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(3x ^{2} + 2) – 9 = 8x^{2} + 7, Emily wrote 4(3x^{2} + 2) = 8x^{2} + 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

**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, …}

**3. If A = 3x ^{2} + 5x – 6 and B = – 2x^{2} – 6x + 7, then A – B equals**

- (1) – 5x
^{2}– 11x + 13 - (2) 5x
^{2}+ 11x – 13 - (3) – 5x
^{2}– x + 1 - (4) 5x
^{2}– x + 1

**4. Given: y + x >2 y ≤ 3x – 2**

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

- (1) 8.25
- (2) 8.89
- (3) 19.25
- (4) 44.92

**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 No money is deposited or withdrawn after the initial amount is deposited.**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

**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

**8. Which equation has the same solution as x ^{2} – 6x – 12 = 0?**

- (1) (x + 3)
^{2}= 21 - (2) (x – 3)2 = 21
- (3) (x + 3)
^{2}= 3 - (4) (x – 3)2 = 3

**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

**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

**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

**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)

**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

**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

**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

**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

- (1) f(x) < 0
- (2) f(x) > 0
- (3) If x < 0, then f(x) < 0.
- (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

**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.

**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

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