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 No money is deposited or withdrawn after the initial amount is deposited.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) = 3^x
(2) F(x) = 3_x
(3) F(x) = 2^x 1
(4) F(x) = 2_x 3

Answer: (3) F(x) = 2^x 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.