Algebra 3 June 2014

Algebra 3 June 2014 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA I (Common Core)
Tuesday, June 3, 2014 — 9:15 a.m. to 12:15 p.m., only
Student Name:________________________________________________________
School Name:_________________________________________________________

1. When solving the equation 4(3x2 + 2) – 9 = 8x2 + 7, Emily wrote 4(3x2 + 2) = 8x2 + 16 as her first step. Which property justifies Emily’s first step?

  • (1) addition property of equality
  • (2) commutative property of addition
  • (3) multiplication property of equality
  • (4) distributive property of multiplication over addition
Answer: (1) addition property of equality 

2. Officials in a town use a function, C, to analyze traffic patterns. C(n) represents the rate of traffic through an intersection where n is the number of observed vehicles in a specified time interval. What would be the most appropriate domain for the function?

  • (1) {… – 2,  – 1, 0, 1, 2, 3, …}
  • (2) {- 2, – 1, 0, 1, 2, 3}
  • (3) {0, 1 /2 , 1, 1 /2 , 2, 1 /2 }
  • (4) {0, 1, 2, 3, …}
Answer: (4) {0, 1, 2, 3, …} 

3. If A = 3x2 + 5x – 6 and B = – 2x2 – 6x + 7, then A – B equals

  • (1) – 5x2 – 11x + 13
  • (2) 5x2 + 11x – 13
  • (3) – 5x2 – x + 1
  • (4) 5x2 – x + 1
Answer: (1) 5x2 + 11x – 13 

4. Given: y + x >2  y ≤ 3x – 2

Which graph shows the solution of the given set of inequalities?

Answer: (2)  
  • (1) 8.25
  • (2) 8.89
  • (3) 19.25
  • (4) 44.92
Answer: (1) 8.25 

6. The table below shows the average yearly balance in a savings  account where interest is compounded annually. No money is deposited or withdrawn after the initial amount is deposited.

Which type of function best models the given data?

  • (1) linear function with a negative rate of change
  • (2) linear function with a positive rate of change
  • (3) exponential decay function
  • (4) exponential growth function
Answer: (4) exponential growth function 

7. A company that manufactures radios first pays a start-up cost, and then spends a certain amount of money to manufacture each radio. If the cost of manufacturing r radios is given by the function c(r) = 5.25r + 125, then the value 5.25 best represents

  • (1) the start-up cost
  • (2) the profit earned from the sale of one radio
  • (3) the amount spent to manufacture each radio
  • (4) the average number of radios manufactured
Answer: (3) the amount spent to manufacture each radio 

8. Which equation has the same solution as x2 – 6x – 12 = 0?

  • (1) (x + 3)2 = 21
  • (2) (x – 3)2 = 21
  • (3) (x + 3)2 = 3
  • (4) (x – 3)2 = 3
Answer: (2) (x – 3)2 = 21 

9. A ball is thrown into the air from the edge of a 48-foot-high cliff so  that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.

For which interval is the ball’s height always decreasing?

  • (1) 0 ≤ x ≤ 2.5
  • (2) 0 < x < 5.5
  • (3) 2.5 < x < 5.5
  • (4) x ≥ 2
Answer: (3) 2.5 < x < 5.5 

10. What are the roots of the equation x2 + 4x – 16 = 0?

  • (1) 2 ± 2√5
  • (2) – 2 ± 2√5
  • (3) 2 ± 4√5
  • (4) – 2 ± 4√5
Answer: (2) – 2 ± 2√5 

11. What is the correlation coefficient of the linear fit of the data shown  below, to the nearest hundredth?

  • (1) 1.00
  • (2) 0.93
  • (3) – 0.93
  • (4) – 1.00
Answer: (3) – 0.93 

12. Keith determines the zeros of the function f(x) to be – 6 and 5. What could be Keith’s function?

  • (1) f(x) = (x + 5)(x + 6)
  • (2) f(x) = (x + 5)(x – 6)
  • (3) f(x) = (x – 5)(x + 6)
  • (4) f(x) = (x – 5)(x – 6)
Answer: (3) f(x) = (x – 5)(x + 6) 

13. Given: L = √2
                    M = 3√3
                    N = √16
                    P = √9
Which expression results in a rational number?

  • (1) L + M
  • (2) M + N
  • (3) N + P
  • (4) P + L
Answer: (3) N + P 

14. Which system of equations has the same solution as the system  below?

2x + 2y = 16
3x – y = 4

  • (1) 2x + 2y = 16
    6x – 2y = 4
  • (2) 2x + 2y = 16
    6x – 2y = 8
  • (3) x + y = 16
    3x – y = 4
  • (4) 6x + 6y = 48
    6x + 2y = 8
Answer: (2) 2x + 2y = 16 6x – 2y = 8 

15. The table below represents the function F.

The equation that represents this function is

  • (1) F(x) = 3x
  • (2) F(x) = 3x
  • (3) F(x) = 2x 1
  • (4) F(x) = 2x 3
Answer: (3) F(x) = 2x 1 

16. John has four more nickels than dimes in his pocket, for a total of $1.25. Which equation could be used to determine the number of dimes, x, in his pocket?

  • (1) 0.10(x + 4) + 0.05(x) = $1.25
  • (2) 0.05(x + 4) + 0.10(x) = $1.25
  • (3) 0.10(4x) + 0.05(x) = $1.25
  • (4) 0.05(4x) + 0.10(x) = $1.25
Answer: (2) 0.05(x + 4) + 0.10(x) = $1.25 
  • (1) f(x) < 0
  • (2) f(x) > 0
  • (3) If x < 0, then f(x) < 0.
  • (4) If x > 0, then f(x) > 0.
Answer: (4) If x > 0, then f(x) > 0. 

18. The Jamison family kept a log of the distance they traveled during a  trip, as represented by the graph below.

During which interval was their average speed the greatest?

  • (1) the first hour to the second hour
  • (2) the second hour to the fourth hour
  • (3) the sixth hour to the eighth hour
  • (4) the eighth hour to the tenth hour
Answer: (1) the first hour to the second hour 

19. Christopher looked at his quiz scores shown below for the first and second semester of his Algebra class.

Semester 1: 78, 91, 88, 83, 94
Semester 2: 91, 96, 80, 77, 88, 85, 92

Which statement about Christopher’s performance is correct?

  • (1) The interquartile range for semester 1 is greater than the interquartile range for semester 2.
  • (2) The median score for semester 1 is greater than the median score for semester 2.
  • (3) The mean score for semester 2 is greater than the mean score for semester 1.
  • (4) The third quartile for semester 2 is greater than the third quartile for semester 1.
Answer: (3) The mean score for semester 2 is greater than the mean score for semester 1. 

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

Which point could be used to find f(2)?

  • (1) A
  • (2) B
  • (3) C
  • (4) D
Answer: (1) A 

Download Algebra 3 June 2014 Questions Answers Keys

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