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Name___________________________________ Exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Expand the binomial. 1) (4x + 1)4 A) 256x4 + 256x3 + 96x2 + 16x + 1 C) 256x4 + 256 x3 + 96x2 + 16x + 1 2) (x - y)5 A) x5 - 5x4 y + 10x3y2 - 10x2 y3 + 5xy4 - y5 C) x5 + 5x4 y + 10x3y2 + 10x2 y3 + 5xy4 + y5 3) ( x y)4 B) x2 + 4x xy + 6xy + 4y xy + y2 D) -x2 - 4x xy - 6xy - 4y xy - y2 4) B) 256x3 + 256x2 + 96x + 16 D) (16x2 + 4x + 1)4 2) B) x5 - y5 D) -x5 + 5x4 y - 10x3 y2 + 10x2 y3 - 5xy4 + y5 3) 1) A) x2 + y2 C) x2 - 4x xy + 6xy - 4y xy + y2 4) (x-3 + 2)5 A) x-15 + 32 B) x-15 + 5x-12 + 10x-9 + 10x-6 + 5x-3 + 1 C) 32x-15 D) x-15 + 10x-12 + 40x-9 + 80x-6 + 80x-3 + 32 Find the coefficient of the given term in the binomial expansion. 5) x3y13 term, (x + y)16 A) 560 6) x6y6 term, (x + y)12 A) 110,880 7) x7 term, (x - 2)14 A) -439,296 C) 439,296 8) x4 term, (x - 3)15 A) 241,805,655 9) x6 term, (x - 3)15 A) -15,015 B) 1 C) 1820 D) 7280 5) 6) B) 924 C) 6 D) 665,280 7) B) -2.21405184e+09 D) 3432 8) B) -4095 C) 1365 D) -241,805,655 9) B) -98,513,415 C) 5005 D) 98,513,415 Write out the first five terms of the sequence. 10) a n = 4n - 2 A) 2, 6, 10, 14, 18 C) 2, 3, 4, 5, 6 B) 6, 10, 14, 18, 22 D) -2, -6, -10, -14, -18 10) 1 11) cn = A) n+2 3 2 45 , 1, , , 2 3 33 B) 22222 ,,,, 33333 45 7 , , 2, 33 3 11) 22222 C) 1 , 2 , 3 , 4 , 5 33333 n+2 n 22222 ,,,, 34567 B) 1, 1, 1, 1, 1 D) 1, 12) cn = A) 12) C) 3, 2, 537 ,, 325 D) 56789 ,,,, 34567 Find the first six terms of the sequence. 13) a 1 = -6, an = 4 an-1 A) -24, -96, -384, -1536, -6144, -24,576 C) -6, -24, -20, -16, -12, -8 14) a 1 = 9, a2 = 9; for n 3, an = an-1 + an-2 A) 9, 9, 18, 27, 36, 45 C) 9, 9, 18, 18, 27, 27 15) a 1 = 4, a2 = 2; for n 3, an = an-1 - an-2 A) 4, 2, 0, -2, -4, -6 C) 4, 2, 6, 8, 11, 19 B) 4, 2, -2, -4, -2, 2 D) 4, 2, 2, -2, 2, -2 B) 9, 9, 18, 27, 45, 72 D) 9, 9, 81, 729, 59,049, 43,046,721 B) -6, -24, -96, -384, -1536, -6144 D) 0, 4, -24, -20, -16, -12 13) 14) 15) Find an explicit rule for the nth term of the arithmetic sequence. 16) -14, -11, -8, -5, ... A) a n = -14 + 3(n+2) B) a n = -14 + 3(n+1) C) a n = -14 3(n-1) 17) -13, -19, -25, -31, ... A) a n = -13 (-6)(n-1) C) a n = -13 - (-6)(n+1) 18) a 17 = -28, a19 = -102 A) a n = 564 - 37(n + 1) C) a n = 564 - 37(n - 1) 19) a 9 = 45, a10 = 6 A) a n = 357 + 39(n + 1) C) a n = 357 - 39(n - 1) Find an explicit rule for the nth term of the sequence. 20) 3, 15, 75, 375, ... A) a n = 3 5 n-1 B) a n = 3 5n+1 B) a n = 357 - 39(n + 1) D) a n = 357 + 39(n - 1) B) a n = 564 - 37(n - 2) D) a n = 564 + 37(n + 1) D) a n = -14 + 3(n-1) 16) 17) B) a n = -13 + (-6)(n+1) D) a n = -13 + (-6)(n-1) 18) 19) 20) C) a n = 5 3 n-1 D) an = 3 5 n 2 21) -12, 4, 36, -108, ... A) a n = 4 3 n-1 21) B) a n = 4 (-3)n-1 C) a n = 4 3 n+1 D) an = 4 (-3)n 22) 22) The second and fifth terms of a geometric sequence are 12 and 324, respectively. A) a n = 4 3 n+1 B) a n = 4 3n-1 C) a n = 4 3 n+3 D) an = 4 3 n-2 Find a recursive rule for the nth term of the sequence. 23) -2, -1, 0, 1, ... A) a n = a n-1 - 1 B) a n = an-1 - 2 24) 8, -16, 32, -64, ... A) a n = a n-1 -2 23) C) a n = a n-1 + 2 D) an = a n-1 + 1 24) B) a n = an-1 -4 C) a n = a n-1 -3 D) an = a n-1 -1 Write the series using summation notation. 25) 4 - 12 + 36 - 108 + ... A) 43 n B) 4 3 n+1 n=0 n=0 26) 49 + 64 + 81 + 100 + ... + n 2 + ... A) n 2 B) n-12 n=7 n=7 27) 11 + 13 + 15 + 17 + ... + 2n+1 ... 20 A) (2n+1) B) (2n+1) n=5 n=5 Find the sum of the arithmetic series. 28) 34 + 36 + 38 + 40 + ... + 56 A) 408 B) 540 29) -16 - 11 - 6 - 1 + ... + 39 A) 44 25) C) n=0 4(-3)n D) n=0 4(-3)n-1 26) C) n=8 n2 D) n=7 n+1 2 27) 20 C) (2n+1) D) n=6 (2n+1) n=6 28) C) 58 D) 432 29) B) 138 C) 118 D) 108 30) 30) 247 + 245 + 243 + 241 + ... + 229 A) 2580 B) 227 Find the sum of the geometric series. 31) 3 + 9 + 27 + 81 + 243 A) 366 B) 361 4 16 64 256 1024 + + + + 3 3 3 3 3 A) 1364 15 B) 1360 3 C) 2461 D) 2380 31) C) 363 D) 373 32) 32) C) 272 3 D) 1364 3 3 33) 33 3 3 3 ++ + + 2 8 32 128 512 A) 341 B) 1023 512 C) 1 16 D) 11 512 33) Find the sum of the first n terms of the sequence. 34) 30 + 38 + 46 + 54 + ... ; n = 10 A) 700 B) 770 35) 5 + 2 - 1 - 4 + ... ; n = 11 A) - 110 B) 253 2 34) C) 510 D) 660 35) C) 275 2 D) - 138 36) -6 - 24 - 96 + ... ; n = 11 A) 5592405 36) B) 20132658 C) - 33554430 D) - 8388606 Write the repeating decimal number as a fraction. 37) 0.6666 . . . 6 2 A) B) 999 3 38) 3.96969696 . . . 131 A) 30 39) 0.0140140140 . . . 140 A) 999 37) 66 C) 999 2 D) 33 38) B) 131 33 C) 131 99 D) 131 11 39) 7 B) 495 14 C) 999 14 D) 99 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use mathematical induction to prove the statement is true for all positive integers n. 1n 319 1 12 1 n-1 40) 3 + 3 + 3 + ... + 3 = 9 9 9 1 19 40) 41) 1 2 + 2 3 + 3 4 + ... + n(n + 1) = n(n + 1)(n + 2) 3 5n(5n + 1)(10n + 7) 6 41) 42) 5 7 + 6 8 + 7 9 + ... + 5n(5n + 2) = 42) 4 Answer Key Testname: PRECALTEST4REVIEW 1) A 2) A 3) C 4) D 5) A 6) B 7) A 8) D 9) B 10) A 11) D 12) C 13) B 14) B 15) B 16) D 17) D 18) C 19) C 20) A 21) B 22) B 23) D 24) A 25) C 26) A 27) A 28) B 29) B 30) D 31) C 32) D 33) B 34) D 35) A 36) D 37) B 38) B 39) C 40) Answers will vary. 41) Answers will vary. 42) Answers will vary. 5

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