Mathematics 15 June 2010

Mathematics 15 June 2010 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Mathematics B
Tuesday, June 15, 2010 — 9:15 a.m. to 12:15 p.m., only

1. Pete and Sean decide to raise money for a charity by having a carnival in their backyard. In one of the games that they set up, the probability that a person will win is 0.4. If Robyn plays that game nine times, what is the probability that she wins exactly four times?

• (1) 9C5 (0.4)5 (0.4)4
• (2) 9C4 (0.5)4 (0.5)5
• (3) 9C4 (0.4)4 (0.6)5
• (4) 9C5 (0.4)5 (0.6)4

2. Which number is the largest?

3 The point A(6,3) maps onto A′(2,1) under a dilation with respect to the origin. What is the constant of dilation?

• (1) ¾
• (2) ¼
• (3) – ¾
• (4) – ¼

5. Tracy, a political campaign organizer, realizes that the number of hours needed to get out a mailing for her candidate is inversely proportional to the number of campaign workers she has. If she uses the information in the accompanying graph, how many hours would it take to do the mailing if 125 workers are used?

• (1) 12
• (2) 16
• (3) 20
• (4) 24

10. The roots of the equation 2x2 + 5x − 6 = 0 are

• (1) rational and unequal
• (2) rational and equal
• (3) irrational and unequal
• (4) imaginary

11. If the measure of ∠A = 40°, a = 5, and b = 6, how many different triangles can be constructed?

• (1) 1
• (2) 2
• (3) 3
• (4) 0

12. Which is the equation of the axis of symmetry of the graph of the equation y = x2 − 3x − 6?

13. The air temperature in Dallas, Texas, over a 5-hour period is shown in the accompanying graph.

What is the range of this set of data?

• (1) 0 ≤ x ≤ 5
• (2) 56 ≤ x ≤ 70
• (3) 0 ≤ y ≤ 80
• (4) 56 ≤ y ≤ 70
Answer: (4) 56 ≤ y ≤ 70

15. If f(x) = 2x − 1 and g(x) = 3x + 5, then (f º g)(x) is equal to

• (1) 5x + 4
• (2) 6x + 2
• (3) 6x + 9
• (4) 6x2 + 7x − 5

16. Which equation is represented by the accompanying graph?

• (1) y = 2x
• (2) y = 2– x
• (3) y = log x
• (4) y = log2 x
Answer: (4) y = log2 x

17. Which quadratic equation has the roots 2 − √3 and 2 + √3 ?

• (1) x2 − 4x + 7 = 0
• (2) x2 + 4x + 7 = 0
• (3) x2 − 4x + 1 = 0
• (4) x2 + 4x − 1 = 0
Answer: (3) x2 − 4x + 1 = 0

18. What is the solution set of √4x + 21 = x ?

• (1) {−3}
• (2) {−3, 7}
• (3) {7}
• (4) { }

19. The graph of the product of (4 + 3i) and (2 − 3i) lies in which quadrant?

• (1) I
• (2) II
• (3) III
• (4) IV

20. Which equation represents an ellipse?

• (1) 3x2 = 4 − 5y2
• (2) 4x2 = 9 − 4y
• (3) 6x2 = 9 + 8y2
• (4) xy = 12
Answer: (1) 3x2 = 4 − 5y2

Mathematics 15 June 2010 Questions Answers Keys

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