# Algebra 13 August 2014

Algebra 13 August 2014 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA I (Common Core)
Wednesday, August 13, 2014 — 8:30 to 11:30 a.m., only
Student Name:________________________________________________________
School Name: ________________________________________________________

1. Which statement is not always true?

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

2. A satellite television company charges a one-time installation fee and a monthly service charge. The total cost is modeled by the function y 40 90x. Which statement represents the meaning of each part of the function?

• (1) y is the total cost, x is the number of months of service, \$90 is the installation fee, and \$40 is the service charge per month.
• (2) y is the total cost, x is the number of months of service, \$40 is the installation fee, and \$90 is the service charge per month.
• (3) x is the total cost, y is the number of months of service, \$40 is the installation fee, and \$90 is the service charge per month.
• (4) x is the total cost, y is the number of months of service, \$90 is the installation fee, and \$40 is the service charge per month.
Answer: (2) y is the total cost, x is the number of months of service, \$40 is the installation fee, and \$90 is the service charge per month.

3. If 4x2 – 100 = 0, the roots of the equation are

• (1) – 25 and 25
• (2) – 25, only
• (3) – 5 and 5
• (4) – 5, only
Answer: (3) – 5 and 5

4. Isaiah collects data from two different companies, each with four  employees. The results of the study, based on each worker’s age and salary, are listed in the tables below

Which statement is true about these data?

• (1) The median salaries in both companies are greater than \$37,000.
• (2) The mean salary in company 1 is greater than the mean salary in company 2.
• (3) The salary range in company 2 is greater than the salary range in company 1.
• (4) The mean age of workers at company 1 is greater than the mean age of workers at company 2.
Answer: (3) The salary range in company 2 is greater than the salary range in company 1.

5. Which point is not on the graph represented by y = x2 + 3x – 6?

• (1) (- 6,12)
• (2) (- 4,- 2)
• (3) (2,4)
• (4) (3,- 6)

6. A company produces x units of a product per month, where C(x)  represents the total cost and R(x) represents the total revenue for the month. The functions are modeled by C(x) = 300x + 250 and R(x) = – 0.5x2 + 800x – 100. The profit is the difference between revenue and cost where P(x) = R(x) – C(x). What is the total profit, P(x), for the month?

• (1) P(x) = – 0.5x2 + 500x – 150
• (2) P(x) = – 0.5x2 + 500x – 350
• (3) P(x) = – 0.5x2 – 500x + 350
• (4) P(x) = – 0.5x2 + 500x + 350
Answer: (2) P(x) = – 0.5x2 + 500x – 350

7. What is one point that lies in the solution set of the system of inequalities graphed below?

• (1) (7,0)
• (2) (3,0)
• (3) (0,7)
• (4) (- 3,5)

8. The value of the x-intercept for the graph of 4x – 5y = 40 is

• (1) 10
• (2) – 4/5
• (3) – 4/ 5
• (4) – 8

9. Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy’s age, j, if he is the younger man?

• (1) j2 + 2 = 783
• (2) j2 – 2 = 783
• (3) j2 + 2j = 783
• (4) j2 – 2j = 783
Answer: (3) j2 + 2j = 783

10. A population that initially has 20 birds approximately doubles every 10 years. Which graph represents this population growth?

11. Let f be a function such that f(x) = 2x – 4 is defined on the domain 2 ≤ x ≤ 6. The range of this function is

• (1) 0 ≤ y ≤ 8
• (2) 0 ≤ y < ∞
• (3) 2 ≤ y ≤ 6
• (4) – ∞ < y < ∞
Answer: (1) 0 ≤ y ≤ 8

12. Which situation could be modeled by using a linear function?

• (1) a bank account balance that grows at a rate of 5% per year, compounded annually
• (2) a population of bacteria that doubles every 4.5 hours
• (3) the cost of cell phone service that charges a base amount plus 20 cents per minute
• (4) the concentration of medicine in a person’s body that decays by a factor of one-third every hour
Answer: (3) the cost of cell phone service that charges a base amount plus 20 cents per minute

13. Which graph shows a line where each value of y is three more than half of x?

14. The table below shows the average diameter of a pupil in a person’s  eye as he or she grows older

What is the average rate of change, in millimeters per year, of a person’s pupil diameter from age 20 to age 80?

• (1) 2.4
• (2) 0.04
• (3) -2.4
• (4) -0.04

15. Which expression is equivalent to x4 – 12x2 + 36?

• (1) (x2 – 6)(x2 – 6)
• (2) (x2 + 6)(x2 + 6)
• (3) (6 – x2)(6 + x2)
• (4) (x2 + 6)(x2 – 6)
Answer: (1) (x2 – 6)(x2 – 6)

16. The third term in an arithmetic sequence is 10 and the fifth term is 26. If the first term is a1, which is an equation for the nth term of this sequence?

• (1) an = 8n +10
• (2) an = 8n – 14
• (3) an = 16n + 10
• (4) an = 16n – 38
Answer: (2) an = 8n – 14

17. The graph of the equation y = ax2 is shown below.

• (1) wider and opens downward
• (2) wider and opens upward
• (3) narrower and opens downward
• (4) narrower and opens upward
Answer: (1) wider and opens downward

18. The zeros of the function f(x) = (x + 2)2 – 25 are

• (1) – 2 and 5
• (2) – 3 and 7
• (3) – 5 and 2
• (4) – 7 and 3
Answer: (4) – 7 and 3

19. During the 2010 season, football player McGee’s earnings, m, were 0.005 million dollars more than those of his teammate Fitzpatrick’s earnings, f. The two players earned a total of 3.95 million dollars. Which system of equations could be used to determine the amount each player earned, in millions of dollars?

• (1) m + f = 3.95
m + 0.005 = f
• (2) m – 3.95 = f
f +0.005 = m
• (3) f – 3.95 = m
m + 0.005 = f
• (4) m + f = 3.95
f + 0.005 = m
Answer: (4) m + f = 3.95  f + 0.005 = m
• (1) 4
• (2) 6
• (3) 8
• (4) 11