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)

**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.

**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 = 4
^{t}+ 5 - (2) w = (1.4)
^{t}+2 - (3) w = 5(2.1)
^{t} - (4) w = 8(.75)
^{t}

**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

**6. Which function is even?**

- (1) f(x) = sin x
- (2) f(x) = x² – 4
- (3) f(x) = |x – 2| + 5
- (4) f(x) = x
^{4}+ 3x³ + 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]

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

**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?

**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%

**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

**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 + 250 _{x} – 300 and the revenue function is r(x) = – 0.3x² + 150_{x}. The cost function for the Acme Corporation is**

- (1) c(x) = 0.2x
**²**– 100x + 300 - (2) c(x) = 0.2x
**²**+ 100x + 300 - (3) c(x) = – 0.2x
**²**+ 100x – 300 - (4) c(x) = – 0.8x
**²**+ 400x – 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

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

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

**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

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

**19. The graph of y log _{2} 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)

**Algebra II (Common Core) 18 June 2018 Questions Answers Keys**

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