# Mathematics 28 January 2005

Mathematics 28 January 2005 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Mathematics B
Friday, January 28, 2005 — 9:15 a.m. to 12:15 p.m., only

1. If f(x) = –2x + 7 and g(x) = x2 – 2, then f(g(3)) is equal to

• (1) –7
• (2) –3
• (3) –1
• (4) 7

2. The shaded portion of the accompanying map indicates areas of night, and the unshaded portion indicates areas of daylight at a particular moment in time.

Which type of function best represents the curve that divides the area of night from the area of daylight?

• (2) cosine
• (3) tangent
• (4) logarithmic

3. If R varies inversely as S, when S is doubled, R is multiplied by

• (1) ½
• (2) 2
• (3) ¼
• (4) 4
• (1) {x|x ∈ real numbers, x ≠ 7}
• (2) {x|x ∈ real numbers, x ≠ ±7}
• (3) {x|x ∈ real numbers}
• (4) {x|x ∈ real numbers, x ≠ 0}
Answer: (2) {x|x ∈ real numbers, x ≠ ±7}
• (1) 5
• (2) 10
• (3) 25
• (4) 45

6. The product of (5ab) and (–2a2b)3 is

• (1) –30a6b4
• (2) –30a7b4
• (3) –40a6b4
• (4) –40a7b4

7. Which transformation is an example of an opposite isometry?

• (1) (x,y) → (x + 3,y – 6)
• (2) (x,y) → (3x,3y)
• (3) (x,y) → (y,x)
• (4) (x,y) → (y,–x)

9. Which graph represents the solution set of the inequality x2 – 4x – 5 < 0?

10. A small fragment of something brittle, such as pottery, is called a shard. The accompanying diagram represents the outline of a shard from a small round plate that was found at an archaeological dig.

• (1) 45°
• (2) 90°
• (3) 135°
• (4) 225°

11. Which graph is not a function?

13. The roots of the equation 2x2 – 8x – 4 = 0 are

• (1) imaginary
• (2) real, rational, and equal
• (3) real, irrational, and unequal
• (4) real, rational, and unequal
Answer: (3) real, irrational, and unequal

14. What is the equation of a circle with center (–3,1) and radius 7?

• (1) (x – 3)2 + (y + 1)2 = 7
• (2) (x – 3)2 + (y + 1)2 = 49
• (3) (x + 3)22 + (y – 1)2 = 7
• (4) (x + 3)2 + (y – 1)2 = 49
Answer: (4) (x + 3)2 + (y – 1)2 = 49

15. Which scatter diagram shows the strongest positive correlation?

17. The accompanying diagram shows the construction of a model of an elliptical orbit of a planet traveling around a star. Point P and the center of the star represent the foci of the orbit.

18. The expression i16/i3 is equivalent to

• (1) 1
• (2) –1
• (3) i
• (4) –i

19. If log5 x = 2, what is a value of √x?

• (1) 2 2/5
• (2) √5
• (3) 5
• (4) 25

20. If the coordinates of point A are (–2,3), what is the image of A under r y–axis° D3?

• (1) (–6,–9)
• (2) (9,–6)
• (3) (5,6)
• (4) (6,9)

Mathematics 28 January 2005 Questions Answers Keys

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