Algebra 28 January 2016 Questions Answer Keys

**The University Of The State Of New York**

Regents High School Examination

Algebra I

Thursday, January 28, 2016 — 1:15 to 4:15 p.m., only

Student Name _________________________________________________________

School Name __________________________________________________________

**1. In the function f(x) = (x – 2) ^{2} + 4, the minimum value occurs when x is**

- (1) – 2
- (2) 2
- (3) – 4
- (4) 4

**2. The graph below was created by an employee at a gas station.**

Which statement can be justified by using the graph?

- (1) If 10 gallons of gas was purchased, $35 was paid.
- (2) For every gallon of gas purchased, $3.75 was paid.
- (3) For every 2 gallons of gas purchased, $5.00 was paid.
- (4) If zero gallons of gas were purchased, zero miles were driven.

**3. For a recently released movie, the function y = 119.67(0.61) ^{x} models the revenue earned, y, in millions of dollars each week, x, for several weeks after its release.**

Based on the equation, how much more money, in millions of dollars, was earned in revenue for week 3 than for week 5?

- (1) 37.27
- (2) 27.16
- (3) 17.06
- (4) 10.11

**4. Given the following expressions:**

Which expression(s) result in an irrational number?

- (1) II, only
- (2) III, only
- (3) I, III, IV
- (4) II, III, IV

**5. Which inequality is represented by the graph below?**

- (1) y ≤ 2x – 3
- (2) y ≥ 2x – 3
- (3) y ≤ 3x + 2
- (4) y ≥ 3x + 2

**6. Michael borrows money from his uncle, who is charging him simple interest using the formula I = Prt. To figure out what the interest rate, r, is, Michael rearranges the formula to find r. His new formula is r equals**

**7. Which equation is equivalent to y – 34 = x(x – 12)?**

- (1) y = (x – 17)(x + 2)
- (2) y = (x – 17)(x – 2)
- (3) y = (x – 6)
^{2}+ 2 - (4) y = (x – 6)
^{2}– 2

**8. The equation A 1300(1.02) ^{7} is being used to calculate the amount of money in a savings account. What does 1.02 represent in this equation?**

- (1) 0.02% decay
- (2) 0.02% growth
- (3) 2% decay
- (4) 2% growth

**9. The zeros of the function f(x) = 2x ^{2} – 4x – 6 are**

- (1) 3 and – 1
- (2) 3 and 1
- (3) – 3 and 1
- (4) – 3 and – 1

**10. When (2x 3) ^{2} is subtracted from 5x^{2}, the result is**

- (1) x
^{2}– 12x – 9 - (2) x
^{2}– 12x + 9 - (3) x
^{2}+ 12x – 9 - (4) x
^{2}+ 12x + 9

**11. Joe has a rectangular patio that measures 10 feet by 12 feet. He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x. Which equation could be used to determine x?**

- (1) (10 + x)(12 + x) = 120
- (2) (10 + x)(12 + x) = 180
- (3) (15 + x)(18 + x) = 180
- (4) (15)(18) 120 + x
^{2}

**12. When factored completely, x ^{3} – 13x^{2} – 30x is**

- (1) x(x + 3)(x – 10)
- (2) x(x – 3)(x – 10)
- (3) x(x + 2)(x – 15)
- (4) x(x – 2)(x + 15)

**13. The table below shows the cost of mailing a postcard in different years. During which time interval did the cost increase at the greatest average rate?**

- (1) 1898–1971
- (2) 1971–1985
- (3) 1985–2006
- (4) 2006–2012

**14. When solving the equation x ^{2} – 8x – 7 = 0 by completing the square, which equation is a step in the process?**

- (1) (x – 4)
^{2}= 9 - (2) (x – 4)
^{2}= 23 - (3) (x – 8)
^{2}= 9 - (4) (x – 8)
^{2}= 23

**15. A construction company uses the function f(p), where p is the number of people working on a project, to model the amount of money it spends to complete a project. A reasonable domain for this function would be**

- (1) positive integers
- (2) positive real numbers
- (3) both positive and negative integers
- (4) both positive and negative real numbers

**16. Which function is shown in the table below?**

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

**17. Given the functions h(x) = 1/2x + 3 and j(x) = |x|, which value of x makes h(x) = j(x)?**

- (1) – 2
- (2) 2
- (3) 3
- (4) – 6

**18. Which recursively defined function represents the sequence 3, 7, 15, 31, …?**

- (1) f(1) = 3, f(n + 1) 2
*f*+ 3^{(n)} - (2) f(1) = 3, f(n + 1) 2
*f*– 1^{(n)} - (3) f(1) = 3, f(n + 1) 2f(n) + 1
- (4) f(1) = 3, f(n + 1) 3f(n) – 2

**19. The range of the function defined as y = 5 ^{x} is**

- (1) y < 0
- (2) y > 0
- (3) y ≤ 0
- (4) y ≥ 0

**20. The graph of y = f(x) is shown below**

What is the graph of y = f(x + 1) – 2?

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