12-13 Spring Semester Exam Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. 1) In how many ways can you answer the questions on an exam that consists of 13 multiple choice questions, each of which has answer choices? A) 67,108,86 B) 67,109,70 C) 28,561 D) 67,108,63 1) 2) The code for some garage door openers consists of 12 electrical switches that can be set to "+", "0", or "-" by the owner. With this type of opener, how many different codes are possible? F) 530,21 G) 531,193 H) 532,701 J) 531,1 2) 3) In the "Big Bucks" lottery game, a person is to pick digits from 0 to 9 in correct order. If a number can be repeated, how many ways are there to play the game? A) 10,000 B) 262,1 C) 1,08,576 D) 100,000 3) Evaluate. ) 8 P 6 F) 20,160 G) 10,080 H) 56 J) ) 5) C1 A) B) 2 C) 12 D) 2 5) Tell whether permutations or combinations are being described. 6) 15 students are selected to form a committee. F) Combinations G) Permutations 6) 7) 5 pageant contestants are selected to be given awards and titles, the first being the winner, the second being the first runner-up, the third being the second runner-up, and so forth. A) Permutations B) Combinations 7) Solve. 8) A baseball manager has 10 players of the same ability. How many 9 player starting lineups can he create? F) 10 G) 3,628,800 H) 90 J) 362,880 8) Solve the problem. 9) How many committees of 5 people can be selected from 9 men and 5 women if the committee must have 3 men and 2 women? A) 980 B) 10,080 C) 80 D) 820 9) Solve. 10) There are 6 women running in a race. How many first, second, and third place possibilities can occur? F) 18 G) 20 H) 120 J) 216 10) 1
Solve the problem. 11) How many ways are there to choose 9 books from a collection of 12 different books? A) 79,833,600 B) 55 C) 220 D) 660 11) Expand the binomial. 12) (a - b) 6 F) - a 6 + 6a 5 b - 15a b 2 + 20a 3 b 3-15a 2 b + 6ab 5 - b 6 G) a 6-6a 5 b - 15a b 2-20a 3 b 3-15a 2 b - 6ab 5 - b 6 H) a 6-6a 5 b + 15a b 2-20a 3 b 3 + 15a 2 b - 6ab 5 + b 6 J) a 6 + 6a 5 b + 15a b 2 + 20a 3 b 3 + 15a 2 b + 6ab 5 + b 6 12) 13) (x + 2) 3 A) 16x 2 + 16x + B) 16x 6 + 8x 3 + 6 C) 6x 3 + 96x 2 + 96x + 8 D) 6x 3 + 96x 2 + 8x + 8 13) Evaluate. 1) 138 3 1) F) 138! 135! G) 28536 H) 2,571,216 J) 135 15) 25 21 A) 303,600 B) 75,900 C) 12,650 D) 15) Find the coefficient of the given term in the binomial expansion. 16) x6y term, (x + y)10 F) 25,200 G) 6 H) 151,200 J) 210 16) Write the sum using summation notation, assuming the suggested pattern continues. 17) 729 + 1000 + 1331 + 1728 +... + n3 +... A) (n+1)3 B) n3 C) n = 9 n = 10 n3 D) n = 9 n = 9 (n-1)3 17) 18) -3 + 6 + 15 + 2 +... + 132 F) 15-27n G) n = 0 H) -27n J) n = 0 15 n = 0 n = 0 (-3 + 9n) (-3 + 9n) 18) 2
Find the sum of the geometric sequence. 19) 1 3, 2 3, 3, 8 3, 16 3 19) A) 10 B) 31 15 C) 31 3 D) 2 Find the sum of the arithmetic sequence. 20) 3, 5, 7, 9,..., 21 F) 23 G) 39 H) 20 J) 120 20) Determine whether the sequence converges or diverges. If it converges, give the limit. 21) 72, 18, 9 2, 9 8,... 21) A) Converges; - 6120 B) Diverges C) Converges; 0 D) Converges; 96 22) 1 23, 1 81, 1 27, 1 9,... 22) F) Converges; 3 5 H) Converges; 1 32 G) Diverges J) Converges; 0 Find an explicit rule for the nth term of the arithmetic sequence. 23) -15, -11, -7, -3,... A) an = -15 + (n+1) B) an = -15 + (n+2) C) an = -15 (n-1) D) an = -15 + (n-1) 23) Find an explicit rule for the nth term of the sequence. 2) -2, -8, -32, -128,... F) an = -2 n-1 G) an = -2n+1 H) an = -2n J) an = -2 n 2) Find a recursive rule for the nth term of the sequence. 25) 8, 32, 128, 512,... A) an= an-1 + B) an= an-1 C) an= an-1 8 D) an= an-1 + 8 25) Solve. 26) The population of a town was 25,600 at the beginning of 1970. If the population decreased 250 people per year, how many people lived in the town at the beginning of 1985? F) 3750 G) 22,100 H) 21,600 J) 21,850 26) 3
Write out the first five terms of the sequence. 27) cn = n+2 3 27) A) 1, 3, 5 3, 2, 7 3 B) 2 3, 1, 3, 5 3, 2 C) 2 3, 2 3, 2 3, 2 3, 2 3 D) 1 2 3, 2 2 3, 3 2 3, 2 3, 5 2 3 Find the probability of the event. 28) Give the probability that the roll of a die will show a number less than 7. F) 1 6 G) 1 H) 7 6 J) 1 28) An experiment is conducted for which the sample space is S = {a, b, c, d}. Decide if the given probability function is valid. 29) 29) Outcome Probability a 0.50 b 0.38 c 0.1 d 0.28 A) No B) Yes Find the probability. 30) The maker of a certain candy claims that the proportions of colors of candy produced are: 0.2 red, 0.2 blue, 0. green, and 0.2 yellow. What is the probability that a randomly selected candy from a newly-opened bag will be green? F) 1 G) 0.8 H) 0. J) 0.2 30) 31) A 5-card hand is dealt from a deck of 52 cards. What is the probability that 3 cards are queens and two are kings? A) 0.0962 B) 0.00000923 C) 0.000181 D) 0.000000923 31) Find the vertex, focus, directrix, and focal width of the parabola. 32) - 1 0 x 2 = y 32) F) Vertex: (0, 0); Focus: (0, 10); Directrix: y = -10; Focal width: 10 G) Vertex: (0, 0); Focus: (-20, 0); Directrix: x = 10; Focal width: 160 H) Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 0 J) Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 160 Find the standard form of the equation of the parabola. 33) Focus at (6, -2), directrix y = -8 A) (y + 2)2 = 12(x - 6) B) (x + 2)2 = 12(y + 5) C) (x - 6)2 = 12(y + 5) D) (x - 6)2 = 12(y + 2) 33)
Find the center, vertices, and foci of the ellipse with the given equation. 3) (x + 2) 2 1 + (y + 2) 2 225 = 1 F) Center: (-2, -2); Vertices: (-17, -2), (13, -2); Foci: (-11, -2), (7, -2) G) Center: (-2, -2); Vertices: (-2, -17), (-2, 13); Foci: (-1, -2), (10, -2) H) Center: (-2, -2); Vertices: (-17, -2), (13, -2); Foci: (-2, -1), (-2, 10) J) Center: (-2, -2); Vertices: (-2, -17), (-2, 13); Foci: (-2, -11), (-2, 7) 3) Find an equation in standard form for the ellipse that satisfies the given conditions. 35) Minor axis endpoints (±2, 0), major axis length 2 A) y2 1 + x 2 = 1 B) x 2 1 + y 2 = 1 C) x 2 2 + y 2 12 = 1 D) x 2 12 + y 2 2 = 1 35) Find the vertices and foci of the hyperbola. 36) (x - 5) 2 1 - (y - ) 2 81 = 1 F) Vertices: (17, ), (-7, ); Foci: (-10, ), (20, ) G) Vertices: (1, ), (-, ); Foci: (-, ), (1, ) H) Vertices: (, 17), (, -7); Foci: (, -10), (, 20) J) Vertices: (, 1), (, -); Foci: (, -), (, 1) 36) Find an equation in standard form for the hyperbola that satisfies the given conditions. 37) Foci at (±8, 0), transverse axis with length 1 A) x 2 9 - y 2 15 = 1 B) x 2 6 - y 2 9 = 1 C) x 2 9 - y 2 6 = 1 D) x 2 15 - y 2 9 = 1 37) Solve the system of equations. 38) x + 2y - 3z + w = 7 3x + y - z + 2w = -2x + y + z - w = -3 x - y + 2z - 2w = 1 F) H) 35 22, 7 22, - 51 22, - 2 11 22 35, 22 7, - 22 51, - 11 2 G) 1, 33 28, - 11 3, - 33 106 J) 1, 28 33, - 3 11, - 106 33 38) Determine the value of each variable. 39) x+3 y+ = 6 5 7-6 7 k A) x = 6; y = 5; k = -6 B) x = 3; y = -6; k = 6 C) x = 3; y = 1; k = -6 D) x = -3; y = -1; k = 6 39) 5
Determine the order of the matrix. 0) 3 0 2 6-8 -2 7 F) 2 G) 2 3 H) 2 J) 3 2 0) Find the indicated matrix product or state that the product is undefined. 1) A = -3-7 -6-9, B = 5 2 6 8 6 9 1) BA A) B) -71-8 -81-102 -66-117 C) Undefined D) -15 2-2 -8 6-81 -15-1 -8-5 Find the inverse of A if it has one, or state that the inverse does not exist. 2) A = -3 0-5 2) F) H) 1 5 0-15 - 1 3-1 3 0 G) - 1 3-15 0 1 5 J) Inverse does not exist 15 1 5 Solve the problem. 3) Find the equilibrium point for the given demand and supply curve. p = 370-90x (demand) p = 100x (supply) A) (10, 2300) B) (3, 500) C) (23, 2300) D) (10, 370) 3) Find the component form and magnitude of the indicated vector. ) Given that P = (-1, 6) and Q = (0, 1), find the component form and magnitude of the vector PQ. F) -1, -5, 26 G) -1, 5, 26 H) 1, -5, 26 J) 1, -5, 26 ) Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0, 360 ) rounded to the nearest tenth. 5) 9, -1 5) A) 82, 276.3 B) 82, 96.3 C) 82, 173.7 D) 82, 353.7 6
Find the component form of the indicated vector. 6) Let u = -3, -2, v = 1, -5. Find u - v. F) 2, -3 G) -, 3 H) -2, -7 J) -1, 6 6) Find the component form of the vector v. 7) 7) A) 25.11, 6.73 B) 0.26, 0.97 C) 6.73, 25.11 D) 10.99, 23.56 Find a b. 8) a = i + 8j, b = -2i + 3j F) 2, 11 G) 32 H) 16 J) -8, 2 8) Find the angle between the given vectors to the nearest tenth of a degree. 9) u =, -3, v = -6, -8 A) 0 B) 180 C) 5 D) 90 9) Find the rectangular coordinates of the point with the given polar coordinates. 50) (-6, π) F) (6, 0) G) (0, -6) H) (0, 6) J) (-6, 0) 50) 7
Plot the point with the given polar coordinates. 51) (-3, 750 ) 51) A) B) Determine two pairs of polar coordinates for the point with 0 θ < 360. 52) (5 3, 15) F) (10 3, 300 ), (-10 3, 60 ) G) (10 3, 30 ), (-15 3, 330 ) H) (10 3, 60 ), (-10 3, 20 ) J) (10 3, 30 ), (-10 3, 330 ) 52) Find an equivalent equation in rectangular coordinates. 53) r = 2 sin θ + 5 cos θ 53) A) x + 5y = 2 B) y + 5x = 2 C) x - 5y = D) y + 5x = 2 x2 + y2 Find an equivalent equation in polar coordinates. 5) x 2 + y 2 - x = 0 F) r = sin θ G) r cos 2 θ = sin θ H) r sin 2 θ = cos θ J) r = cos θ 5) Express the complex number in trigonometric form. 55) 6 A) 6(cos 0 + i sin 0 ) B) 6(cos 270 + i sin 270 ) C) 6(cos 90 + i sin 90 ) D) 6(cos 180 + i sin 180 ) 55) 8
Write the complex number in the form a + bi. 56) 6(cos 330 + i sin 330 ) F) 3 3-3i G) 3 3 + 3i H) -3 3-3i J) -3 3 + 3i 56) Find the product or quotient, as indicated. Leave your answer in trigonometric form. 57) Find the product of z1 and z2. z1 = 9[cos (55 ) + i sin (55 )], z2 = 5(cos -160 + i sin -160 ) A) 9 5 [cos (215 ) + i sin (215 )] B) (9 + 5) [cos (-105 ) + i sin (-105 )] C) 9 5 [cos (-8800 ) + i sin (-8800 )] D) 9 5 [cos (-105 ) + i sin (-105 )] 57) Find the product or quotient. Write the answer in standard form. 58) 6 + 3i 7-5i 58) F) 57 7 + 9 7 i G) 9 8-17 i H) 27 8 7 + 51 i J) 19 7 8-17 8 i Use basic identities to simplify the expression. 59) tan θ cot θ 59) A) sin θ B) sec 2 θ C) tan 2 θ D) cos 3 θ 60) 1 + sec θ cos θ cot 2 θ F) 1 G) sec 2 θ H) csc 2 θ J) tan 2 θ 60) Simplify the expression to either 1 or -1. 61) sin(-x) csc x A) -1 B) 1 61) 62) cos π - x csc (-x) 2 62) F) 1 G) -1 Simplify the expression. 63) cos x + sin x tan x A) tan x - 1 B) sec x C) cot x - 1 D) csc x 63) 6) csc 2 x sec x sec 2 x + csc 2 x F) cos x G) cot x H) sec x J) sin x 6) 9
Find an exact value. 65) sin 105 65) A) 6-2 B) - 6 + 2 C) 6 + 2 D) - 6-2 Write the expression as the sine, cosine, or tangent of an angle. 66) sin 52 cos 13 - cos 52 sin 13 F) cos 65 G) sin 39 H) cos 39 J) sin 65 66) 67) cos π 5 cos π 7 + sin π 5 sin π 7 67) A) cos 12π 35 B) sin 2π 35 C) cos 2π 35 D) sin 12π 35 Find an exact value. 68) cos π 12 68) F) 6-2 G) - 6 + 2 H) - 6-2 J) 6 + 2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Prove the identity. 69) 1 + csc x = cos x + cot x 69) sec x 10
Answer Key Testname: UNTITLED1 1) A 2) J 3) A ) F 5) A 6) F 7) A 8) G 9) C 10) H 11) C 12) H 13) D 1) G 15) C 16) J 17) C 18) G 19) C 20) J 21) C 22) G 23) D 2) F 25) B 26) J 27) A 28) J 29) A 30) H 31) B 32) H 33) C 3) J 35) A 36) F 37) A 38) F 39) C 0) H 1) C 2) G 3) C ) H 5) D 6) G 7) C 8) H 9) D 11
Answer Key Testname: UNTITLED1 50) F 51) A 52) H 53) D 5) J 55) A 56) F 57) D 58) H 59) C 60) G 61) A 62) G 63) B 6) F 65) C 66) G 67) C 68) J 69) 1 + csc x sec x = cos x 1 + 1 sin x = cos x (sin x + 1) sinx = cos x sin x sin x + cos x = cos x + cot x. sin x 12