[A] 7 4 [B] 7 45 [C] 7 14 [D] [1] p. [3] 4. Solve. 2 x = 8 [B] 1 3

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1 Simplif. Epress each answer with positive eponents F 9 p I G J HG q KJ [B] 7 45 [C] 7 14 [D] [1] 7 7 p p [B] [C] 16 q q 17 p [D] p + q q Evaluate. 7 9 [B] 1 9 [C] 1 [D] [] [] 4. Solve. = 8 1 [B] 1 [C] [D] c h c h 5. Add [4] [B] 6 4 [C] [D] 6 c h c h [6] 6. Subtract. 4c 4 9c + c 7c 4 8c 6c + 8c 4 c 8c 15c + 9c [B] c 4 8c c 7c 4 [C] c + 8c 15c + 9c [D] c 4 + 8c c 7c 7. Application The initial price of a stock was $5. The first week of trading, the price gained n n+, the second week it gained n + n, and the third week it lost n n+. What epression represents the price of the stock at the end of the third week? n n 4 [B] n + n+ 1 [C] 4n + 7 [D] n + 1 [7] Epand and simplif. 8. ( 5)(5 7) [B] 9+ 5 [C] [D] 9+ 5 b g [5] [B] [C] [D] [8] [9]

2 Simplif. State an restriction(s) on the variables , 1 [B] 18, 9 [C] 1, 1 [D] , ( + ), [B] ( + ), 6 [C] + ( ), ± 6 [D] ( ), ± , ±4, ± 5 [B] [] [11] + + 4, 4 [C] 5, ±4, ± 5 [D] + 4 4, , ± 8 [B] 1, 8 [C] 8 [1] 1 + 8, 8 [D] 14, ± [C] Solve. [1] b+ 1gb 1gb g, ±1, [B] b gb gb g, ±1, b+ 1gb 1gb g, ±1, [D] b > 0 b g g b gb gb g, ±1, [14] 90 [B] 9 [C] 9 [D] 90 [15] > 1 [B] < [C] < [D] > [16]

3 Simplif [B] 0 [C] 0 [D] [17] 15 8 [B] 60 [C] 45 4 [D] [18] 45i [B] i 5 [C] i 5 [D] i 45 [19] 4 i [B] 7 +i [C] 7 i [D] 4 + i [0] 1. Find the maimum or minimum value of the function and the value of when it occurs. = maimum of 1at = 1 [B] maimum of 0 at = 1 [C] minimum of 1at = 1 [D] minimum of 1at = 0 [1]. Application Macro Manufacturing estimates that its profit P, in hundreds of dollars, after producing thousand units, can be epressed as P = + 1. How man units must be produced to obtain the maimum profit? 1600 units [B] 000 units [C] 16 units [D] none of these. Solve b completing the square. Epress solutions in simplest radical form. 6= 4 1 [] + 1 1, 4 4 [C] , 5 5 Solve b factoring. [B] , 4 4 [D] + 1 1, 5 5 [] = = 4 4 4, [B], [C] 4, [D] 4, [4] = 1, [B] =, [C] =, [D] none of these [5]

4 6. Solve using the quadratic formula. Round solutions to the nearest hundredth =0.55, 1.05 [B] 1.65, 0.15 [C] 0.15, 1.65 [D] 1.05,.55 [6] 7. Application A rocket is launched from atop a 57-m cliff with an initial velocit of 8 m/s. The height of the rocket t seconds after launch is given b the equation h= 16t + 8t+ 57. How long after the rocket is launched will it hit the ground? (Hint: The rocket will strike the ground when its height h is 0.) Round to the nearest hundredth of a second s [B] 7. s [C] 5.80 s [D] 0.61 s Simplif [7] 6 [B] [C] 4 [D] 6 [8] 6 [B] 16 [C] 8 [D] [9] [B] 14 [C] 14 [D] 14 9 b g i. 5 6i 5 i i [B] 1+ 84i [C] 55+ 6i [D] 1 84i [B] 5 i 6 [C] 6 5i [D] 6 5i [0] [1] []

5 . Find the domain and range of each relation. 5 [] domain:, range: the set of real numbers [B] domain: the set of real numbers, range: [C] domain: the set of real numbers, range: [D] domain:, range: the set of real numbers 4. The function = fbg has been transformed 5 units upward and units to the right. Identif the function corresponding to the transformation. = fb+ g 5 [B] = fb g + 5 [C] = fb+ g + 5 [D] = fb g 5 5. The graph of the function fbg= is shown on the left below. The graph on the right is the same graph translated two units to the right and three units upward. Write the equation of the graph on the right. [4] = + [B] = + [C] = + [D] = + + [5]

6 6. The graph of = is given. Use transformations to graph = =. b g, starting with the graph of [B] [C] [D] [6]

7 bg= 7. The graph of the function f is shown on the left below. The graph on the right is the graph of bg= f reflected in the -ais. Write the equation of the graph on the right. 0 0 fbg= [B] fbg= + [C] fbg= [D] fbg= + 8. Find the inverse of the function f [7] = 1,,, 1,, 5. [8] b g mb g b g b gr mb, g, b, g, b, gr [B] mb, 1g, b1, g, b 5, gr mb, g, b, g, b, gr [D] mb, 1g, b1, 5g, b 5, gr [C] Sketch the graph of the equation = 1. [9] 5 [B] [C] [D]

8 40. Write an equation for the graph. Assume the graph is a transformation of the graph =. = [B] = + [C] = [D] = 41. The graph of a function = fbg is shown below. Identif the graph of = fbg. [40] [41] [B] [C] [D]

9 4. The graph of f = b g is shown below. Identif the graph of = fb+g. [4] [B] [C] [D] bg= is epanded verticall b a factor of, reflected in the ais, translated 5 units to the left, and translated 6 units upward. Which is the equation of the transformed function, g bg? 1 1 g b g = b 5g + 6 [B] g b g = b+ 5g + 6 [C] g b g = b 5g 6 [D] g b g = b + 5g The graph of f [4]

10 44. In ABC, A = 5 and a = 0 m. Find B, b, and c. A c b B a C B= 65 b = 47. c = 4. 9 [B] B= 65 b = 4. 9 c = 47. [C] B= 60 b = 47. c = 4. 9 [D] B= 60 b = 4. 9 c = What is the length of FG? D [44] 59.5 cm [B].5 cm [C] 57.8 cm [D] 69.8 cm E cm F G [45]

11 46. Application You are building a model sailboat. The plans show that the base of the main sail is 1 cm, the bottom acute angle in the sail is 50, and the distance between the base of the sail and the deck is cm. What is the height of the mast, to the nearest tenth of a centimetre? 50 1 cm cm 16. cm [B] 14. cm [C] 16.6 cm [D] 17.7 cm 47. Use the sine law to find c. [46] C cm B c 46 A 5.8 cm [B] 51.8 cm [C] 50.8 cm [D] 5.8 cm 48. In XYZ, X= 54, = m, and z = 8 m. Find..1 m [B] 5.7 m [C] 7.7 m [D] 6.7 m [47] [48] 49. In ABC, A = 55, B= 41, and b = 61 m. Solve the triangle. C = 84, a = 76. m, c= 9. 5 m [B] C = 64, a = m, c= 741. m [C] C = 64, a = 76. m, c= 9. 5 m [D] C = 84, a = m, c= 741. m [49]

12 50. In VWX, V = 17.9, v =.8 cm, and w = 76. cm. Find W and X. W= 507. and X= 14., or W = and X = 4. 6 [B] W = 17. and X= 85. [C] W= 47. and X= 94., or W = and X = 14. [D] W= 7. and X= Convert.7 rad to degrees. 5. Convert to radians. [50].7 [B] [C] [D] [51] 0.18 [B].19 [C] 0.45 [D] 0.56 [5] 5. Find the eact value. cos 4 π 1 [B] [C] 0 [D] 54. Which equation represents the cosine function with amplitude and period 6π? = cos 1 6 [5] [B] = cos [C] = cos [D] = 1 1 cos A water wave is created in a wave tank. It has an amplitude of 5 and a period of π. Find the equation of 7 [54] this wave as a sine function. = 5sin 14 [B] = π sin Match the graph with the correct equation. 1 π 14 [C] = sin [D] = sin [55] [56] 5 π π 5 F sin H G I K J = π F cos H G I K J [C] = π F sin H G I K J [B] = + π F cos H G I K J [D] = + π

13 57. Solve 5cos = 0 for 0 < , [B] 1158., [C] 66. 4, 958. [D] none of these 58. Find the values of a and d for the arithmetic sequence 6,, 50, a = 6, d = 8 [B] a = 1, d = [C] a = 1, d = [D] a [58] 59. Write the first five terms of the arithmetic sequence with the given first term and common difference. a = 5., d = 1. 5., 4, 7., 14., 01. [B] 5., 689., 178., 067., 756. [C] 5., 66., 79., 9., 5. [D] 5., 689., 178., 067., 756. [57] = 6, d = Find t 64 for the arithmetic sequence 5,, 1, 4, 7, 181 [B] 184 [C] 19 [D] 59 [59] 61. Find S 11 for the arithmetic series K [60] 19 [B] 41 [C] 97 [D] 6 6. Given the first term and the last term, find the sum of the arithmetic series. a = 5, t = [B] 1144 [C] 517 [D] none of these [6] 6. A 0-row theatre has 0 seats in the front row. The second row has 1 seats. If each row has one more seat than the row in front of it, how man seats are there in the theatre? 50 [B] 070 [C] 0 [D] 5 [6] 64. At a local grocer store, cans of black beans are stacked in a triangular formation for displa. Each new row has 4 fewer cans than the row beneath it. If there are 17 rows, and the top row contains one can, how man cans of black beans are in the displa? 559 [B] 561 [C] 67 [D] 65 [61] 65. Find S6, if a = 1 and r =. [64] 1761 [B] 18 [C] 916 [D] 184 [65]

14 66. In a financial deal, ou will be paid $400 the first da, and each da thereafter, 5% of the previous da s amount. When one da s amount drops below $1, pament will cease. On what da will pament cease, and what will be our total income? Use the formula for the nth partial sum of a geometric sequence. 1th da; $614.5 total income [C] 6th da; $615.7 total income [B] 7th da; $614.5 total income [D] none of these [66] 67. Find the amount accumulated if $800 is invested for ears at 5.5% per annum, compounded quarterl. $ [B] $ [C] $94.45 [D] $99.9 [67] 68. Determine the present value of the investment. $000 in ears, invested at 6% per annum, compounded quarterl $ [B] $91.4 [C] $ [D] $ [68] 69. You deposit $400 each month into an annuit earning an annual interest rate of 7%, compounded monthl. What is the balance after 0 ears? What is the balance after 40 ears? $ , $ [B] $ , $ [C] $ , $ [D] $ , $ [69] 70. For the following mortgage, use the amortization table to find the monthl pament for each $00. Monthl Pament for Each $00 of Mortgage Debt Amortization Period Interest rate (%) 15 ears 0 ears 5 ears % per annum, amortized over 0 ears $6.98 [B] $6.5 [C] $6.84 [D] $6. [70] 71. Which of the following is the equation of a circle with centre b4, 45g that passes through the origin? b g b g [B] b g b g b + g + b + g = [D] b g b g = 51 [C] = = 51 [71]

15 7. Application A researcher places a pinpoint of bacteria mm to the left of the centre of a petri dish and 5 mm above the centre. This strain of bacteria grows until it is in a roughl circular pattern with a diameter of about 4 mm. What equation represents the outside of the bacteria colon relative to the centre of the dish? b g b g [B] b g b g b + g + b + g = [D] b g b g = 4 [C] = = 4 [7] 7. Application A bridge is built in the shape of a semi-elliptical arch and has a span of 90 m. The height of the arch, at a distance of 7 m from the centre, is 4 m. What is the height of the arch at its centre? 4 m 90 m 7 m 9 m [B] 0.5 m [C] 9.67 m [D] 0 m 74. Which equation represents the graph? [7] 9 49 = 441 [B] = 1 [C] 9 49 = 1 [D] 9 49 = [74]

16 75. Write an equation for the hperbola in standard form. Then, find the coordinates of the vertices and foci and the equation of the asmptotes. Sketch the graph = 0 =1 9 5 vertices: b, 0g, b0, g foci: F I F I HG 0, 4KJ, HG 0, 4 K J [B] =1 9 5 vertices: b0, g, b0, g foci: F I F I HG 0, KJ, HG 0, KJ asmptotes: = 5, = 5 asmptotes: = 5, = 5 [C] =1 9 5 vertices:, 0,, 0 b g b g d i d i foci: 4, 0, 4, 0 asmptotes: = 5, = 5 [D] none of these [75]

Bishop Kelley High School Summer Math Program Course: Trigonometry and Trigonometry with Pre-Calculus

Bishop Kelley High School Summer Math Program Course: Trigonometry and Trigonometry with Pre-Calculus 015 01 Summer Math Program Course: Trigonometr and Trigonometr with Pre-Calculus NAME: DIRECTIONS: Show all work on loose-leaf paper, which ou will turn in with the packet. (NO WORK IN PACKET!) Put final