Practice Exam 2.pdf - PRINTABLE VERSION Practice Test 2 You...

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Unformatted text preview: PRINTABLE VERSION Practice Test 2 You scored 100 out of 100 Question 1 Your answer is CORRECT. Suppose that = a) csc(θ) b) csc(θ) c) = = θ is an acute angle of a right triangle and that − − 5 √ 21 21 − − 2 √ 21 21 − − √ 21 csc(θ) = 5 − − √ 21 , tan(θ) , tan(θ) , tan(θ) , d) csc(θ) e) csc(θ) f) None of the above. = 2 − − 5 √ 21 21 = tan(θ) , = tan(θ) = = 5 sec(θ) = 2 . Find csc(θ) and tan(θ) . − − √ 21 2 − − 5 √ 21 21 − − √ 21 2 − − √ 21 5 = − − 2 √ 21 21 Question 2 Your answer is CORRECT. Right triangles ABC and BC D with right angle and BD = 10, find the length of AB. Note: The triangle may not be drawn to scale. Loading [MathJax]/extensions/MathZoom.js C are given below. If ∘ ∘ m(A) = 30 , m(D) = 45 , a) 10 b) – 10 √ 2 c) – 5 √2 d) – 10 √ 3 e) 20 f) None of the above. Question 3 Your answer is CORRECT. Right triangles ABC and DBC with right angle , find the length of BD. Note: The triangle may not be drawn to scale. CD = 2 a) b) c) d) 3 − − − 4 √ 209 3 836 9 − − − 2 √ 209 3 Loading [MathJax]/extensions/MathZoom.js C are given below. If 1 cos(A) = , AB = 10 3 and e) f) 1672 9 None of the above. Question 4 Your answer is CORRECT. In right triangle a) b) with right angle ABC − − − √ 115 sin(A) = C , . sin(A) and cot(A) − − − 9 √ 115 ; cot(A) = 9 115 − − − √ 115 − − − 9 √ 115 sin(A) = ; cot(A) = 14 115 9 c) sin(A) = d) sin(A) = e) sin(A) = f) None of the above. ; , find AB = 14 and AC = 9 cot(A) = − − − 9 √ 115 14 115 − − − √ 115 ; cot(A) = 14 9 9 ; − − − √ 115 cot(A) = − − − √ 115 14 9 Question 5 Your answer is CORRECT. In the figure below, angle B is a right angle, m(BAC ) find the length of AD. Note: The triangle may not be drawn to scale. Loading [MathJax]/extensions/MathZoom.js a) 93 ∘ = 30 and the length of . If AC = 4 , CD = 7 b) 8 c) − − 2 √ 93 d) − − √ 93 e) 186 f) None of the above. Question 6 Your answer is CORRECT. Convert the following radian measure to degrees: a) b) c) d) e) f) 660 11 π 6 . ∘ 165 ∘ 2 330 ∘ 2160 ∘ 11 1100 ∘ 3 None of the above. Question 7 Your answer is CORRECT. Find the area of the sector of a circle with central angle a) b) c) 5π cm 2 2 25 π 4 5π 4 cm 2 cm 2 Loading [MathJax]/extensions/MathZoom.js ∘ θ = 45 and radius r = 5 cm. d) e) f) 25 π cm 2 8 5π cm 2 8 None of the above. Question 8 Your answer is CORRECT. A sector of a circle has central angle a) 3 π θ = 6 and area 3π ft . Find the radius of this circle. 2 ft 2 ft b) 6 c) 12 d) 3 e) 24 f) None of the above. ft ft ft Question 9 Your answer is CORRECT. A car has wheels with a 7 inch radius. If each wheel's rate of turn is angular speed in units of radians/second. a) b) 12 π 6π 7 c) 6π d) 3π e) 42 π None of the above. f) Loading [MathJax]/extensions/MathZoom.js 6 revolutions per second, find the Question 10 Your answer is CORRECT. A car has wheels with a 8 inch radius. If each wheel's rate of turn is the car moving in units of inches/sec? a) 16 π b) 112 π c) 56 π d) e) f) 8π 7 7π 8 None of the above. Question 11 Your answer is CORRECT. Evaluate: − b) – −√ 2 c) − d) 0 f) ∘ . – −√ 2 + 2 a) e) ∘ sin(315 ) + cos(225 ) 2 – 4 − √2 2 – √2 4 None of the above. Question 12 Your answer is CORRECT. Loading [MathJax]/extensions/MathZoom.js 7 revolutions per second, how fast is 2π Evaluate: a) b) cos(− π ) + sin(− 3 ) 6 . – 4 + √3 − 2 – −1 + √ 3 2 c) 0 d) − e) −1 f) None of the above. – 1 + √3 2 Question 13 Your answer is CORRECT. Let P (x, y) denote the point where the terminal side of an angle Quadrant IV and a) − − √ 15 b) − − −√ 15 c) − 1 x = 4 θ meets the unit circle. If , find tan(θ) . − − √ 15 15 d) \displaystyle \frac{\sqrt {15}}{15} e) \displaystyle 1515 f) None of the above. − − √ 15 15 Question 14 Your answer is CORRECT. Evaluate: \displaystyle \;\;\cot\left(\frac{11\,\pi }{6}\right) Loading [MathJax]/extensions/MathZoom.js cot( 11 π 6 . ) P is in – a) \displaystyle \sqrt {3}√3 b) \displaystyle -\frac{\sqrt {3}}{3}− c) \displaystyle 33 – √3 3 d) \displaystyle \frac{\sqrt {3}}{3} e) \displaystyle -\sqrt {3}−√– 3 f) None of the above. – √3 3 Question 15 Your answer is CORRECT. Evaluate: \displaystyle \;\;\cos(-330^\circ) a) \displaystyle -\frac{\sqrt {3}}{2}− b) \displaystyle \frac{1}{2} c) \displaystyle \sqrt {3}√– 3 d) \displaystyle -\frac{1}{2}− e) \displaystyle \frac{\sqrt {3}}{2} f) None of the above. ∘ cos(−330 ) – √3 2 1 2 1 2 – √3 2 Question 16 Your answer is CORRECT. Evaluate: \displaystyle \;\;\cot(150^\circ) a) b) ∘ cot(150 ) \displaystyle 33 \displaystyle -\frac{\sqrt {3}}{3}− Loading [MathJax]/extensions/MathZoom.js – √3 3 . . – c) \displaystyle -\sqrt {3}−√3 d) \displaystyle \sqrt {3}√– 3 e) \displaystyle \frac{\sqrt {3}}{3} f) None of the above. – √3 3 Question 17 Your answer is CORRECT. Evaluate: \displaystyle \;\;\sin\left(\frac{\pi }{6}\right) – √3 a) \displaystyle \frac{\sqrt {3}}{3} b) \displaystyle \frac{1}{2} c) \displaystyle \frac{\sqrt {3}}{2} d) \displaystyle -\frac{1}{2}− e) \displaystyle -\frac{\sqrt {3}}{2}− f) None of the above. 3 1 2 – √3 2 1 2 – √3 2 Question 18 Your answer is CORRECT. Evaluate: \displaystyle \;\;\sec(330^\circ) ∘ sec(330 ) a) \displaystyle 22 b) \displaystyle -2−2 c) \displaystyle -\frac{2\,\sqrt {3}}{3}− 3 Loading [MathJax]/extensions/MathZoom.js d) – 2 √3 \displaystyle \frac{2\,\sqrt {3}}{3} – 2 √3 3 . π sin( ) 6 . e) \displaystyle -\frac{\sqrt {3}}{3}− f) None of the above. – √3 3 Question 19 Your answer is CORRECT. Evaluate: \displaystyle \;\;\sec\left(\frac{11\,\pi }{6}\right) a) \displaystyle 22 b) \displaystyle -2−2 c) \displaystyle -\frac{2\,\sqrt {3}}{3}− d) \displaystyle \frac{2\,\sqrt {3}}{3} e) \displaystyle -\frac{\sqrt {3}}{3}− f) None of the above. 11 π sec( ) 6 – 2 √3 3 – 2 √3 3 – √3 3 Question 20 Your answer is CORRECT. Evaluate: \displaystyle \;\;\tan\left(\frac{5\,\pi }{3}\right) a) \displaystyle -\frac{\sqrt {3}}{3}− b) \displaystyle \frac{\sqrt {3}}{3} c) \displaystyle -\sqrt {3}−√– 3 d) \displaystyle \sqrt {3}√– 3 e) \displaystyle 33 Loading [MathJax]/extensions/MathZoom.js – √3 – √3 3 3 5π tan( ) 3 . . f) None of the above. Question 21 Your answer is CORRECT. Which of the following is equivalent to: \;\left(7\sin(x)+7\cos(x)\right)^2 a) 49+49\sin(x)\cos(x)49 + 49 sin(x) cos(x) b) 49+7\sin(x)\cos(x)49 + 7 sin(x) cos(x) c) 49+98\sin(x)\cos(x)49 + 98 sin(x) cos(x) d) 7+7\sin(x)\cos(x)7 + 7 sin(x) cos(x) e) 7+7\sin(x)7 + 7 sin(x) f) None of these. (7 sin(x) + 7 cos(x)) Question 22 Your answer is CORRECT. Simplify the following expression: \;9\sin^2(x)+9\cos^2(x)-10\tan(x)\cot(x) 2 2 9 sin (x) + 9 cos (x) − 10 tan(x) cot(x) a) 9+10\tan(2x)9 + 10 tan(2x) b) 9-10\tan(2x)9 − 10 tan(2x) c) 19 d) -1 e) 19\tan(x)19 tan(x) f) None of these. Question 23 Your answer is CORRECT. Simplify the following expression: \;\displaystyle\frac{6\sin(x)}{(1-\cos(x))(1+\cos(x))} 6 sin(x) (1 − cos(x))(1 + cos(x)) a) 12\cos(2x)12 cos(2x) Loading [MathJax]/extensions/MathZoom.js b) 12\sec(x)12 sec(x) 2 ? c) 6\csc^2(x)6 csc d) 6\sec(x)6 sec(x) e) 6\csc(x)6 csc(x) f) None of these. 2 (x) Question 24 Your answer is CORRECT. Which of the following is equivalent to \; 7\sin^2(\theta)-3\sec^2(\theta)+7\cos^2(\theta)+3\tan^2(\theta) 7 sin (θ) − 3 sec (θ) + 7 cos (θ) + 3 tan (θ)? 2 2 2 a) 3\sec^2(\theta)3 sec b) 7\tan(\theta)7 tan(θ) c) 44 d) 00 e) 1010 f) 2 2 (θ) None of the above. Question 25 Your answer is CORRECT. Which of the following is equivalent to \; 1-2\cos^2(\theta)+\cos^4(\theta) a) 1+\cos^2(\theta)1 + cos b) -\cos^4(\theta)− cos c) -\sin^4(\theta)− sin d) \sin^4(\theta)sin e) \cos^4(\theta)cos f) None of the above. 2 4 4 4 (θ) (θ) (θ) (θ) 4 (θ) Loading [MathJax]/extensions/MathZoom.js 2 4 ? 1 − 2 cos (θ) + cos (θ) ...
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