# Integrated algebra 17 August 2011

Integrated algebra 17 August 2011 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
integrated algebra
Wednesday, August 17, 2011—8:30 to 11:30 a.m., only
Student Name: ________________________________________________________
School Name: _________________________________________________________

1. The number of calories burned while jogging varies directly with the number of minutes spent jogging. If George burns 150 calories by jogging for 20 minutes, how many calories does he burn by jogging for 30 minutes?

• (1) 100
• (2) 180
• (3) 200
• (4) 225

2. The scatter plot below represents the relationship between the number of peanuts a student eats and the student’s bowling score.

Which conclusion about the scatter plot is valid?

• (1) There is almost no relationship between eating peanuts and bowling score.
• (2) Students who eat more peanuts have higher bowling scores.
• (3) Students who eat more peanuts have lower bowling scores.
• (4) No bowlers eat peanuts.
Answer: (1) There is almost no relationship between eating peanuts and bowling score.

3. If the universal set is {pennies, nickels, dimes, quarters}, what is the complement of the set {nickels}?

• (1) { }
• (2) {pennies, quarters}
• (3) {pennies, dimes, quarters}
• (4) {pennies, nickels, dimes, quarters}

4. Which situation does not describe a causal relationship?

• (1) The higher the volume on a radio, the louder the sound will be.
• (2) The faster a student types a research paper, the more pages the paper will have.
• (3) The shorter the distance driven, the less gasoline that will be used.
• (4) The slower the pace of a runner, the longer it will take the runner to finish the race.
Answer: (2) The faster a student types a research paper, the more pages the paper will have.

5. A cylinder has a diameter of 10 inches and a height of 2.3 inches. What is the volume of this cylinder, to the nearest tenth of a cubic inch?

• (1) 72.3
• (2) 83.1
• (3) 180.6
• (4) 722.6

6. Based on the box-and-whisker plot below, which statement is false?

• (1) The median is 7.
• (2) The range is 12.
• (3) The first quartile is 4.
• (4) The third quartile is 11.
Answer: (2) The range is 12.

7. The ninth grade class at a local high school needs to purchase a park permit for \$250.00 for their upcoming class picnic. Each ninth grader attending the picnic pays \$0.75. Each guest pays \$1.25. If 200 ninth graders attend the picnic, which inequality can be used to determine the number of guests, x, needed to cover the cost of the permit?

(1) 0.75x − (1.25)(200) ≥ 250.00
(2) 0.75x + (1.25)(200) ≥ 250.00
(3) (0.75)(200) − 1.25x ≥ 250.00
(4) (0.75)(200) + 1.25x ≥ 250.00

Answer: (4) (0.75)(200) + 1.25x ≥ 250.00

8. Which equation represents the line that passes through the point (1,5) and has a slope of −2?

• (1) y = −2x + 7
• (2) y = −2x + 11
• (3) y = 2x − 9
• (4) y = 2x + 3
Answer: (1) y = −2x + 7

9. What is the solution of the system of equations 2x − 5y = 11 and −2x + 3y = −9?

• (1) (−3,−1)
• (2) (−1,3)
• (3) (3,−1)
• (4) (3,1)

10. Which algebraic expression represents 15 less than x divided by 9?

11. What are the vertex and the axis of symmetry of the parabola shown in the graph below?

• (1) vertex: (1,6); axis of symmetry: y = 1
• (2) vertex: (1,6); axis of symmetry: x = 1
• (3) vertex: (6,1); axis of symmetry: y = 1
• (4) vertex: (6,1); axis of symmetry: x = 1
Answer: (2) vertex: (1,6); axis of symmetry: x = 1

12. The diagram below shows right triangle ABC.

Which ratio represents the tangent of ∠ABC?

13. What is the value of the expression −3x2y + 4x when x = −4 and y = 2?

• (1) −112
• (2) −80
• (3) 80
• (4) 272

14. Which expression is equivalent to −3x(x − 4) − 2x(x + 3)?

• (1) −x2 − 1
• (2) −x2 + 18x
• (3) −5×2 − 6x
• (4) −5×2 + 6x

15. The data in the table below are graphed, and the slope is examined.

The rate of change represented in this table can be described as

• (1) negative
• (2) positive
• (3) undefined
• (4) zero

16. The length of a rectangle is 3 inches more than its width. The area of the rectangle is 40 square inches. What is the length, in inches, of the rectangle?

• (1) 5
• (2) 8
• (3) 8.5
• (4) 11.5

17. In interval notation, the set of all real numbers greater than −6 and less than or equal to 14 is represented by

• (1) (−6, 14)
• (2) [−6, 14)
• (3) (−6, 14]
• (4) [−6, 14]

18. Which equation represents a quadratic function?

• (1) y = x + 2
• (2) y = |x + 2|
• (3) y = x2
• (4) y = 2x

19. Ben has four more than twice as many CDs as Jake. If they have a total of 31 CDs, how many CDs does Jake have?

• (1) 9
• (2) 13
• (3) 14
• (4) 22

20. What are the roots of the equation x2 − 5x + 6 = 0?

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