Integrated Algebra 18 August 2010

Integrated Algebra 18 August 2010 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Integrated Algebra
Wednesday, August 18, 2010 — 8:30 to 11:30 a.m., only

Student Name: ______________________________________________________

School Name: _______________________________________________________

1. The school store did a study comparing the cost of a sweatshirt with the number of sweatshirts sold. The price was changed several times and the numbers of sweatshirts sold were recorded. The data are shown in the table below.

Which scatter plot represents the data?

Answer: (3)

2. What is the solution of 3(2m – 1) ≤ 4m + 7?

(1) m ≤ 5
(2) m ≥ 5
(3) m ≤ 4
(4) m ≥ 4

Answer: (1) m ≤ 5

3. Which set represents the intersection of sets A, B, and C shown in the diagram below?

(1) {3, 4, 5, 6, 7}
(2) {2}
(3) {2, 3, 4, 5, 6, 7}
(4) {1, 2, 3, 4, 5, 6, 7, 8, 9}

Answer: (2) {2}

4. The end of a dog’s leash is attached to the top of a 5-foot-tall fence post, as shown in the diagram below. The dog is 7 feet away from the base of the fence post.

How long is the leash, to the nearest tenth of a foot?

(1) 4.9
(2) 8.6
(3) 9.0
(4) 12.0

Answer: (2) 8.6

5. What is the slope of the line passing through the points A and B, as shown on the graph below?

(1) −3
(2) −¹/₃
(3) 3
(4) ¹/₃

Answer: (2) −¹/₃

6. The quotient of (9.2 × 10⁶) and (2.3 × 10²) expressed in scientific notation is

(1) 4,000
(2) 40,000
(3) 4 × 10³
(4) 4 × 10⁴

Answer: (2) 40,000

7. In a recent town election, 1,860 people voted for either candidate A or candidate B for the position of supervisor. If candidate A received 55% of the votes, how many votes did candidate B receive?

(1) 186
(2) 837
(3) 1,023
(4) 1,805

Answer: (2) 837

8. Which expression is equivalent to 121 − x²?

(1) (x − 11)(x − 11)
(2) (x + 11)(x − 11)
(3) (11 − x)(11 + x)
(4) (11 − x)(11 − x)

Answer: (3) (11 − x)(11 + x)

9. Given:

U = {1, 2, 3, 4, 5, 6, 7, 8}
B = {2, 3, 5, 6}

Set B is a subset of set U. What is the complement of set B?

(1) { }
(2) {2, 3, 5, 6}
(3) {1, 4, 7, 8}
(4) {1, 2, 3, 4, 5, 6, 7, 8}

Answer: (3) {1, 4, 7, 8}

10. Which graph can be used to find the solution of the following system of equations?

y = x² + 2x + 3
2y − 2x = 10

Answer: (1)

11. The width of a rectangle is 3 less than twice the length, x. If the area of the rectangle is 43 square feet, which equation can be used to find the length, in feet?

(1) 2x(x − 3) = 43
(2) x(3 − 2x) = 43
(3) 2x + 2(2x − 3) = 43
(4) x(2x − 3) = 43

Answer: (4) x(2x − 3) = 43

12. Which value of x is the solution of ^{2x – 3}/_{x – 4} = ²/₃?

(1) –¹/₄
(2) ¹/₄
(3) −4
(4) 4

Answer: (2) ¹/₄

13. What is the perimeter of a regular pentagon with a side whose length is x + 4?

(1) x² + 16
(2) 4x + 16
(3) 5x + 4
(4) 5x + 20

Answer: (4) 5x + 20

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

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

Answer: (2) x = 4

15. The diagram below shows the graph of y = −x² − c.

Which diagram shows the graph of y = x² − c?

Answer: (1)

16. Which point lies on the line whose equation is 2x − 3y = 9?

(1) (−1,−3)
(2) (−1,3)
(3) (0,3)
(4) (0,−3)

Answer: (4) (0,−3)

17. Which phrase best describes the relationship between the number of miles driven and the amount of gasoline used?

(1) causal, but not correlated
(2) correlated, but not causal
(3) both correlated and causal
(4) neither correlated nor causal

Answer: (3) both correlated and causal

18. The height, y, of a ball tossed into the air can be represented by the equation y = −x² + 10x + 3, where x is the elapsed time. What is the equation of the axis of symmetry of this parabola?

(1) y = 5
(2) y = −5
(3) x = 5
(4) x = −5

Answer: (3) x = 5

19. In the diagram below, MATH is a rectangle, GB = 4.6, MH = 6, and HT = 15.

What is the area of polygon MBATH?

(1) 34.5
(2) 55.5
(3) 90.0
(4) 124.5

Answer: (2) 55.5

20. This year, John played in 10 baseball games. In these games he had hit the ball 2, 3, 0, 1, 3, 2, 4, 0, 2, and 3 times. In the first 10 games he plays next year, John wants to increase his average (mean) hits per game by 0.5. What is the total number of hits John needs over the first 10 games next year to achieve his goal?