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°

**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

**11. Which relation is a function?**

- (1) xy = 7
- (2) x = 7
- (3) x
^{2}– y^{2}= 7 - (4) x
^{2}+ y^{2}= 7

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

- (1) 3x
^{2}+ 10y^{2}= 288,000 - (2) 3x
^{2}– 10y^{2}= 288,000 - (3) 3x + 10y = 288,000
- (4) 30xy = 288,000

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

- (1) y = –x
^{2}+ 3x + 5 - (2) y = –x
^{2}+ 6x + 2 - (3) y = x
^{2}+ 6x + 3 - (4) y = x
^{2}+ x + 3

**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

**16. If (a ^{x})^{2}/_{3 }= 1/a^{2} , 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 cos
^{2}x - (2) 270 cos
^{2}x - (3) 60 cos
^{3}x - (4) 90 cos
^{3}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

**19. The graphs of the equations y = 2 ^{x} 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

Which measure represents sin θ?

- (1) SO
- (2) RO
- (3) PR
- (4) QS

**Mathematics 23 June 2005 Questions Answers Keys**

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