Test # 3 Review Math Name (6.5 to 6.7, 10.1 to 10.3,and 10.5)

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1 Test # Review Math 14 Name (6.5 to 6.7, 10.1 to 10.,and 10.5) Date: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the product of the complex numbers. Leave answer in polar form. 1) z1 = 7(cos π 4 + i sin π 4 ) 1) z = 4(cos π 6 + i sin π 6 ) A) 11(cos 5π 1 C) 8(cos 5π 1 + i sin 5π 1 ) B) 11(cos π 1 + i sin π 1 ) + i sin 5π 1 ) D) 8(cos π 1 + i sin π 1 ) Find the quotient z 1 of the complex numbers. Leave answer in polar form. z ) z1 = 6(cos π + i sin π ) ) z = 1(cos 5π 6 + i sin 5π 6 ) A) 1 (cos 4π + i sin 4π ) B) 1 (cos 4π - i sin 4π ) C) 1 (cos π + i sin π ) D) 1 (cos π - i sin π ) Find all the complex roots. Write the answer in the indicated form. ) The complex cube roots of 8i (rectangular form) A) i, - i, - - i B) -i, + i, - + i C) i, + i, - + i D) -i, - - i, - i ) 4) The complex fourth roots of -16 (rectangular form) A) 1 + i, 1 - i, -1 + i, -1 - i B) + i, - i, - + i, - - i C) + i, - i, - + i, - - i D) i, 8-8 i, i, -8-8 i 4) Write the complex number in rectangular form. 5) (cos 5 + i sin 5 ) A) i B) + - i C) + - i D) + i 5) Find the absolute value of the complex number. 6) z = - A) B) 0 C) 44 D) - 6) 1

2 Use DeMoivreʹs Theorem to find the indicated power of the complex number. Write answer in rectangular form. 7) (- + i)6 7) A) i B) 64i C) i D) -64 8) Let vector u have initial point P1 = (0, ) and terminal point P = (, -). Let vector v have initial point Q1 = (, 0) and terminal point Q = (6, -4). u and v have the same direction. Find u and v. Is u = v? A) u = 7, v = 7; yes B) u = 5, v = 5; no C) u = 5, v = 5; yes D) u = 7, v = 7; no 8) A vector v has initial point P1 and terminal point P. Write v in terms of ai + bj. 9) P1 = (0, 0); P = (-5, 6) A) v = -6i + 5j B) v = -5i + 6j C) v = 5i - 6j D) v = 6i + 6j 9) Find the magnitude and direction angle (to the nearest tenth) for the vector. Give the measure of the direction angle as an angle in [0,60 ]. 10) -4, - 10) A) 7; 16.9 B) 5;.1 C) 5; 6.9 D) 5; ) One rope pulls a barge directly east with a force of 50 newtons, and another rope pulls the barge directly north with a force of 74 newtons. Find the magnitude of the resultant force acting on the barge. A) 14 newtons B) 89 newtons C) 700 newtons D) 4 newtons 11) A vector v has initial point P1 and terminal point P. Write v in terms of ai + bj. 1) P1 = (-, ); P = (-5, -6) A) v = -9i - j B) v = -i - 9j C) v = -4i - 8j D) v = -8i - 4j 1) Find the specified vector or scalar. 1) u = -i - 6j, v = -6i + 8j; Find u + v. A) -4i + j B) 4i - 9j C) -8i + j D) -9i + j 1) 14) An aircraft going from Atlanta to Savannah on a heading of 17 (from north) is travelling at a speed of 510 miles per hour. The wind is out of the north at a speed of 18 miles per hour. Find the actual speed and direction of the aircraft. A) 499 miles per hour; 19 from north B) 714 miles per hour; 18 from north C) 51 miles per hour; 19 from north D) 505 miles per hour; 19 from north 14) Find the magnitude v of the vector. 15) v = 9i + 1j A) 15 B) 1 C) 5 D) 15 15)

3 Find projwv. 16) v = i - j; w = 5i + 1j A) i + 9 j B) - 1 i - 7 j C) i - 7 j D) - i j 16) Use the given vectors to find the specified scalar. 17) v = i + 7j; Find v v. A) 81 B) 196 C) 8 D) 5 17) Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. 18) v = i + j, w = i - j A) orthogonal B) parallel C) neither 18) Use the given vectors to find the specified scalar. 19) u = 1i - 7j and v = -6i + 7j; Find u v. A) -49 B) -17 C) -78 D) -9 19) 0) A person is pulling a freight cart with a force of 50 pounds. How much work is done in moving the cart 0 feet if the cartʹs handle makes an angle of with the ground? A) foot-pounds B) foot-pounds C) foot-pounds D) 56. foot-pounds 0) 1) Find the work done by a force of pounds acting in the direction of 40 to the horizontal in moving an object 9 feet from (0, 0) to (9, 0). A) 0.7 foot-pounds B).1 foot-pounds C) 17.4 foot-pounds D) 41.4 foot-pounds 1) Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. ) v = i, w = -i A) orthogonal B) parallel C) neither ) Find the angle between the given vectors. ) u = 4j, v = 9i - j A) 10.5 B) 150. C) -1.5 D) 64. ) Find the indicated sum ) 9i i = 1 A) 1 6 B) C) D) 5 6 4) 5) 5 i = 1 (-1)i - 1 (i + 1)! A) B) C) 60 D) )

4 Write the first four terms of the sequence whose general term is given. n4 6) an = (n - 1)! A) 4 0, 8 0, 6, 8 B) 1 0, 16 0, 81, 18 C) 1, 16, 81, 18 D) 4, 8, 6, 8 6) 7) an = (n + 1)! A) 4, 1, 48, 40 B), 8, 6, 19 C) 4, 4, 144, 960 D), 4, 1, 48 7) Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a0, the 0th term of the sequence. 8) a1 = 4, d = -0. A) an = 4n - 4.; a0 = 75.7 B) an = -0.n + 4.; a0 = -1.7 C) an = 4n - 0.; a0 = 79.7 D) an = -0.n + 4; a0 = - 8) Write the first five terms of the arithmetic sequence. 9) an = an ; a1 = 5 A) 4, 10.8, 17.6, 4.4, 1. B) 5, 6.8, 11.8, 18.6, 5.4 C) 6.8, 11.8, 16.8, 1.8, 6.8 D) 5, 11.8, 18.6, 5.4,. 9) Write out the first three terms and the last term of the arithmetic sequence. 70 0) -5i i=1 A) B) C) D) ) Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. 1) Find a when a1 = -8, d = -. 1) A) -104 B) 88 C) -101 D) 85 Find the indicated sum. ) Find the sum of the first 70 terms of the arithmetic sequence: -19, -1, -5,,... A) 15,575 B) 15,80 C) 471 D) 15,580 ) Write the first five terms of the arithmetic sequence. ) a1 = 6; d = -1 A) 5, 4,,, 1 B) 6, 5, 4,, C) 7, 6, 5, 4, D) 6, 5,,, ) Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. 4) Find a8 when a1 =, d =. 4) A) -11 B) 19 C) -1 D) 17 4

5 Write the first five terms of the geometric sequence. 5) an = -an-1; a1 = -4 A) -, -1, -6, -108, -4 B) 1, -6, 108, -4, 97 C) -4, -7, -10, -1, -16 D) -4, 1, -6, 108, -4 5) Write a formula for the general term (the nth term) of the geometric sequence. 6) 4, 1, 1 4, 1 16, 1 64,... 6) A) an = n + 1 B) an = n - 1 C) an = n D) an = n - 1 Use the formula for the sum of the first n terms of a geometric sequence to solve. 7) Find the sum of the first 14 terms of the geometric sequence: 5, 15, 45, 15, 405,.... A) 11,957,4 B) 11,957,457 C) 11,957,400 D) 11,957,40 7) Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. 8) Find a10 when a1 = 6, r =. 8) A) B) 118,098 C) 118,10 D) 54,94 The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 9) an = n - 5 9) A) arithmetic, d = B) arithmetic, d = -5 C) geometric, r = D) neither Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 5 40) 4 i i = 1 A) 48 B) C) 75 D) ) Use the Binomial Theorem to expand the binomial and express the result in simplified form. 41) (5x + )4 A) 1875x x + 150x + 160x + 81 B) 65x4 + 81x4 C) 65x x + 150x + 540x + 81 D) 65x x + 150x ) Find the term indicated in the expansion. 4) (x - y)1; 9th term A) -6,60x4y9 B) 16,70x8y4 C) -6,60x8y4 D) 16,70x4y8 4) 4) (x + y)10; 9th term A) 9,660x8y B) 9,660xy9 C) 1,180,980xy8 D) 590,490x8y 4) 5

6 44) (x - y)1; 11th term A) -,79x10y B) -,79xy11 C) 67,584xy10 D) 67,584x10y 44) Use the Binomial Theorem to expand the binomial and express the result in simplified form. 45) (x + y)6 A) x6 + 18x5y + 6x4y + 54xy + 6xy4 + 18x y5 + y6 B) x6 + 18x5y + 79x4y + 60xy + 79xy4 + 18xy5 + y6 C) x6 + 18x5y + 15x4y + 540xy + 115xy xy5 + 79y6 D) x6 + 18x5y + 108x4y + 486xy + 97xy xy5 + 79y6 45) 6

7 Answer Key Testname: TEST # REVIEW MATH 14 FALL 011 1) C ) C ) B 4) C 5) A 6) A 7) D 8) C 9) B 10) D 11) B 1) B 1) C 14) C 15) A 16) C 17) D 18) A 19) B 0) B 1) A ) B ) A 4) B 5) B 6) C 7) A 8) B 9) D 0) A 1) C ) A ) B 4) D 5) D 6) B 7) D 8) B 9) D 40) A 41) C 4) D 4) C 44) C 45) C 7