# Mathematics 13 August 2009

Mathematics 13 August 2009 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
MATHEMATICS B
Thursday, August 13, 2009 — 8:30 to 11:30 a.m., only

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1. Which equation is represented by the accompanying graph? • (1) y = 2x
• (2) y = −2x
• (3) y = 2-x
• (4) y = x2 − 2
Answer: (2) y = −2x

2. What are the coordinates of the turning point of the parabola whose equation is y = −x2 + 4x + 1?

• (1) (−2,−11)
• (2) (−2,−3)
• (3) (2,5)
• (4) (2,13)
Answer: (3) (2,5)

3. The graph of the equation y = |sin x| will contain no points in Quadrants

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

4. What is the value of • (1) 15
• (2) 19
• (3) 21
• (4) 43
Answer: (3) 21 Answer: (2)

6. On a graph, if point A represents 2 − 3i and point B represents −2 − 5i, which quadrant contains 3A − 2B?

• (1) I
• (2) II
• (3) III
• (4) IV
Answer: (1) I Which statement is needed to prove ΔBAT ≅ ΔFLU? Answer: (1)

8. Which type of transformation is (x ,y) (x + 2,y − 2)?

• (1) dilation
• (2) reflection
• (3) rotation
• (4) translation
Answer: (4) translation

9. Which functions are positive for angles terminating in Quadrant II?

• (1) sine and cosine
• (2) sine and secant
• (3) sine and tangent
• (4) sine and cosecant
Answer: (4) sine and cosecant Answer: (3)

11. Banks use the formula A = P(1 + r)x when they compound interest annually. If P represents the amount of money invested and r represents the rate of interest, which expression represents log A, where A represents the amount of money in the account after x years?

• (1) x log P + log (1 + r)
• (2) log P + x log (1 + r)
• (3) log P + x log 1 + r
• (4) log P + log x + log (1 + r)
Answer: (2) log P + x log (1 + r)

12. If the equation of the axis of symmetry of a parabola is x = 2, at which pair of points could the parabola intersect the x-axis?

• (1) (3,0) and (5,0)
• (2) (3,0) and (2,0)
• (3) (3,0) and (1,0)
• (4) (−3,0) and (−1,0)
Answer: (3) (3,0) and (1,0)

13. Jack is driving from New York to Florida. The number of hours that he  drives and the speed at which he drives are inversely proportional. Which graph could be used to describe this situation if one axis represents speed and the other represents hours? Answer: (2)

14. What is the length of the altitude of an equilateral triangle whose side has a length of 8?

• (1) 32
• (2) 4√2
• (3) 4√3
• (4) 4
Answer: (3) 4√3

15. What is the third term in the expansion of (3x − 2)5?

• (1) 1,080x2
• (2) 270x3
• (3) 540x3
• (4) 1,080x3
Answer: (4) 1,080x3

16. If the dilation Dk  is an isometry, what must be the value of k?

• (1) 1
• (2) 2
• (3) −2
• (4) 0
Answer: (1) 1

17. If f(x) = x2 and g(x) = 2x + 1, which expression is equivalent to (f ο g) (x) ?

• (1) 2x2 + 1
• (2) 2(x + 1)2
• (3) 4x2 + 1
• (4) 4x2 + 4x + 1
Answer: (4) 4x2 + 4x + 1

18. What is the inverse of the function y = 2x − 3? Answer: (1)

19. If a > 0, which function represents the reflection of y = ax in the y-axis? Answer: (2)

20. The graph of the equation 2x2 − 3y2 = 4 forms

• (1) a circle
• (2) an ellipse
• (3) a hyperbola
• (4) a parabola
Answer: (3) a hyperbola

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