# Mathematics 30 January 2003

Mathematics 30 January 2003 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
MATHEMATICS B
Thursday, January 30, 2003 — 9:15 a.m. to 12:15 p.m., only
Print Your Name: ______________________________________________________
Print Your School’s Name:_________________________________________________

1. A monitor displays the graph y = 3 sin 5x. What will be the amplitude after a dilation of 2?

• (1) 5
• (2) 6
• (3) 7
• (4) 10
Answer: (2) 6

2. The probability that Kyla will score above a 90 on a mathematics test is 45. What is the probability that she will score above a 90 on three of the four tests this quarter? Answer: (1)

3. Which equation represents the parabola shown in the accompanying graph? • (1) f(x) = (x + 1)2 – 3
• (2) f(x) = –(x – 3)2 + 1
• (3) f(x) = –(x + 3)2 + 1
• (4) f(x) = –(x – 3)2 – 3
Answer: (3) f(x) = –(x + 3)2 + 1 • (1) 2 – 5i
• (2) 2 – 6i
• (3) 8 – 5i
• (4) 8 – 6i
Answer: (4) 8 – 6i

5. What is the solution set of the equation √9x + 10= x?

• (1) {–1}
• (2) {9}
• (3) {10}
• (4) {10,–1}
Answer: (3) {10}

6. Which statements could be used to prove that ΔABC and ΔA′B′C′ are congruent? Answer: (2)

7. Ileana buys a large circular pizza that is divided into eight equal slices. She measures along the outer edge of the crust from one piece and finds it to be 5 ½ inches. What is the diameter of the pizza to the nearest inch?

• (1) 14
• (2) 8
• (3) 7
• (4) 4
Answer: (1) 14

8. The national mean for verbal scores on an exam was 428 and the standard deviation was 113. Approximately what percent of those taking this test had verbal scores between 315 and 541?

• (1) 68.2%
• (2) 52.8%
• (3) 38.2%
• (4) 26.4%
Answer: (1) 68.2%

9. In ΔABC, if AC = 12, BC = 11, and m∠A = 30, angle C could be

• (1) an obtuse angle, only
• (2) an acute angle, only
• (3) a right angle, only
• (4) either an obtuse angle or an acute angle
Answer: (4) either an obtuse angle or an acute angle

10. For a rectangular garden with a fixed area, the length of the garden varies inversely with the width. Which equation represents this situation for an area of 36 square units?

• (1) x + y = 36
• (2) y = 36x
• (3) x – y = 36
• (4) y = 36x
Answer: (3) x – y = 36

11. In which quadrant would the image of point (5,–3) fall after a dilation using a factor of –3?

• (1) I
• (2) II
• (3) III
• (4) IV
Answer: (2) II Answer: (3)

13. If the roots of ax2 + bx + c = 0 are real, rational, and equal, what is true about the graph of the function y = ax2 + bx + c?

• (1) It intersects the x-axis in two distinct points.
• (2) It lies entirely below the x-axis.
• (3) It lies entirely above the x-axis.
• (4) It is tangent to the x-axis.
Answer: (2) II • (1) x = 2
• (2) x < 2
• (3) x ≥ 2
• (4) x > 2
Answer: (4) x > 2 Answer: (2)

16. The expression log 10(x+2)   – log 10x is equivalent to

• (1) –2
• (2) 2
• (3) 100
• (4) 1100
Answer: (2) 2

17. If (sec x – 2)(2 sec x – 1) = 0, then x terminates in

• (1) Quadrant I, only
• (2) Quadrants I and II, only
• (3) Quadrants I and IV, only
• (4) Quadrants I, II, III, and IV
Answer: (3) Quadrants I and IV, only

18. Which graph represents the solution set of x2 – x – 12 < 0? Answer: (2) Answer: (4)

20. If sin 6A = cos 9A, then m∠A is equal to

• (1) 6
• (2) 36
• (3) 54
• (4) 1½
Answer: (1 or 3) 6 or 54

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