# Algebra 17 June 2015

Algebra 17 June 2015 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA I (Common Core)
Wednesday, June 17, 2015 — 1:15 to 4:15 p.m., only
Student Name:________________________________________________________
School Name: _________________________________________________________

1. The cost of airing a commercial on television is modeled by the computations. function C(n) = 110n + 900, where n is the number of times the commercial is aired. Based on this model, which statement is true?

• (1) The commercial costs \$0 to produce and \$110 per airing up to \$900.
• (2) The commercial costs \$110 to produce and \$900 each time it is aired.
• (3) The commercial costs \$900 to produce and \$110 each time it is aired.
• (4) The commercial costs \$1010 to produce and can air an unlimited number of times.
Answer: (3) The commercial costs \$900 to produce and \$110 each time it is aired.

2. The graph below represents a jogger’s speed during her 20-minute jog around her neighborhood.

Which statement best describes what the jogger was doing during the 9–12 minute interval of her jog?

• (1) She was standing still.
• (2) She was increasing her speed.
• (3) She was decreasing her speed.
• (4) She was jogging at a constant rate.
Answer: (4) She was jogging at a constant rate.

3. If the area of a rectangle is expressed as x4 – 9y2 , then the product of the length and the width of the rectangle could be expressed as

• (1) (x – 3y)(x + 3y)
• (2) (x2 – 3y)(x2 + 3y)
• (3) (x2 – 3y)(x2 – 3y)
• (4) (x4 + y)(x – 9y)
Answer: (2) (x2 – 3y)(x2 + 3y)

4. Which table represents a function?

5. Which inequality is represented in the graph below?

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

6. Mo’s farm stand sold a total of 165 pounds of apples and peaches. She sold apples for \$1.75 per pound and peaches for \$2.50 per pound. If she made \$337.50, how many pounds of peaches did she sell?

• (1) 11
• (2) 18
• (3) 65
• (4) 100

7. Morgan can start wrestling at age 5 in Division 1. He remains in that division until his next odd birthday when he is required to move up to the next division level. Which graph correctly represents this information?

8. Which statement is not always true?

• (1) The sum of two rational numbers is rational.
• (2) The product of two irrational numbers is rational.
• (3) The sum of a rational number and an irrational number is irrational.
• (4) The product of a nonzero rational number and an irrational number is irrational.
Answer: (2) The product of two irrational numbers is rational.

9. The graph of the function fx = √x + 4 is shown below.

The domain of the function is

• (1) { x | x > 0}
• (2) { x | x ≥ 0}
• (3) { x | x > – 4}
• (4) { x | x ≥ -4}
Answer: (4) { x | x ≥ -4}

10. What are the zeros of the function f(x) = x2 – 13x – 30?

• (1) – 10 and 3
• (2) 10 and – 3
• (3) – 15 and 2
• (4) 15 and – 2
Answer: (4) 15 and – 2

11. Joey enlarged a 3-inch by 5-inch photograph on a copy machine. He enlarged it four times. The table below shows the area of the photograph after each enlargement.

What is the average rate of change of the area from the original photograph to the fourth enlargement, to the nearest tenth?

• (1) 4.3
• (2) 4.5
• (3) 5.4
• (4) 6.0

12. Which equation(s) represent the graph below?

I         y = (x + 2)(x2 – 4x – 12)
II       y = (x – 3)(x2 + x – 2)
III     y = (x – 1)(x2 – 5x – 6)

• (1) I, only
• (2) II, only
• (3) I and II
• (4) II and III

13. A laboratory technician studied the population growth of a colony of  bacteria. He recorded the number of bacteria every other day, as shown in the partial table below.

Which function would accurately model the technician’s data?

• (1) f(t) = 25t
• (2) f(t) = 25t1
• (3) f(t) = 25t
• (4) f(t) = 25(t + 1)

14. Which quadratic function has the largest maximum?

(1) h(x) = (3 – x)(2 + x)                    (3)  k(x) = – 5x2 – 12x + 4

Answer: (3)  k(x) = – 5x2 – 12x + 4

15. If f(x) = 3x and g(x) = 2x + 5, at which value of x is f(x) < g(x)?

• (1) -1
• (2) 2
• (3) -3
• (4) 4

16. Beverly did a study this past spring using data she collected from a cafeteria. She recorded data weekly for ice cream sales and soda sales. Beverly found the line of best fit and the correlation coefficient, as shown in the diagram below.

Given this information, which statement(s) can correctly be concluded?

I.        Eating more ice cream causes a person to become thirsty.
II.      Drinking more soda causes a person to become hungry.
III.    There is a strong correlation between ice cream sales and soda sales.

• (1) I, only
• (2) III, only
• (3) I and III
• (4) II and III

17. The function V(t) = 1350(1.017)t represents the value V(t), in dollars, of a comic book t years after its purchase. The yearly rate of appreciation of the comic book is

• (1) 17%
• (2) 1.7%
• (3) 1.017%
• (4) 0.017%
• (1) x2 + 5x + 7 = 0
• (2) x2 + 5x + 3 = 0
• (3) x2 – 5x + 7 = 0
• (4) x2 – 5x + 3 = 0
Answer: (4) x2 – 5x + 3 = 0

20. The table below shows the annual salaries for the 24 members of a professional sports team in terms of millions of dollars.

The team signs an additional player to a contract worth 10 million dollars per year. Which statement about the median and mean is true?

• (1) Both will increase.
• (2) Only the median will increase.
• (3) Only the mean will increase.
• (4) Neither will change.
Answer: (3) Only the mean will increase.