Algebra II (Common Core) 01 June 2016

Algebra II (Common Core) 01 June 2016 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Algebra II (Common Core)
Wednesday, June 1, 2016 — 9:15 a.m. to 12:15 p.m., only
Student Name:____________________________________________________
School Name:_____________________________________________________

Answer: (4)

2. Julie averaged 85 on the first three tests of the semester in her mathematics class. If she scores 93 on each of the remaining tests, her average will be 90. Which equation could be used to determine how many tests, T, are left in the semester?

Answer: (3)

3. Given i is the imaginary unit, (2 – yi)² in simplest form is

(1) y² – 4yi + 4
(2) –y² – 4yi + 4
(3) – y² + 4
(4) y² + 4

Answer: (2) –y² – 4yi + 4

4. Which graph has the following characteristics?

• three real zeros
• as x → ∞, f(x) → ∞
• as x → ∞, f(x) → ∞

Answer: (3)

5. The solution set for the equation √56 – x = x is

(1) {–8,7}
(2) {–7,8}
(3) {7}
(4) { }

Answer: (3) {7}

6. The zeros for f(x) = x⁴ – 4x³ – 9x² + 36x are

(1) {0, ± 3,4}
(2) {0,3,4}
(3) {0, ± 3, –4}
(4) {0,3, –4}

Answer: (1) {0, ± 3,4}

7. Anne has a coin. She does not know if it is a fair coin. She flipped the coin 100 times and obtained 73 heads and 27 tails. She ran a computer simulation of 200 samples of 100 fair coin flips. The output of the proportion of heads is shown below.

Given the results of her coin flips and of her computer simulation, which statement is most accurate?

(1) 73 of the computer’s next 100 coin flips will be heads.
(2) 50 of her next 100 coin flips will be heads.
(3) Her coin is not fair.
(4) Her coin is fair.

Answer: (3) Her coin is not fair.

8. If g(c) = 1 c² and m(c) = c + 1, then which statement is not true?

(1) g(c) • m(c) = 1 + c – c² c³
(2) g(c) + m(c) = 2 + c – c²
(3) m(c) – g(c) = c + c²
(4) ^m(c)/_g(c)= ^–1/_1–c

Answer: (4) ^m(c)/_g(c)= ^–1/_1–c

9. The heights of women in the United States are normally distributed with a mean of 64 inches and a standard deviation of 2.75 inches. The percent of women whose heights are between 64 and 69.5 inches, to the nearest whole percent, is

(1) 6
(2) 48
(3) 68
(4) 95

Answer: (2) 48

10. The formula below can be used to model which scenario?

a¹ = 3000

a_n = 0.80a_n–1

(1) The first row of a stadium has 3000 seats, and each row thereafter has 80 more seats than the row in front of it.
(2) The last row of a stadium has 3000 seats, and each row before it has 80 fewer seats than the row behind it.
(3) A bank account starts with a deposit of $3000, and each year it grows by 80%.
(4) The initial value of a specialty toy is $3000, and its value each of the following years is 20% less.

Answer: (4) The initial value of a specialty toy is $3000, and its value each of the following years is 20% less.

11. Sean’s team has a baseball game tomorrow. He pitches 50% of the games. There is a 40% chance of rain during the game tomorrow. If the probability that it rains given that Sean pitches is 40%, it can be concluded that these two events are

(1) independent
(2) dependent
(3) mutually exclusive
(4) complements

Answer: (1) independent

12. A solution of the equation 2x² + 3x + 2 = 0 is

Answer: (1) – ¾ + ¼i √7

13. The Ferris wheel at the landmark Navy Pier in Chicago takes 7 minutes to make one full rotation. The height, H, in feet, above the ground of one of the six-person cars can be modeled by H(t) = 70 sin (^2π/₇ (t – 1.75)) + 80, where t is time, in minutes. Using H(t) for one full rotation, this car’s minimum height, in feet, is

(1) 150
(2) 70
(3) 10
(4) 0

Answer: (3) 10

Answer: (2)

15. Which function represents exponential decay?

(1) y = 2^0.3t
(2) y = 1.2^3t
(3) y = (¹/₂)^–t
(4) y = 5^–t

Answer: (4) y = 5^–t

16. Given f^–1(x) = –¾ x + 2, which equation represents f(x)?

(1) f(x) = ⁴/₃x – ⁸/₃
(2) f(x) = –⁴/₃x + ⁸/₃
(3) f(x) = ¾x – 2
(4) f(x) = –¾x + 2

Answer: (2) f(x) = –⁴/₃x + ⁸/₃

17. A circle centered at the origin has a radius of 10 units. The terminal side of an angle, θ, intercepts the circle in Quadrant II at point C. The y-coordinate of point C is 8. What is the value of cos θ?

(1) – ³/₅
(2) – ¾
(3) ³/₅
(4) ⁴/₅

Answer: (1) – ³/₅

18. Which statement about the graph of c(x) = log₆x is false?

(1) The asymptote has equation y = 0.
(2) The graph has no y-intercept.
(3) The domain is the set of positive reals.
(4) The range is the set of all real numbers.

Answer: (1) The asymptote has equation y = 0.

19. The equation 4x² – 24x + 4y² – 72y = 76 is equivalent to

(1) 4(x – 3)² + 4(y + 9)² = 76
(2) 4(x – 3)² + 4(y + 9)² = 121
(3) 4(x – 3)² + 4(y + 9)² = 166
(4) 4(x – 3)² + 4(y +9)² = 436

Answer: (4) 4(x – 3)² + 4(y +9)² = 436

20. There was a study done on oxygen consumption of snails as a function of pH, and the result was a degree 4 polynomial function whose graph is shown below.