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.

Mathematics 23 June 2005

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
Answer: (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
Answer: (3) III

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°
Mathematics 23 June 2005
Answer: (2) 1/

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

Mathematics 23 June 2005
Answer: (2) 

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)
Answer: (3) (–3,4)

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

Mathematics 23 June 2005
  • (1) 11
  • (2) 14.5
  • (3) 15
  • (4) 16
Answer: (3) 15

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
Mathematics 23 June 2005
Answer: (3) 5/2 
Mathematics 23 June 2005
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
Mathematics 23 June 2005
Answer: (4) 

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
Answer: (3) –3 

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 
Mathematics 23 June 2005

Which measure represents sin θ?

  • (1) SO
  • (2) RO
  • (3) PR
  • (4) QS
Answer: (4) QS 

 

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