# Algebra 26 January 2015

Algebra 26 January 2015 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA I (Common Core)
Monday, January 26, 2015 — 1:15 to 4:15 p.m., only
Student Name:________________________________________________________
School Name: ________________________________________________________

1. The owner of a small computer repair business has one employee,  who is paid an hourly rate of \$22. The owner estimates his weekly profit using the function P(x) 8600 22x. In this function, x represents the number of.

• (1) computers repaired per week
• (2) hours worked per week
• (3) customers served per week
• (4) days worked per week
Answer: (2) hours worked per week

2. Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds. He converts his speed into miles per hour, as shown below.

Which ratio is incorrectly written to convert his speed?

3. Which equation has the same solutions as 2x2 + x – 3 = 0?

• (1) (2x – 1)(x + 3) = 0
• (2) (2x + 1)(x – 3) = 0
• (3) (2x – 3)(x + 1) =0
• (4) (2x + 3)(x – 1) = 0
Answer: (4) (2x + 3)(x – 1) = 0

4. Krystal was given \$3000 when she turned 2 years old. Her parents invested it at a 2% interest rate compounded annually. No deposits or withdrawals were made. Which expression can be used to determine how much money Krystal had in the account when she turned 18?

• (1) 3000(1 + 0.02)16
• (2) 3000(1 – 0.02)16
• (3) 3000(1 + 0.02)18
• (4) 3000(1 – 0.02)18

5. Which table of values represents a linear relationship?

6. Which domain would be the most appropriate set to use for a function that predicts the number of household online-devices in terms of the number of people in the household?

• (1) integers
• (2) whole numbers
• (3) irrational numbers
• (4) rational numbers
• (1) x > 9
• (2) x >  3/5
• (3) x < 9
• (4) x < – 3/5

8. The value in dollars, v(x), of a certain car after x years is represented by the equation v(x) = 25,000(0.86)x. To the nearest dollar, how much more is the car worth after 2 years than after 3 years?

• (1) 2589
• (2) 6510
• (3) 15,901
• (4) 18,490

9. Which function has the same y-intercept as the graph below?

• (1) y = 12 – 6x/4
• (2) 27 + 3y = 6x
• (3) 6y + x = 18
• (4) y + 3 = 6x
Answer: (4) y + 3 = 6x

10. Fred is given a rectangular piece of paper. If the length of Fred’s computations. piece of paper is represented by 2x – 6 and the width is represented by 3x – 5, then the paper has a total area represented by

• (1) 5x – 11
• (2) 6x2 – 28x + 30
• (3) 10x – 22
• (4) 6x2 – 6x – 11
Answer: (2) 6x2 – 28x + 30

11. The graph of a linear equation contains the points (3,11) and (-2,1). Which point also lies on the graph?

• (1) (2,1)
• (2) (2,4)
• (3) (2,6)
• (4) (2,9)

12. How does the graph of f(x) = 3(x – 2)2+ 1 compare to the graph of g(x) x2?

• (1) The graph of f(x) is wider than the graph of g(x), and its vertex is moved to the left 2 units and up 1 unit.
• (2) The graph of f(x) is narrower than the graph of g(x), and its vertex is moved to the right 2 units and up 1 unit.
• (3) The graph of f(x) is narrower than the graph of g(x), and its vertex is moved to the left 2 units and up 1 unit.
• (4) The graph of f(x) is wider than the graph of g(x), and its vertex is moved to the right 2 units and up 1 unit.
Answer: (2) The graph of f(x) is narrower than the graph of g(x), and its vertex is moved to the right 2 units and up 1 unit.

13. Connor wants to attend the town carnival. The price of admission to the carnival is \$4.50, and each ride costs an additional 79 cents. If he can spend at most \$16.00 at the carnival, which inequality can be used to solve for r, the number of rides Connor can go on, and what is the maximum number of rides he can go on?

• (1) 0.79 + 4.50r ≤ 16.00; 3 rides
• (2) 0.79 + 4.50r ≤ 16.00; 4 rides
• (3) 4.50 + 0.79r ≤ 16.00; 14 rides
• (4) 4.50 + 0.79r ≤ 16.00; 15 rides
Answer: (3) 4.50 + 0.79r ≤ 16.00; 14 rides

14. Corinne is planning a beach vacation in July and is analyzing the daily high temperatures for her potential destination. She would like to choose a destination with a high median temperature and a small interquartile range. She constructed box plots shown in the diagram below

Which destination has a median temperature above 80 degrees and the smallest interquartile range?

• (1) Ocean Beach
• (2) Whispering Palms
• (3) Serene Shores
• (4) Pelican Beach

15. Some banks charge a fee on savings accounts that are left inactive for an extended period of time. The equation y = 5000(0.98)x represents the value, y, of one account that was left inactive for a period of x years.

What is the y-intercept of this equation and what does it represent?

• (1) 0.98, the percent of money in the account initially
• (2) 0.98, the percent of money in the account after x years
• (3) 5000, the amount of money in the account initially
• (4) 5000, the amount of money in the account after x years
Answer: (3) 5000, the amount of money in the account initially

16. The equation for the volume of a cylinder is V = πr2h. The positive value of r, in terms of h and V, is

17. Which equation has the same solutions as x2 + 6x – 7 = 0?

• (1) (x + 3)2 = 2
• (2) (x – 3)2 = 2
• (3) (x – 3)2 = 16
• (4) (x + 3)2 = 16
Answer: (4) (x + 3)2 = 16

18. Two functions, y = |x = 3| and 3x + 3y = 27, are graphed on the same set of axes. Which statement is true about the solution to the system of equations?

• (1) (3,0) is the solution to the system because it satisfies the equation y = |x – 3|.
• (2) (9,0) is the solution to the system because it satisfies the equation 3x + 3y = 27.
• (3) (6,3) is the solution to the system because it satisfies both equations.
• (4) (3,0), (9,0), and (6,3) are the solutions to the system of equations because they all satisfy at least one of the equations.
Answer: (3) (6,3) is the solution to the system because it satisfies both equations.

19. Miriam and Jessica are growing bacteria in a laboratory. Miriam uses the growth function f(t) = n2t while Jessica uses the function g(t) = n4t , where n represents the initial number of bacteria and t is the time, in hours. If Miriam starts with 16 bacteria, how many bacteria should Jessica start with to achieve the same growth over time?

• (1) 32
• (2) 16
• (3) 8
• (4) 4

20. If a sequence is defined recursively by f(0) = 2 and f(n + 1) = -2f(n) + 3 for n ≥ 0, then f(2) is equal to

• (1) 1
• (2) -11
• (3) 5
• (4) 17