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 x ^{2} − 36y^{2} is equivalent to**

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

**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

- (1) −4w
^{6} - (2) −4w
^{3}y - (3) 9w
^{6} - (4) 9w
^{3}y

**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

** 5. What are the factors of the expression x ^{2} + 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)

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

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

** 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

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

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

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

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

- (1) absolute value
- (2) exponential
- (3) linear
- (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

** 13. Melissa graphed the equation y = x ^{2} and Dave graphed the equation y = −3x^{2} 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.

** 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

** 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?

** 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)}

** 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

**18. Which ordered pair is a solution of the system of equations y = x + 3 and y = x ^{2} − x?**

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

** 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

** 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?**

- (1) 0.0168
- (2) 0.0167
- (3) 0.0165
- (4) 0.0164

**Integrated algebra 16 June 2011 Questions Answers Keys**

Integrated algebra Examination Question |

Scoring Key and Rating Guide |

**See also: **