Integrated algebra 16 June 2011

Integrated algebra 16 June 2011 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
INTEGRATED ALGEBRA
Thursday, June 16, 2011—1:15 to 4:15 p.m., only
Student Name: ________________________________________________________
School Name: _________________________________________________________

1. The expression x² − 36y² is equivalent to

(1) (x − 6y)(x − 6y)
(2) (x − 18y)(x − 18y)
(3) (x + 6y)(x − 6y)
(4) (x + 18y)(x − 18y)

Answer: (3) (x + 6y)(x − 6y)

2. The legs of an isosceles right triangle each measure 10 inches. What is the length of the hypotenuse of this triangle, to the nearest tenth of an inch?

(1) 6.3
(2) 7.1
(3) 14.1
(4) 17.1

Answer: (2) 7.1

(1) −4w⁶
(2) −4w³y
(3) 9w⁶
(4) 9w³y

Answer: (1) −4w⁶

4. The spinner shown in the diagram below is divided into six equal sections.

Which outcome is least likely to occur on a single spin?

(1) an odd number
(2) a prime number
(3) a perfect square
(4) a number divisible by 2

Answer: (3) a perfect square

5. What are the factors of the expression x² + x − 20?

(1) (x + 5) and (x + 4)
(2) (x + 5) and (x − 4)
(3) (x − 5) and (x + 4)
(4) (x − 5) and (x − 4)

Answer: (2) (x + 5) and (x − 4)

6. What is 3 √250 expressed in simplest radical form?

(1) 5 √10
(2) 8 √10
(3) 15 √10
(4) 75 √10

Answer: (3) 15 √10

7. A survey is being conducted to determine which school board candidate would best serve the Yonkers community. Which group, when randomly surveyed, would likely produce the most bias?

(1) 15 employees of the Yonkers school district
(2) 25 people driving past Yonkers High School
(3) 75 people who enter a Yonkers grocery store
(4) 100 people who visit the local Yonkers shopping mall

Answer: (1) 15 employees of the Yonkers school district

8. An 8-foot rope is tied from the top of a pole to a stake in the ground, as shown in the diagram below.

If the rope forms a 57° angle with the ground, what is the height of the pole, to the nearest tenth of a foot?

(1) 4.4
(2) 6.7
(3) 9.5
(4) 12.3

Answer: (2) 6.7

9. How many different ways can five books be arranged on a shelf ?

(1) 5
(2) 15
(3) 25
(4) 120

Answer: (4) 120

10. What is the slope of the line passing through the points (−2,4) and (3,6)?

Answer: (3)

11. Which type of function is represented by the graph shown below?

(1) absolute value
(2) exponential
(3) linear
(4) quadratic

Answer: (4) quadratic

12. Which equation represents a line parallel to the y-axis?

(1) y = x
(2) y = 3
(3) x = −y
(4) x = −4

Answer: (4) x = −4

13. Melissa graphed the equation y = x² and Dave graphed the equation y = −3x² on the same coordinate grid. What is the relationship between the graphs that Melissa and Dave drew?

(1) Dave’s graph is wider and opens in the opposite direction from Melissa’s graph.
(2) Dave’s graph is narrower and opens in the opposite direction from Melissa’s graph.
(3) Dave’s graph is wider and is three units below Melissa’s graph.
(4) Dave’s graph is narrower and is three units to the left of Melissa’s graph.

Answer: (2) Dave’s graph is narrower and opens in the opposite direction from Melissa’s graph.

14. In right triangle ABC shown below, AB = 18.3 and BC = 11.2.

What is the measure of ∠A, to the nearest tenth of a degree?

(1) 31.5
(2) 37.7
(3) 52.3
(4) 58.5

Answer: (4) 225

15. The maximum height and speed of various roller coasters in North America are shown in the table below.

Which graph represents a correct scatter plot of the data?

Answer: (2)

16. Which set of ordered pairs represents a function?

(1) {(0,4), (2,4), (2,5)}
(2) {(6,0), (5,0), (4,0)}
(3) {(4,1), (6,2), (6,3), (5,0)}
(4) {(0,4), (1,4), (0,5), (1,5)}

Answer: (2) {(6,0), (5,0), (4,0)}

17. A hiker walked 12.8 miles from 9:00 a.m. to noon. He walked an additional 17.2 miles from 1:00 p.m. to 6:00 p.m. What is his average rate for the entire walk, in miles per hour?

(1) 3.75
(2) 3.86
(3) 4.27
(4) 7.71

Answer: (1) 3.75

18. Which ordered pair is a solution of the system of equations y = x + 3 and y = x² − x?

(1) (6,9)
(2) (3,6)
(3) (3,−1)
(4) (2,5)

Answer: (2) (3,6)

19. Which verbal expression can be represented by 2(x − 5)?

(1) 5 less than 2 times x
(2) 2 multiplied by x less than 5
(3) twice the difference of x and 5
(4) the product of 2 and x, decreased by 5

Answer: (3) twice the difference of x and 5

20. The dimensions of a rectangle are measured to be 12.2 inches by 11.8 inches. The actual dimensions are 12.3 inches by 11.9 inches. What is the relative error, to the nearest ten-thousandth, in calculating the area of the rectangle?