Mathematics 22 June 2004

Mathematics 22 June 2004 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Mathematics B
Tuesday, June 22, 2004 — 1:15 to 4:15 p.m., only

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1. What is the sum of 2 – √–4 and –3 + √–16 expressed in a + bi form?

(1) –1 + 2i
(2) –1 + i√20
(3) –1 + 12i
(4) –14 + i

Answer: (1) –1 + 2i

2. The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 0.7. Which expression can be used to find the probability that it will rain on exactly three of the seven days they are there?

(1) ₇C₃(0.7)³(0.3)⁴
(2) ₇C₃(0.3)³(0.7)⁴
(3) ₄C₃(0.7)³(0.7)⁴
(4) ₄C₃(0.4)⁴(0.3)³

Answer: (1) ₇C₃(0.7)³(0.3)⁴

3. What is the amplitude of the function y = ²/₃sin 4x?

(1) ^π/₂
(2) ²/₃
(3) 3π
(4) 4

Answer: (2) ²/₃

4. Which quadratic function is shown in the accompanying graph?

(1) y = –2x²
(2) y = 2x²
(3) y = – ½x²
(4) y = ½x²

Answer: (2) y = 2x²

5. In the accompanying graph, the shaded region represents set A of all points (x,y) such that x² + y² ≤ 1. The transformation T maps point (x,y) to point (2x,4y).

Which graph shows the mapping of set A by the transformation T?

Answer: (3)

6. If f(x) = 4x⁰ + (4x)^–1, what is the value of f(4)?

(1) –12
(2) 0
(3) 1¹/₁₆
(4) 4¹/₁₆

Answer: (4) 4¹/₁₆

(1) all real numbers except 0
(2) all real numbers except 3
(3) all real numbers except 3 and –3
(4) all real numbers

Answer: (3) all real numbers except 3 and –3

8. Which graph represents an inverse variation between stream velocity and the distance from the center of the stream?

Answer: (1)

9. If logb x = y, then x equals

(1) y • b
(2) ^y/_b
(3) y^b
(4) b^y

Answer: (4) b^y

10. The expression i⁰ • i¹ • i² • i³ • i⁴ is equal to

(1) 1
(2) –1
(3) i
(4) –i

Answer: (2) –1

11. Which equation models the data in the accompanying table?

(1) y = 2x + 5
(2) y = 2^x
(3) y = 2x
(4) y = 5(2^x)

Answer: (4) y = 5(2^x)

12. The amount of juice dispensed from a machine is normally distributed with a mean of 10.50 ounces and a standard deviation of 0.75 ounce. Which interval represents the amount of juice dispensed about 68.2% of the time?

(1) 9.00–12.00
(2) 9.75–10.50
(3) 9.75–11.25
(4) 10.50–11.25

Answer: (3) 9.75–11.25

13. If θ is an acute angle such that sin θ = ⁵/₁₃, what is the value of sin 2θ?

(1) ¹²/₁₃
(2) ¹⁰/₂₆
(3) ⁶⁰/₁₆₉
(4) ¹²⁰/₁₆₉

Answer: (4) ¹²⁰/₁₆₉

14. Which function is symmetrical with respect to the origin?

(1) y = √x + 5
(2) y = |5 – x|
(3) y = –⁵/_x
(4) y = 5^x

Answer: (3) y = –⁵/_x

Answer: (1) ^xy/_{y – x}

16. Sam is designing a triangular piece for a metal sculpture. He tells Martha that two of the sides of the piece are 40 inches and 15 inches, and the angle opposite the 40-inch side measures 120°. Martha decides to sketch the piece that Sam described. How many different triangles can she sketch that match Sam’s description?