GENERAL SANTOS HOPE CHRISTIAN SCHOOLBlock 8, City Heights, General Santos City FIRST PERIODICAL EXAMINATION TRIGONOMETRY I THIRD YEAR A and B SY: 2011 – 2012 NAME : _______________________ SCORE Teacher: ROGELIO B. PONTEJO Date: ___________ . I. Multiple Choice: Choose the correct answer. Write the answer in the space provided before each item. _______1. Using common logarithms or natural logarithms and a calculator, evaluate to four decimal places. A. 0.6826 B. 1.6667 C. 3.3732 D. 1.4650 _______2.Expand the logarithmic expression using the properties of logarithms. A. B. C. D. _______3. Use the properties of logarithms to condense the expression to a single logarithm whose coefficient is 1. A. B. C. D. _______4. Use the properties of logarithms to condense the expression to a single logarithm whose coefficient is 1. A. C. B. D. _______5. Use a calculator to evaluate the expression to four decimal places. . A. –0.5405 B. –1.8502 C. 1.7160 D. 0.5119 ______6. Evaluate the expression. A. 2 B. 2/3 C. ½ D. -2 ______7. Express the logarithmic form of the exponential equation. A. B. C. D. ______8. What is the x-intercept of the function? A. 1 B. -1 C. 2 D. -2 ______9. Find the domain of the logarithmic function in interval notation. A. B. C. D. ______10. Write the expression as a single logarithm with a coefficient of 1. A. B. C. D. ______11. Expand the expression and evaluate, if possible. A. B. C. D. ______12. Solve for x. A. 1.06 B. 2.92 C. 2.01 D. 3.06 ______13. Solve for x. A. {2/3} B. {5} C. 13/2 D. {-2/3,5} _______14. Solve for x. A. {5} B. {-5,1) C. no solution D. {5,-1) ______15. Identify the graphs of f and g. A. C. B. D. ______16. Rewrite as a single logarithm: ln x − 2 ln y + ln z _______17. What will be the value of x if Log x 3 = 1/3. A. 18 B. 20 C. 30 D. 27 ______18. Solve 4 x = 22 to three decimal places. A. 3.961 B. 5.500 C. 2.230 D. 3.414 ______19. Solve 3 2x -1 = 25.6 to three decimal places. A. 4.767 B. 1.204 C. 0.739 D. 1.976 ______20. Solve 3 x + 4 = 7 x - 1 to three decimal places. A. 1.254 B. 2.397 C. 7.483 D. -1.993 ______21. Find the next four terms of the arithmetic sequence 16, 24, 32, . . . . A. 25, 40, 45, 50 C. 38, 44, 50, 56 B. 36, 40, 44, 48 D. 40, 48, 56, 64 ______22. Find the 18th term of the sequence where a 1 = 3 and d = 7 A. 236 B. 129 C. 119 D. 122 ______23. What are the arithmetic means of the sequence 31, ___, ___, ___, 3? A. 38, 45, 52 B. 25, 20, 15 C. 28, 29, 12 D. 24, 17, 10 ______24. Write an equation for the nth term of the arithmetic sequence 18, 30, 42, 54, 66, . . A. a n = 30n + 6 B. a n = 18n + 12 C. n + 18 D. a n = 12n + 6 ______25. Determine the sum of an arithmetic series where n = 45, a 1 = 14.3, and a n = 80.3. A. 2128.5 B. 3627.8 C. 4257 D. 3613.5 ______26. What is S n if a 1 = 27.5, d = 1.5, and n = 35? A. 2152.5 B. 1855 C. 1245 D. 98,175 ______27. Find the first three terms of the arithmetic series in which a 1 = 6, a n = 201, and S n = 4140. A. 5, 10, 15 B. 6, 46, 86 C. 6, 25, 40 D. 6, 11, 16 _____28. . A. –7 + 8 + (-9) + 10; 2 C. 7 + 8 + 9 + 10; 34 B. –7 + (-8) + (-9) + (-10); -34 D. 7 – 8 + 9 – 10; -2 _____29. A. 860 B. 430 C. 838.5 D. 820 _____30. Find the next two terms of the geometric sequence 64, -32, 16, -8, . A. 4, -2 B. 16, -32 C. -4, 2 D. -16, -32 _____31. Write the first four terms of the geometric sequence in which a 1 = -3 and r = -4 A. -12, 48, -192 C. 3, 12, 48, 192 B. B. -3, -12, -48, -192 D. -3, 12, -48, 192 _____32. What is the fifth term of a geometric sequence if a 1 = 7 and r = 0.2? A. 1.4 B. 0.0112 C. 5.6 D. 0.28 _____33. Find the sum of the first five terms of the geometric series for which a 1 = 2 and r = 2 A. 14 B. 126 C. 62 D. 30 ______34. Determine the sum of the geometric series for which a 1 = -486, , and a n = -6. A. -726 B. 325 C. 322.6 D. 732 ______35. Find the sum of the geometric series –5, -10, -20, -40, . . . for 7 terms. A. -635 B. -689 C. -599 D. -527 ______36. Identify a 1 in a geometric series for which S 8 = 42.5 and r = -0.5. A. B. 63.75 C. 64 D. 1.5 ______37. Find the sum of the infinite series 2 + 1 + ½ + ¼ . . . . if it exists. A. 1 B. 4 C. 8 D. does not exist ______38. If it exists, what is the sum of the infinite series: 16 - 4 + 1 - ¼ . . . . A. 20 B. The sum does not exist C. D. ______39. A. 28 B. the sum does not exist C. D. ______40. Solve 2 x+4 = 2 2x+5 A. -1 B. -2 C. -3 D. -4 ______41. Choose the angle measure represented by 4.7 rotations clockwise. A. 1692° B. -846° C. -1692° D. 846° ______42. Choose the angle measure represented by 5.2 rotations counterclockwise. A. 1872° B. -936° C. 936° D. -1872° ______43. Find the measure of the reference angle of -200°. A. 160° B. -200° C. 20° D. 40° ______44. Angles are measured from the positive horizontal axis, and the positive direction is counterclockwise. What are the values of sin o and cos o in the 4 th quadrant? A. sin o > 0 and cos o < 0 C. sin o < 0 and cos o < 0 B. sin o > 0 and cos o > 0 D. sin o < 0 and cos o > 0 _______45. If sec 2 | is 5/2, the quantity 1 – sin 2 | is equivalent to A. 2.5 B. 1.5 C. 0.4 D. 0.6 ______46. The coordinate of P, the point on the terminal side of the angle in the special position θ = 7t which intersect the unit circle, is; A. (1, 0) B. (0, 1) C. (-1, 0) D. (0, -1 ) ______47. Evaluate sin -1 (cos 180 0 ) A. 45 o B. 90 o C. -45 o D. -90 o ______ 48. If | = 45 o and r = 2 , find sin| . A. 2 2 B. 2 C. 2 D. 1 ______49. If sin | = ½ , cosecant | is. A. 2 2 B. 2 C. 2 D. 1 ______ 50. Which of the following relations is not a function? A. {(3,4), (-1,0), (2,2)} C. {(-1, -6) ,(-6,-1)} B. {(1,2), (3,2) , (5,2), (6,2)} D. {(3,1), (0,1), (3,2)} II. PROBLEM SOLVING 51 – 55. The length of the arc of the swing of a pendulum is 120 mm. If the length of the arc of each succeeding swing is decreased by 10%, find the total distance the pendulum travels before it stops. 56 – 60. How much money will Raphael have at the end of 5 years if he deposits P15,000.00 at 9% interest compounded quarterly? 61 – 65. Find the value of x from the series of numbers shown. x + 3x + 9x + 27x + . . . + 729x = 3279 “Science can purify religion from error and superstition. Religion can purify science from idolatry and false absolutes” GOD BLESS = P 1 nt r A n | | + | \ . | | ( ) 1 n 2 + 1 = 2 n a n d S ÷ 1 1 = a n n a r ÷ ( ) 1 n + a = 2 n n a S | | ( ) 1 n 2 + 1 = 2 n a n d S ÷ 1 1 = a r 1 1 n n r S r | | ÷ = | ÷ \ . 1 a - ra = r 1 1 n n S r = ÷