 125
Answer: (1) 7

15. What is the inverse of f(x) = x³ – 2? Answer: (3)

16. A 4th degree polynomial has zeros – 5, 3, i, and – i. Which graph could represent the function defined by this polynomial? Answer: (2)

17. The weights of bags of Graseck’s Chocolate Candies are normally distributed with a mean of 4.3 ounces and a standard deviation of 0.05 ounces. What is the probability that a bag of these chocolate candies weighs less than 4.27 ounces?

• (1) 0.2257
• (2) 0.2743
• (3) 0.7257
• (4) 0.7757
Answer: (2) 0.2743 When this equation is written in terms of the number e, the base of the natural logarithm, it is equivalent to I = 100e kd. What is the approximate value of the constant, k?

• (1) – 0.087
• (2) 0.087
• (3) – 11.542
• (4) 11.542
Answer: (1) – 0.087

19. The graph of y log2 x is translated to the right 1 unit and down 1 unit. The coordinates of the x-intercept of the translated graph are

• (1) (0,0)
• (2) (1,0)
• (3) (2,0)
• (4) (3,0)
Answer: (4) (3,0) Answer: (2)

Algebra II (Common Core) 18 June 2018 Questions Answers Keys Algebra II (Common Core) Examination Question Scoring Key and Rating Guide

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