# Algebra II (Common Core) 27 January 2017

Algebra II (Common Core) 27 January 2017 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Algebra II (Common Core)
Friday, January 27, 2017 — 9:15 a.m. to 12:15 p.m., only.
Student Name:____________________________________________________
School Name:_____________________________________________________

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

• (1) π/right
• (2) π/left
• (3) π/up
• (4) π/down

2. A rabbit population doubles every 4 weeks. There are currently fi ve 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?

• (1) 56
• (2) 152
• (3) 3688
• (4) 81,920

3. When factored completely, m5 + m3 – 6m is equivalent to

• (1) (m + 3)(m 2)
• (2) (m3 + 3m)(m2 – 2)
• (3) m(m4 + m2 – 6)
• (4) m(m2 + 3)(m2 – 2)
Answer: (4) m(m2 + 3)(m2 – 2)

4. If sin2 (32°) cos2 (M) = 1, then M equals

• (1) 32°
• (2) 58°
• (3) 68°
• (4) 72°

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?

• (1) {(0, –2)}
• (2) {(0, –2),(1,6)}
• (3) {(1,6)}
• (4) {(1,1),(6,16)}

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

8. What is the inverse of the function y log3x?

• (1) y = x3
• (2) y = logx3
• (3) y = 3x
• (4) x = 3y
Answer: (3) y = 3

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 signifi cant, 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.

Given these results, what is an appropriate inference that can be drawn?

• (1) There was no effect observed between the two groups.
• (2) There was an effect observed that could be due to the random assignment of plants to the groups.
• (3) There is strong evidence to support the hypothesis that tomatoes from plants planted in black plastic mulch are larger than those planted without mulch.
• (4) There is strong evidence to support the hypothesis that tomatoes from plants planted without mulch are larger than those planted in black plastic mulch.
Answer: (2) There was an effect observed that could be due to the random assignment of plants to the groups.

10. If p(x) = abx and r(x) = cdx, then p(x) • r(x) equals

• (1) ac(b + d)x
• (2) ac(b + d)2x
• (3) ac(bd)x
• (4) ac(bd)x2

11. The solution to the equation 18x2 – 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?

• (1) ( –0.9,1.8)
• (2) ( –0.9,1.9)
• (3) (1.4,3.3)
• (4) (1.4,3.4)

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

• (1) y = 0.59x – 14.82
• (2) y = 1.04(1.43)x
• (3) y = 1.43(1.04)x
• (4) y = 24sin(14x) + 25
Answer: (3) y = 1.43(1.04)x

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

• (1) –82
• (2) –80
• (3) 80
• (4) 82

How would a sound with intensity 6.3 × 103 W/m2 be classified?

• (1) moderate
• (2) loud
• (3) very loud
• (4) deafening
Answer: (3) very loud

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?

• (1) 7
• (2) 8
• (3) 13
• (4) 36
• (1) –1
• (2) –5
• (3) all real numbers
• (4) no real solution

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 refl ects 95% of the Critical Reading scores?

• (1) 430 ± 115
• (2) 430 ± 230
• (3) 496 ± 115
• (4) 496 ± 230
Answer: (4) 496 ± 230

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

f(x) = 3 sin 2x, from – π < x < π    h(x) = log2x

g(x) = (x – 0.5)(x + 4)(x – 2)         j(x) = –|4x – 2| + 3

• (1) f(x) and j(x) have a maximum y-value of 3.
• (2) f(x), h(x), and j(x) have one y-intercept.
• (3) g(x) and j(x) have the same end behavior as x → – ∞.
• (4) g(x), h(x), and j(x) have rational zeros.
Answer: (2) f(x), h(x), and j(x) have one y-intercept.

20. When g(x) is divided by x + 4, the remainder is 0. Given g(x) = x4 + 3x3 – 6x2 – 6x + 8, which conclusion about g(x) is true?

• (1) g(4) = 0
• (2) g(–4) = 0
• (3) x – 4 is a factor of g(x).
• (4) No conclusion can be made regarding g(x)
Answer: (2) g(–4) = 0

Algebra II (Common Core) 27 January 2017 Questions Answers Keys

 Algebra II (Common Core) Examination Question Scoring Key and Rating Guide