# Mathematics 29 January 2004

Mathematics 29 January 2004 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Mathematics B
Thursday, January 29, 2004 — 9:15 a.m. to 12:15 p.m., only

1. The expression cos 40° cos 10° + sin 40° sin 10° is equivalent to

• (1) cos 30°
• (2) cos 50°
• (3) sin 30°
• (4) sin 50°

2. The expression secθ/cscθ is equivalent to

• (1) sin θ
• (2) cos θ
• (3) sinθ/cosθ
• (4) cosθ/sinθ

3. An overhead view of a revolving door is shown in the accompanying diagram. Each panel is 1.5 meters wide.

What is the approximate width of d, the opening from B to C?

• (1) 1.50 m
• (2) 1.73 m
• (3) 3.00 m
• (4) 2.12 m

4. What is a positive value of x for which 9–cos x= 1/3

• (1) 30°
• (2) 45°
• (3) 60°
• (4) 90°

5. The expression 7/2 – √3 is equivalent to

• (1) 14 – 7√3
• (2) 14 + 7√3
• (3) 2 – √3/7
• (3) 14 + √3/7

6. Jean’s scores on five mathematics tests were 98, 97, 99, 98, and 96. Her scores on five English tests were 78, 84, 95, 72, and 79. Which statement is true about the standard deviations for the scores?

• (1) The standard deviation for the English scores is greater than the standard deviation for the math scores.
• (2) The standard deviation for the math scores is greater than the standard deviation for the English scores.
• (3) The standard deviations for both sets of scores are equal.
• (4) More information is needed to determine the relationship between the standard deviations.
Answer: (1) The standard deviation for the English scores is greater than the standard deviation for the math scores.

7. In ΔABC, a = 19, c = 10, and m∠A = 111. Which statement can be used to find the value of ∠C?

• (1) 42a + b + ½ c
• (2) 2ab – ½ c
• (3) a2 + b –½ c
• (4) 2a + b – ½ c
Answer: (4) 2a + b – ½ c

10. The accompanying diagram shows the elliptical orbit of a planet. The foci of the elliptical orbit are F1 and F2

If a, b, and c are all positive and a ≠ b ≠ c, which equation could represent the path of the planet?

• (1) ax2 – by2 = c2
• (2) ax2 + by2 = c2
• (3) y = ax2 + c2
• (4) x2 + y2 = c2
Answer: (2) ax2 + by2 = c2

11. Battery lifetime is normally distributed for large samples. The mean lifetime is 500 days and the standard deviation is 61 days. Approximately what percent of batteries have lifetimes longer than 561 days?

• (1) 16%
• (2) 34%
• (3) 68%
• (4) 84%

12. The expression log3 (8 – x) is defined for all values of x such that

• (1) x > 8
• (2) x ≥ 8
• (3) x < 8
• (4) x ≤ 8

14. The graph below represents f(x).

Which graph best represents |f(x)|?

15. If f(x) = x3 – 2x2, then f(i) is equivalent to

• (1) –2 + i
• (2) –2 – i
• (3) 2 + i
• (4) 2 – i

16. Which statement must be true if a parabola represented by the equation y = ax2 + bx + c does not intersect the x-axis?

• (1) b2 – 4ac = 0
• (2) b2 – 4ac < 0
• (3) b2 – 4ac > 0, and b2 – 4ac is a perfect square.
• (4) b2 – 4ac > 0, and b2 – 4ac is not a perfect square.
Answer: (2) b2 – 4ac < 0

17. A garden in the shape of an equilateral triangle has sides whose lengths are 10 meters. What is the area of the garden?

• (1) 25 m2
• (2) 25 √3 m2
• (3) 50 m2
• (4) 50 √3 m2

18. If x is an acute angle and sin x = 12/13, then cos 2x equals

• (1) 25/169
• (2) – 119/169
• (3) 25/169
• (4) – 119/169

19. What is the axis of symmetry of the graph of the equation x = y2?

• (1) x-axis
• (2) y-axis
• (3) line y = x
• (4) line y = –x

20. The cells of a particular organism increase logarithmically. If g represents cell growth and h represents time, in hours, which graph best represents the growth pattern of the cells of this organism?

Mathematics 29 January 2004 Questions Answers Keys

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