# Algebra 28 January 2016

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
Answer: (2) 2

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.
Answer: (2) For every gallon of gas purchased, \$3.75 was paid.

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
Answer: (3) 17.06

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
Answer: (1) II, only

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
Answer: (2) y ≥ 2x – 3

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 Answer: (2) 3

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
Answer: (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
Answer: (4) 2% growth

9. The zeros of the function f(x) = 2x2 – 4x – 6 are

• (1) 3 and – 1
• (2) 3 and 1
• (3) – 3 and 1
• (4) – 3 and – 1
Answer: (1) 3 and – 1

10. When (2x 3)2 is subtracted from 5x2, the result is

• (1) x2 – 12x – 9
• (2) x2 – 12x + 9
• (3) x2 + 12x – 9
• (4) x2 + 12x + 9
Answer: (3) x2 + 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 + x2
Answer: (2) (10 + x)(12 + x) = 180

12. When factored completely, x3 – 13x2 – 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)
Answer: (3) 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
Answer: (4) 2006–2012

14. When solving the equation x2 – 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
Answer: (2) (x – 4)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
Answer: (1) positive integers

16. Which function is shown in the table below? • (1) f(x) 3x
• (2) f(x) = x + 3
• (3) f(x) = – x3
• (4) f(x) = 3x
Answer: (4) f(x) = 3x

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
Answer: (1) – 2

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

• (1) f(1) = 3, f(n + 1)  2 f(n) + 3
• (2) f(1) = 3, f(n + 1)  2 f(n) – 1
• (3) f(1) = 3, f(n + 1)  2f(n) + 1
• (4) f(1) = 3, f(n + 1)  3f(n) – 2
Answer: (3) f(1) = 3, f(n + 1)  2f(n) + 1

19. The range of the function defined as y = 5x is

• (1) y < 0
• (2) y > 0
• (3) y ≤ 0
• (4) y ≥ 0
Answer: (2) y > 0

20. The graph of y = f(x) is shown below What is the graph of y = f(x + 1) – 2? Answer: (2) 1

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