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# 41efsp07 - MATH 41 FINAL EXAM.‘ FORM A SPRING 2007 5 3.ln...

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Unformatted text preview: MATH 41 FINAL EXAM.‘ FORM A SPRING 2007 5 . . . 3 .ln 1. The common ratio in a geometric sequence is g, and the fourth term 6- Find the Inverse funCtlon 0f = (1 _ 33 }" - is Find the third term. a) fﬁl{:r) 2 (1 — m5)3 a) 2 b) r1 (m) = M1 — x5) 5 b _ 7 3 1 )7 c) f 101:): (1—525) c) E‘- d) Pond—mi 5 l 2 9) f_1(w) : d) E (1 amt 7 7 1+5 - - ' e) : 7. Express the equation a ‘ : 0.1 in logarithmlc form. L) 17 a.) .1:=O.1+l!16 2. Find all solutions of the equation 2 + 2 + — = O. z b) (r: 76+ln0.1 a) z=—4+16i.z=74716i c) :1::6+111CL1 b) No solutions (1} I = 0.1 — ln 6 c) z:4+2i,z:4—21 e) :r=61n0.1 d) z 71+4i‘z= 4—43 9) z : LZ : _1 8. Find all the real zeros of the polynomial P(a:) = x3 + 9:1:2 + 7.7: — 1. z ~:—4‘ =—1 V17 3‘ Find the. polynomial of degree 2 with integer coefﬁcients and 1) J m j: zeros?—iand2+i. b) I=_4.x=_4i\/17 ‘ C ":l‘ =ﬁ-1:I:v17 a) :r‘i + 49: — 4 J “L a: ‘ ":71..:1i\/17 b) m2—4r+5 d) “L 'T c) J32+2m+5 c) 55:71.1'2—4iv’17 d) 13+21—4 ‘ L A 9. For the function = 4365, ﬁnd M. e) x2—2w+4 h _ a.) 40.3 + 121111 + 12112 4. Determine the correct equation for the line passing through the point (1‘11) and the point (15‘8). b) 12112 — 12cm, +4112 c) 1263 + 4m + 12h? n)14y—3x+157=0 d) 12a2 + 120.}; + 4n? h) My + 31' + 157 = U o) Baa + 12ah, — 4h2 c) 14y+3gr — 157 :0 d 14 e 3 . — 1’? = 0 . } y I d 10. Use the Laws of Logarithms to rewrite the expression log 9 e) 11y—15x—8=0 a) logm _ 2 10159 5. Use HI.) = 21‘ 7 9 nndy(:r:) :10 — m to evaluate b) (IOEQEWOE 9) a) 2 C) loga- 9 b) 9 d) logs? —l(_1g9 C) 739 e) iogw + logQ d) 723 e) 18 MATH 41 FINAL EXAM, FORM A SPRING 2007 1]. The fox population in a certain region has a relative growth rate of 16. The 15th term of an arithmetic sequence is 11 and the second term . r 7% per year. It is estimated that the population in 1996 was 14000. is 3' Find the ﬁrst term. Find a function that models the populatlon L years aFter 1996. 4 a. 2 a) 71.00 : 14090500" +1996 ) b) 1.25 b) '11.“): 14000.9I c) —0.25 c) n.(t) = 1400087f d) 1 d) n(t) : 14000610"- 3) 0.5 e) = 14000 + e“ l 1 17. Solve the equation + ﬂ : 2m + . 12. Rewrite the expression logr 32 + log 2 7 loge; as a single logarithm. \/§ 2!.) —3 a) luglx/i 4 b) 3 b) log 4V6 c) 2 c) In NZ d) —3 1 . cl) log e.) —2 10148 18. Find the third term ofthe recursively deﬁned sequence on = 601111,] 7 6) and a1 : 8. 13. Solve 2M: + 8| + 9 > 6. a) 38 6. a) l 00) b) 6 b w , —" 3. )(oc ow co) C) .12 C) (—90‘ 0°) (1) 36 — . 715 U 1'1 dwoo )(aoo) Q48 9) E 19. Indicate all 3’." and y—intercepts on the graph of the function y : 1.2 + 6 1:3 7 27. 14. Find the vertical asymptote of the rational function r(:c) = 9 . a. 7 a) ctr—intercept 3, y—intercept 27 a) .1" = 79 b) wiintercept 3, y—inturcept —3 b} :r = —6 c) a:-intercept 27, y—intercept 3 c) (F = 6 cl) miinlercept 27, ykintercept —3 d) .1.- : 9 e) Ji-il'ltEl'CCpt 3. y—intercept 727 e) :r = 18 I _ _ _ _ _ _ 20. Test the equation y = 93:3 + 2.2: for symmetry. 15. Find the pomt on the y—axts that IS equlchstant from the points (1. —8) and (7, 0). a) The symmetry is around the point (2. 2) a) (0.- 4) b) The symmetry is around the .T—ﬂxib‘. b) (*1. 0) c} The symmetry is around the y—axis. c‘) (0, 0) d) The symmetry is around the origin. d) (0, —3) e) There is no symmetry. e) (0. —1) MATH 41 FINAL EXAM, FORM A SPRING 2007 21. In a. triangle ABC, B 2 120°. C = 30° and h : 20 inches. Find the 1 . J —1 _ _ length of the side c. 26' Evaluate hm ( 2 . . a) I a) 20 inchea 2 2 7r b) i inches b) *g x/ﬁ 7r c) 20% inches C) E d) 20\/§ inches d) I 6 t' 30 inches ) o) O 22. Use the law of cosines to ﬁnd a. true statement from the list below, 1 if B = 90°. ‘27. 1f 005A = i with A in uadrant IV ﬁnd cot 2A. V10 q ’ :1) b2=a2+c2+ac a) ,E 4 b) b2:a2+cz+aC\/§ 4 . b) T c) l.»2 : a2 + c3 5 cl) (12 :r),2+c'2 —a.c (3) —§ 9) b2 : a? + c2 — acﬁ 4 d) 7 6 23. Find the remaining sides of a 30° 7 60° — 90° triangle if the longest 8) § side is 8. g 5 mfg 28. Solvecoswi2sinmcosa:=0if0£x(£2711 3“) 5‘ 2 a) E 7r 5n b) 3,-3\/3 2.2.3.3 . 5 C) if b) wall—75 2 2 d 3 d) 5, WE c) 0W1!” 5 6 p) 4.4f3 d) E 31. 7. 5T. ' 2’ 2 ’ 6’ 6 . . ‘ ‘ - 2 24. Simplify (H? :9 — 3m Scot 9. e) 01 7]., 2_7r, 4—77 .3 3 a) sin!) . . 29. erte the eqnatmn r 2 6 cos :9 in rectangular coordinates. b) tanﬂ C) C0129 a) 592 'i 1’2 2 5"" d) 2(3056 b) m2 + y 2 6.1: e) sinﬂmsB C) 1‘2"!)2 2553 d) mg + y2 = 6x 25. Simplify sin2 45° — 20 sin 45° cos 45° + 00.32 45°. 6) r2 _ U2 : 6x a.) —9 b) 20— x/E c) —12 d) 20 e) 1 MATH 41 FINAL EXAM, FORM A 30. Evalute (cos 15° + isin 15°)9 by wing DeMo'wrc’s theorem. a) 1—1 G) e) —%-1% SPRING 2007 SPRING 07 MATH 041 FINAL ITEM NO. FORM: w komemU'IID-LLJNH l—l ON w UIJUIUFW wturam U mtjﬁjm Mtjflw U UIUDJW m mtﬁﬂjd m ...
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