Integrated algebra 26 January 2011

Integrated algebra 26 January 2011 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
INTEGRATED ALGEBRA
Wednesday, January 26, 2011— 1:15 to 4:15 p.m., only
Student Name: ________________________________________________________
School Name: _________________________________________________________

1. Given:

X = {1, 2, 3, 4}
Y = {2, 3, 4, 5}
Z = {3, 4, 5, 6}

What is the intersection of sets X, Y, and Z ?

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

Answer: (1) {3, 4}

2. Which graph could be used to find the solution of the system of equations y = 2x + 6 and y = x² + 4x + 3?

Answer: (4)

3. What is the relationship between the independent and dependent variables in the scatter plot shown below?

(1) undefined correlation
(2) negative correlation
(3) positive correlation
(4) no correlation

Answer: (3) positive correlation

4. Tim ate four more cookies than Alice. Bob ate twice as many cookies as Tim. If x represents the number of cookies Alice ate, which expression represents the number of cookies Bob ate?

(1) 2 + (x + 4)
(2) 2x + 4
(3) 2(x + 4)
(4) 4(x + 2)

Answer: (3) 2(x + 4)

5. Which relation is a function?

(1) {(³ ⁄₄,0), (0,1), (³ ⁄₄,2)}
(2) {(−2,2), (−½,1), (−2,4)}
(3) {(−1,4), (0,5), (0,4)}
(4) {(2,1), (4,3), (6,5)}

Answer: (4) {(2,1), (4,3), (6,5)}

6. What is the value of x in the equation 2(x − 4) = 4(2x + 1)?

(1) −2
(2) 2
(3) −½
(4) ½

Answer: (1) −2

7. The rectangle shown below has a diagonal of 18.4 cm and a width of 7 cm.

To the nearest centimeter, what is the length, x, of the rectangle?

(1) 11
(2) 17
(3) 20
(4) 25

Answer: (2) 17

8. When a³ − 4a is factored completely, the result is

(1) (a − 2)(a + 2)
(2) a(a − 2)(a + 2)
(3) a² (a − 4)
(4) a (a − 2)²

Answer: (2) a(a − 2)(a + 2)

9. Which ratio represents sin x in the right triangle shown below?

Answer: (1)

10. What is the value of the expression (a³ + b⁰)² when a = −2 and b = 4?

(1) 64
(2) 49
(3) −49
(4) −64

Answer: (2) 49

11. A student correctly graphed the parabola shown below to solve a given quadratic equation.

What are the roots of the quadratic equation associated with this graph?

(1) −6 and 3
(2) −6 and 0
(3) −3 and 2
(4) −2 and 3

Answer: (4) −2 and 3

Answer: (1)

13. What is the range of the data represented in the box-and-whisker plot shown below?

(1) 40
(2) 45
(3) 60
(4) 100

Answer: (3) 60

14. Which equation illustrates the associative property?

(1) x + y + z = x + y + z
(2) x(y + z) = xy + xz
(3) x + y + z = z + y + x
(4) (x + y) + z = x + (y + z)

Answer: (4) (x + y) + z = x + (y + z)

15. Josh and Mae work at a concession stand. They each earn $8 per hour. Josh worked three hours more than Mae. If Josh and Mae earned a total of $120, how many hours did Josh work?

(1) 6
(2) 9
(3) 12
(4) 15

Answer: (2) 9

16. Which data set describes a situation that could be classified as quantitative?

(1) the phone numbers in a telephone book
(2) the addresses for students at Hopkins High School
(3) the zip codes of residents in the city of Buffalo, New York
(4) the time it takes each of Mr. Harper’s students to complete a test

Answer: (4) the time it takes each of Mr. Harper’s students to complete a test

17. Which is the graph of y = x + 2?

Answer: (3)

18. Sam’s grades on eleven chemistry tests were 90, 85, 76, 63, 94, 89, 81, 76, 78, 69, and 97. Which statement is true about the measures of central tendency?