# Mathematics 23 June 2005

Mathematics 23 June 2005 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Mathematics B
Thursday, June 23, 2005 — 9:15 a.m. to 12:15 p.m., only

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1. The accompanying graph shows the heart rate, in beats per minute, of a jogger during a 4-minute interval.

What is the range of the jogger’s heart rate during this interval?

• (1) 0–4
• (2) 1–4
• (3) 0–110
• (4) 60–110

2. If sin θ is negative and cos θ is negative, in which quadrant does the terminal side of θ lie?

• (1) I
• (2) II
• (3) III
• (4) IV

3. Expressed as a function of a positive acute angle, sin (–230°) is equal to

• (1) sin 50°
• (2) –sin 50°
• (3) cos 50°
• (4) –cos 50°
Answer: (1) sin 50°

5. Which graph represents the solution set for the expression |2x + 3| > 7?

6. What are the coordinates of the center of the circle represented by the equation (x + 3)2 + (y – 4)2 = 25?

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

7. What is the mean of the data in the accompanying table?

• (1) 11
• (2) 14.5
• (3) 15
• (4) 16

8. In a given rectangle, the length varies inversely as the width. If the length is doubled, the width will

• (1) be divided by 2
• (2) remain the same
• (3) be multiplied by 2
• (4) increase by 2
Answer: (1) be divided by 2
Answer: (4) x+ y/2

11. Which relation is a function?

• (1) xy = 7
• (2) x = 7
• (3) x2 – y2 = 7
• (4) x2 + y2 = 7
Answer: (1) xy = 7

12. Which equation, when graphed on a Cartesian coordinate plane, would best represent an elliptical racetrack?

• (1) 3x2 + 10y2 = 288,000
• (2) 3x2 – 10y2 = 288,000
• (3) 3x + 10y = 288,000
• (4) 30xy = 288,000
Answer: (1) 3x2 + 10y2 = 288,000

14. For which quadratic equation is the axis of symmetry x = 3?

• (1) y = –x2 + 3x + 5
• (2) y = –x2 + 6x + 2
• (3) y = x2 + 6x + 3
• (4) y = x2 + x + 3
Answer: (2) y = –x2 + 6x + 2

15. A crate weighing w pounds sits on a ramp positioned at an angle of θ with the horizontal. The forces acting on this crate are modeled by the equation Mw cos θ = w sin θ, where M is the coefficient of friction. What is an expression for M in terms of θ?

• (1) M = tan θ
• (2) M = cot θ
• (3) M = sec θ
• (4) M = csc θ
Answer: (1) M = tan θ

16. If (ax)2/3 = 1/a2 , what is the value of x?

• (1) 1
• (2) 2
• (3) –3
• (4) –1

17. What is the third term in the expansion of (cos x + 3)5?

• (1) 90 cos2 x
• (2) 270 cos2 x
• (3) 60 cos3 x
• (4) 90 cos3 x
Answer: (4) 90 cos3 x

18. Which equation has imaginary roots?

• (1) x(5 + x) = 8
• (2) x(5 – x) = –3
• (3) x(x + 6) = –10
• (4) (2x + 1)(x – 3) = 7
Answer: (3) x(x + 6) = –10

19. The graphs of the equations y = 2x and y = –2x + a intersect in Quadrant I for which values of a?

• (1) 0 < a < 1
• (2) a < 1
• (3) a ≥ 1
• (4) a > 1
Answer: (4) a > 1

Which measure represents sin θ?

• (1) SO
• (2) RO
• (3) PR
• (4) QS

Mathematics 23 June 2005 Questions Answers Keys

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