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41e2fa06 - MATH 41 EXAM II FORM A FALL 2006 1 Indicate...

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Unformatted text preview: MATH 41 EXAM II, FORM A FALL 2006 1. Indicate the 'J?- and y‘ intercept on the graph of the function y = 5. Factor the polynomial PW) = 33 +332 + 43: +4 completely and ﬁnd 1‘3 — 54- all its zeros. n) .r-intercept 4, y-intcrcept 64 a) 21" _gi‘ _1 b) :r-intercept 64. y-intercept —4 b) 21', _21" 71‘ 1 c) sic-intercept 4, y-intercept 74 c) 2‘ #21 Cl) tic-intercept 4. y-interr'ept —64 d) 21‘ _21" l; 0 e) r-interrept 64. y—intercept 4 e) 2‘ -2‘0 4:33 + 8:162 + 135?. Find the polynomial P(a:) of degree 3 with integer coefﬁcients, and 2 Find the quotiLnt and rtmalnder 119mg 011g divmon for 23:2 + 5 zeros 5 and 51. a.) Tho quotient is 3:1: 7 20; the remainder is 2m + 4. a) r3 _ 103:2 + 25:3 b) The quotient is 21' 7 4; the remainder is 31‘ — ‘2. b) 1.3 _ 5332 + 25:1: _ 31 C) The quotient is 33: - 20; the renminder is 2.: — 4. c) x3 u 55:2 + 25\$ _ 125 d) The quotient is 23': + 4; the. remainder is 3:1: — 20. (1) \$3 + 103:2 _ 5.1: + 125 e The uotie t ’ 2:1: 4; the. remainder is 29: 5. ) q “15 + + e) 3x2—10x+25 3. Use the Factor Theorem and choose a factor of P(:r:) : .123 + 5-122 + . . . a: k 12 73: + 3. 8. Find the :c- and y-intercepts of the ratlonal function f(:r) = + 4 . :1: a) 5': + 1 a.) wrintercept (12,0), y—intercept {0, —5) b) .1: +3 b) :r-intercept (73. 0), y-intercept (0,12) (z) :r — 1 c) J's-intercept (—12.0), y-intercept (O. —2) d) :r — 3 cl) m-intercept (12,0), y-intercept (O. —3} 1 _' . ‘ 7 _' e) as + g e) 1' ltltLI‘uept ( 1. (J), y intercept (0,12) _ 7 9. Find the horizontal 2 i t' oi as m t in." rft} t' l f .t" 4. Find all rational zeros of the polynomlal P(:r:) : 1'3 — 1083': — 432. 9 ”K ver lc y p 0 b J 16 re. 10ml unr‘ Jon 1' :17 : —_ ( ) a: +9 a) *6. 712 a) horizontal asymotote y : 9; vertical asymptote :1: 2 —9 b) —5. 12 h) horizontal asymotote y = 9; vertical asymptote .1: = 9 c) 6,76 c) horizontal asymotote y : 0; vertical asymptote a: : 79 d) 6. '12 (1) horizontal asymototo y : 0; vertical asymptote :1; : 718 e) 712. 12 e) horizontal asymotote y = 0; vertical asymptote 1' : 9 5. Find all the real zeros of the polynomial P(u:) : 1‘3 + 8.7.12 + 8:1: — 8. I 10. State the range of the function h.(x) = 4 + (%) . a) ‘21 —2 ﬂ: V13 ii 74,4 b) -3.—3i\/13 l) ( l b \$4.00 c) —2.—3i\/13 ) ( l C} (Q 00) d) 72. 2 :l: V13 d) (—00-00) 0;!) —i5. —2 :: V 13 8) (4~ 00) MATH 41 EXAM 11, FORM A FALL 2006 11. Express the equation ear—3 = 0.1 in logarithmic form. 16. The area of a circle is 60 (1112. Figd the area of a sector of this circle that subtends a central angle of E rad. a) :r = 3+thl.1 13) 1i" = 0.1 + 1n3 a) 7: c.1112 I') :r = 0.1 +1n3 b) g cm2 d) a: : 0.1—1.13 c) 5 cm2 9) 1' = —3 +1n 0.1 d) 10 cm2 e) 6 cm2 12. Evaluate the expression logs V7 625, 17. Evaluate sin 30° sin 60° + cos 60° cos 30°. 7 a) 0 b} 7 ,. 4 b) E c) 4 2 1 d) é o) E e) 28 d) 1 \/§ 1:) — 2 1 13. Rewrite the expression log 24 + i log 5 — log-8 as a single logarithm. . . . _ . . 3 1 18. Find the value of the trigonometric function tanE) if st = E and a) 103 5%; 6 is in the second quadrant. 1)) log 5\/§ 3 a) 7 C) log3\/g 4 4 d) log 15 b) g 1 . e) log 3 ﬂ C) k i . . . 4 14. Solve the logarithmic equation 10g3(5 7 cc) = 1 for a“. d) —E e 1 a) 1' = 3 ) b) at : 2 . .o _ _ _ 19. If a = ‘20,!) = 28 and 4A : .30 ID a triangle ABC, ﬁnd 511145. c) a: = —3 a) 1 C!) a. — *8 10 e .r : 8 2 ) b) .— .3 15. The number of bacteria in a culture is modeled by the function G) E n(t) = 3009.0“ where L is measured in hours. What is the initial 15 number of bacteria? 5 d) — 7 a) 1 bacteria. 2 e) F b) 600 bacteria C) 60 bacteria d) 300 bacteria e) U bacteria MATH 41 EXAM IL FORM A FALL 2006 20. Find the area of the triangle ABC whose sides are a, = 13.6 = 2L) and c : 21. a) 17 b) 54 c.) 260 d) 126 9) 27 FALL 06 MATH 041 EXAM 2 ITEM NO. FORM: A 1 D 2 D 3 AB 4 B 5 C 6 A 7 C 8 D 9 C 10 E 11 A 12 A 13 C 14 B 15 D 16 E 17 B 18 C 19 A 20 D ...
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