Mathematics 16 August 2006 Questions Answer Keys
The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
MATHEMATICS B
Wednesday, August 16, 2006 — 8:30 to 11:30 a.m., only
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2. What is the solution of the equation √2x – 3 – 3 = 6 ?
- (1) 42
- (2) 39
- (3) 3
- (4) 6
3. What is the minimum point of the graph of the equation y = 2x2 + 8x + 9?
- (1) (2,33)
- (2) (2,17)
- (3) (–2,–15)
- (4) (–2,1)
4. If x is a positive acute angle and cos x = √3⁄4 , what is the exact value of sin x?
- (1) √3⁄5
- (2) √13⁄4
- (3) 3⁄5
- (4) 4⁄5
5. Which equation does not represent a function?
- (1) x = π
- (2) y = 4
- (3) y = | x|
- (4) y = x2 + 5x
- (1) 12 − √3
- (2) 6 – 2√3
- (3) 4 − 2√3
- (4) 2 + √3
7. The function y = 2x is equivalent to
- (1) x = y log 2
- (2) x = log2y
- (3) y = x log 2
- (4) y = log2x
9. A designer who is planning to install an elliptical mirror is laying out the design on a coordinate grid. Which equation could represent the elliptical mirror?
- (1) x2 = 144 + 36y2
- (2) x2 + y2 = 144
- (3) x2 + 4y2 = 144
- (4) y = 4y2 + 144
10. A solution set of the equation 5 sin θ + 3 = 3 contains all multiples of
- (1) 45°
- (2) 90°
- (3) 135°
- (4) 180°
11. What is the total number of points of intersection for the graphs of the equations y = x2 and y = –x2?
- (1) 1
- (2) 2
- (3) 3
- (4) 0
12. For which equation is the sum of the roots equal to the product of the roots?
- (1) x2 + x + 1 = 0
- (2) x2 + 3x – 6 = 0
- (3) x2 – 8x – 4 = 0
- (4) x2 – 4x + 4 = 0
13. If the perimeter of an equilateral triangle is 18, the length of the altitude of this triangle is
- (1) 6
- (2) 6√3
- (3) 3
- (4) 3√3
15. What is the period of the graph of the equation y = 2 sin 1⁄3 x = 2 ?
- (1) 2⁄3π
- (2) 2π
- (3) 6π
- (4) 3π⁄2
16. What is the solution set of the equation | x2 – 2x | = 3x – 6?
- (1) {2,±3}
- (2) {2}
- (3) {±3}
- (4) {2,3}
- (1) 2 ⁄sin θ
- (2) 2 cos θ
- (3) 2 cot θ
- (4) 2 tan θ
18. The accompanying diagram shows unit circle O, with radius OB = 1.
Which line segment has a length equivalent to cos θ?
20. Which graph represents a quadratic function with a negative discriminant?
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