Algebra II (Common Core) 24 January 2018 Questions Answer Keys

**The University of the State of New York**

Regents High School Examination

Algebra II (Common Core)

Wednesday, January 24, 2018 — 1:15 to 4:15 p.m., only

Student Name:____________________________________________________

School Name:_____________________________________________________

**1. The operator of the local mall wants to find out how many of the 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

**2. What is the solution set for x in the equation below?**

**√x + 1 – 1 = x**

- (1) {1}
- (2) {0}
- (3) {1,0}
- (4) {0,1}

**3. For the system shown below, what is the value of z?**

y = **–**2x + 14

3x **– **4z = 2

3x **– **y = 16

- (1) 5
- (2) 2
- (3) 6
- (4) 4

**4. 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?**

- (1) 9.4
- (2) 10.4
- (3) 12.1
- (4) 12.2

**5. 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?

- (1) Every hour, the amount of pain reliever remaining is cut in half.
- (2) In 12 hours, there is no pain reliever remaining in the body.
- (3) In 24 hours, there is no pain reliever remaining in the body.
- (4) In 12 hours, 110 mg of pain reliever is remaining

**6. The expression (x + a)(x + b) can not be written as**

- (1) a(x + b) + x(x + b)
- (2) x
^{2}+ abx + ab - (3) x
^{2}+ (a + b)x + ab - (4) x(x + a) + b(x + a)

**7. 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**

- (1) 3
- (2) 5
- (3) 10
- (4) 22

**8. 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?**

** **

**9. What is the quotient when 10x ^{3} – 3x^{2} – 7x + 3 is divided by 2x – 1?**

- (1) 5x
^{2}+ x + 3 - (2) 5x
^{2}– x + 3 - (3) 5x
^{2}– x – 3 - (4) 5x
^{2}+ x – 3

**10. 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?**

- (1) 2%
- (2) 2.2%
- (3) 0.02%
- (4) 0.022%

**11. If n = √a ^{5} and m = a, where a > 0, an expression for ^{n}/_{m} could be**

- (1) a
^{5/2} - (2) a
^{4} - (3)
^{3}√a^{2} - (4) √a
^{3}

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

- (1) 2.29 and 3.63
- (2) 2.37 and 3.54
- (3) 2.84 and 3.17
- (4) 2.92 and 3.06

**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?**

- (1) 3
- (2)
**–**^{3√8/8} - (3)
**–**^{1}/_{3} - (4)
**–**^{√8}/_{3}

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

- (1) y = 5
- (2) y = 1
- (3) y =
**–**2 - (4) y =
**–**6

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

G(t) = –0.0049*t*^{4} + 0.*0923t ^{3}* – 0.56

*t*

^{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

- (1) $1.60
- (2) $3.92
- (3) $4.01
- (4) $7.73

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

- (1)
**–**230 - (2) 0
- (3) 40
- (4) 240

**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.**

Based on the results of the simulation, which statement is false?

- (1) Five heads occurred most often, which is consistent with the theoretical probability of obtaining a heads.
- (2) Eight heads is unusual, as it falls outside the middle 95% of the data.
- (3) Obtaining three heads or fewer occurred 28% of the time.
- (4) Seven heads is not unusual, as it falls within the middle 95% of the data.

**Algebra II (Common Core) 24 January 2018 Questions Answers Keys**

Algebra II (Common Core) Examination Question |

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