Review Test 1. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Review Test 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the function. 1) f() = + 1 if < 1-4 if 1 1) - - A) B) C) D)

2 ) f() = - + < ) - A) B) C) D)

3 3) f() = 1 if -1 < 4 if 4 < 7 if ) A) (7, 7) (4, 4) (7,.6) (14, 3.7) (-1, -1) (4, -1) - - B) (7, 7) (4, 4) (-1, 1) (7,.6) (4, 1) (14, 3.7) - - 3

4 C) (7, 7) (4, 4) (-1, 1) (7,.6) (4, 1) (14, 3.7) - - D) (7, 7) (4, 4) (7,.6) (14, 3.7) (-1, -1) (4, -1) - - Locate an intercepts of the function. 4) f() = if < if 1 A) (0, -3) B) (0, -3), (3, 0), ( 1 3, 0) 4) C) (0, 9), (3, 0), ( 1, 0) D) (0, 9) 3 ) 1 if -4 < -8 f() = if -8 < 4 3 if 4 33 A) (0, 0), (0, 1) B) (0, 0), (1, 0) C) (0, 0) D) none ) 4

5 Based on the graph, find the range of = f(). 6) 6) f() = if 0-6 if = (0, -6) - A) (-, ) B) (-, 0) or (0, ) C) (-, ) D) (-, 0) or {0} or (0, ) Use the Rational Zero Theorem to list all possible rational zeros for the given function. 7) f() = ) A) ± 1, ± 1 B) ± 1 4, ± 4, ± C) ± 1, ± D) ±, ± 1 8) f() = ) A) ± 1, ± 1, ± 1 1 B) ± 1, ±, ± 3, ± 4, ± 6, ± 1 C) ± 1, ± 1 3, ± 1 4, ± 1 6, ± 1, ± 1, ±, ± 3, ± 4, ± 6, ± 1 1 D) ± 1, ± 1, ± 1 3, ± 1 4, ± 1 6, ± 1 1 9) f() = ) A) ± 1 7, ± 3 7, ± 1, ± 3, ± 7 B) ± 1 7, ± 3 7, ± 1, ± 3 C) ± 1 7, ± 1 3, ± 1, ± 3, ± 7 D) ± 1 3, ± 7 3, ± 1, ± 7 Find a rational zero of the polnomial function and use it to find all the zeros of the function. ) f() = A) {-, 1, 3} B) {-1} C) {-3} D) {-3, -1, } )

6 11) f() = A) {, 3 +, 3 - } B) {1, -1, 8} C) {, 6 + 8, 6-8} D) {-, 6 +, 6 - } 11) 1) f() = ) A) {- 1 3, 3, - 3} B) {-3, 3, - 3} C) {1 3, 3, - 3} D) {3, 3, - 3} 13) f() = A) {-3, - 1, -3 + i, -3 - i} B) {3, - 1, -3 + i, -3 - i} 13) C) {-3, + 1, - + 3i, - - 3i} D) {3, + 1, - + 3i, - - 3i} Solve the polnomial equation. In order to obtain the first root, use snthetic division to test the possible rational roots. 14) = 0 14) A) {-3, -1, } B) {-1} C) {-3} D) {-, 1, 3} 1) = 0 A) {1, -3 +, -6 - } B) {-1, -3 + i, -3 - i} C) {-1, + 3i, - 3i} D) {-1, +, - } 1) 16) = 0 A) {1, -4, 1 + i, 1 - i} B) {-1, 4, 1 + i, 1 - i} C) {-1, 4, 1 + 6i, 1-6i} D) {1, -4, 1 +, 1 - } 16) Find an nth degree polnomial function with real coefficients satisfing the given conditions. 17) n = 3; 3 and i are zeros; f() = A) f() = B) f() = C) f() = D) f() = ) n = 3; and i are zeros; leading coefficient is 1 A) f() = B) f() = C) f() = D) f() = ) n = 4; i, 4, and -4 are zeros; leading coefficient is 1 A) f() = B) f() = C) f() = D) f() = ) 18) 19) Find the domain of the rational function. 8 0) h() = - 9 A) { 0} B) { 9} C) { -9} D) all real numbers 0) 6

7 1) h() = A) all real numbers B) { -,, -8} C) { 0, 4} D) { -, } + 7 ) h() = + 36 A) { 0, -36} B) { -6, 6} C) all real numbers D) { -6, 6, -7} 1) ) Find the vertical asmptotes, if an, of the graph of the rational function. 3) f() = + 4) h() = A) = 0 and = B) = 0 and = - C) = - D) no vertical asmptote ( - ) A) = 0 and = B) = 0 and = - C) = D) no vertical asmptote ) g() = - 16 A) = 4 B) = 4, = -4 C) = 4, = -4, = 0 D) no vertical asmptote 3) 4) ) 6) A) = - 81 B) =, = 3, = - 81 C) =, = 3 D) = -, = -3 6) Find the horizontal asmptote, if an, of the graph of the rational function. 8 7) f() = + 1 7) A) = 0 B) = 1 4 C) = 4 D) no horizontal asmptote 8) g() = + 1 8) A) = 1 B) = 0 C) = D) no horizontal asmptote 7

8 9) h() = A) = - B) = -3 C) = - 1 D) no horizontal asmptote -9 30) f() = ) 30) A) = -3 B) = C) = 0 D) no horizontal asmptote Graph the rational function. 4 31) f() = ) A) B)

9 C) D) ) f() = -4-3) A) B)

10 C) D) ) f() = ) A) B)

11 C) D) ) f() = ) A) B)

12 C) D) Find the slant asmptote, if an, of the graph of the rational function. 3) f() = A) = B) = + 7 C) = + 9 D) no slant asmptote 3) 36) f() = A) = + B) = - 8 C) = + 3 D) no slant asmptote 36) 37) h() = A) = - 3 B) = + 6 C) = - 6 D) = 37) Graph the function. 38) f() = )

13 A) B) C) D) Find the component form and magnitude of the indicated vector. 39) Given that P = (1, 3) and Q = (3, ), find the component form and magnitude of the vector PQ. A) -, -7, 3 B), 7, 3 C) -, -7, 3 D), 7, 3 39) 40) Given that P = (-4, 13) and Q = (-, 8), find the component form and magnitude of the vector QP. A) -1, -, 6 B) 1,, 6 C) -9,, 16 D) 1,, 6 40) 41) Given that P = (-, 1) and Q = (-8, 8), find the component form and magnitude of the 41) vector QP. A) -, 7, 3 B) -, 7, 6 C), -7, 6 D) 7, 3, 3 Find the component form of the indicated vector. 4) Let u = -4, 8, v = 4, 3. Find u + v. A) 4, 7 B) 0, 11 C) -1, 1 D) -8, 4) 43) Let u = 7, -1, v = -4, 7. Find v - u. A) 0, -3 B) -8, 11 C) -11, 8 D) 3, 6 43) 44) Let u = -6, -. Find u. A) 30, B) -30, C) -30, - D) 30, - 44) 13

14 4) Let u = -7, 9. Find -8u. A) -6, -7 B) 6, 7 C) -6, 7 D) 6, -7 4) 46) Let u = -1, -3, v =,. Find -3u + v. A) -1, -6 B) -, -16 C) 8, D) 8, 34 46) Find the unit vector in the direction of the given vector. Write our answer in the indicated form. 47) Let u = 3, 1. Find the unit vector in the direction of u, and write our answer in component form. 3 A) 1, 1 B), 1 3 C), 1 3 D) 4, ) 48) Let u = 1,. Find the unit vector in the direction of u, and write our answer as a linear combination of the standard unit vectors i and j. 1 A) 6 i + 6 j B) 1 6 i + 6 j C) i + j D) 1 6 i + 6 j 48) 49) Let u =, 1. Find the unit vector in the direction of u, and write our answer as a linear combination of the standard unit vectors i and j. A) i + j B) 6 i j C) 6 i j D) 6 i j 49) Find the component form of the vector v. 0) 0) A) -7.07, 8.43 B) -8.43, 7.07 C) -0.77, 0.64 D) -7.78,

15 1) 1) A) 6.73,.11 B).11, 6.73 C).99, 3.6 D) 0.6, 0.97 ) A) -8.46, 3.08 B) -9, 1.8 C) -0.98, 0.17 D) -8.86, 1.6 ) 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. 3) -1, 14 3) A) 197, 4.1 B) 197, 94.1 C) 197, 8.9 D) 197, ) -1, - A) 9, 97.6 B) 9, C) 9, 6.4 D) 9, ) ) -4, 4 3 A) 1, 40 B) 8, 10 C) 1, 300 D) 8, 40 ) 6) (cos 136 i + sin 136 j) A), 136 B), 44 C) 0, 44 D), 136 6) 1

16 Solve the problem. 7) A plane is heading due south with an airspeed of 98 mph. A wind from a direction of 1.0 is blowing at 18.0 mph. Find the bearing of the plane. (Note that bearings are measured from north, clockwise.) Round results to an appropriate number of significant digits. A) 87 B) 183 C) 9 D) 178 7) 8) An airplane flies on a compass heading of 90.0 at 390 mph. The wind affecting the plane is blowing from 344 at 3.0 mph. What is the true course and ground speed of the airplane? Round results to an appropriate number of significant digits. A) 89, 41 mph B) 93, 41 mph C) 89, 396 mph D) 93, 397 mph 8) 9) Two forces of 433 N and 7 N act at a point. The resultant force is 16 N. Find the angle between the forces. A).7 B) 90.8 C) 89. D) ) 60) One rope pulls a barge directl east with a force of 8 N, and another rope pulls the barge directl north with a force of 71 N. Find the magnitude of the resultant force acting on the barge. A) 13 N B) 9 N C) 4118 N D) 19 N 60) 61) An airplane is fling on a bearing of 80 at 00 mph. Find the component form of the velocit of the airplane. Round our answer to the nearest hundredth. A) , B) -13.9, C).00, 1.79 D) , ) Find a b. 6) a = 4, 7, b = 1, 4 A) 4 B), 11 C) 4, 8 D) 3 6) 63) a = 3, -, b =, 1 A) 13 B) 17 C) 1, - D) 8, -1 63) 64) a = 6i + j, b = 4i + 3j A), B) -18 C) 30 D) 4, 6 64) 6) a = 8i + j, b = -0.i - 3j A) 7., -1 B) - C) -4, -6 D) - 6) 66) a = 1j, b = i + 4j A) 0, 48 B) -48 C) 1, 48 D) 48 66) Find the angle between the given vectors to the nearest tenth of a degree. 67) u = -9, 1, v = -8, 7 A) 7. B) 44.9 C) 34.9 D) ) 68) u = i - 7j, v = i + j A) 6.9 B) 90.4 C) 96.4 D) ) 69) u = 3, -8, v = -8, -3 A) 180 B) 90 C) 0 D) 4 69) 16

17 Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, projvu. 70) u = 8, 6, v =, 4 70) A) -1, - + 9, -4. B), 4 + 6, C) 4, 8 + 4, - D) 3, 6 +, -. 71) u = -8,, v = 1, A) 1, + -9, 0 B) 0., , 1 C) 1, + -, 1 D) -0.8, , ) 7) u = 3, 6, v = 7, -1 A) 3., , -13 B) 7, , 7 C).1, , 6.3 D) 7, , 7 7) Solve the problem. 73) What is the minimum force required to prevent a ball weighing 7.0 lb from rolling down a ramp which is inclined 13.6 with the horizontal? A) 6.3 lb B) 3. lb C) 13.1 lb D) 6. lb 73) 74) A constant force F = 19, moves an object along a vector D = 16, 13, where units are in pounds and feet. Find the work done. A) 69 foot-pounds B) 1 foot-pounds C) -1 foot-pounds D) foot-pounds 74) 7) Find the work done b a force F of pounds acting in the direction 1, in moving an object 8 feet from (0, 0) to (8, 0). A) 17.4 foot-pounds B) foot-pounds C) foot-pounds D) 176 foot-pounds 7) 76) The angle between a -pound force F and AB = i + 4j is 30. Find the work done b F in moving an object from A to B. A) foot-pounds B) foot-pounds C) 81 foot-pounds D) foot-pounds 76) 17

18 Answer Ke Testname: REVIEW TEST 1 PRECALC 1) A ) D 3) C 4) D ) C 6) B 7) C 8) B 9) B ) D 11) A 1) C 13) A 14) A 1) B 16) B 17) D 18) C 19) D 0) B 1) D ) A 3) C 4) A ) B 6) C 7) A 8) C 9) C 30) C 31) B 3) A 33) D 34) C 3) C 36) B 37) C 38) C 39) D 40) D 41) B 4) B 43) C 44) C 4) D 46) D 47) B 48) A 49) D 0) B 18

19 Answer Ke Testname: REVIEW TEST 1 PRECALC 1) A ) D 3) B 4) B ) B 6) D 7) B 8) D 9) C 60) B 61) D 6) D 63) A 64) C 6) B 66) D 67) C 68) C 69) B 70) C 71) D 7) C 73) A 74) A 7) C 76) C 19