For all questions, answer choice E) NOTA" means none of the above answers is correct.

Transcription

1 0 MA Natonal Conventon For all questons, answer choce " means none of the above answers s correct.. In calculus, one learns of functon representatons that are nfnte seres called power seres. For nstance, e.... Whch of the followng s the equvalent epresson of e? (Defne 0 for all ) A) B) 0! C) 0! D)!!. Refer to queston : Whch of the followng s the power seres for cosh, where s a real number? (Agan, defne 0 for all ) A) B) 0! C) 0! D) 0! 0! 3. Another mportant result of power seres s 0 z number such that z. What s the value of the seres A) does not converge B) 4. A result of power seres s that z, where z s a comple n n n 4 4? C) D) z. Usng ths, what s the coeffcent of the 5z z z, where z? z, where z s a comple number such that z z term of the power seres for A) 5 B) 3 C) D) 3 5. Consderng all dstnct permutatons of the letters n POWERSERIES, what s the probablty that a randomly selected permutaton begns wth POWER? A) 4640 B) 30 C) 940 D) 540

2 0 MA Natonal Conventon 6. When the graph of 7 5y 0 y 3 0, where, s revolved around the lne 0, whch of the followng best represents the surface that s formed? A) a submarne B) a nuclear coolng tower C) one car headlght D) two car headlghts 7. A crcular waterwheel wth radus 7 meters has a small bucket attached to ts outsde. The waterwheel begns spnnng, and you observed that two seconds later, the bucket s at ts greatest heght. If the waterwheel rotates at 6 revolutons/mnute, and ts center s 6 meters above the water, whch equaton descrbes the dstance d of the bucket above the surface of the water n terms of the number of seconds t after the waterwheel begns spnnng? 5 A) d 7 6cos t 0 D) d 6 7cos t 0 B) d 7 6cos t 5 C) d 6 7cos t. Where defned, whch of the followng s equvalent to csc? A) csc cos sn B) cot csc C) csc cos sn D) cot csc sec 9. Let 3 n be an nteger. Smplfy the product n A) n B) n C) n D) n y y 0. Solve for y : y y y 76 A) 4 B) 3 C) D). Functon f satsfes f y f f y for all real numbers and y. If whch of the followng statements s true? I) f 0 II) f.5 5 III) f 0 0 f, A) III only B) I and II only C) II and III only D) I, II, and III

3 0 MA Natonal Conventon. If 0 and cos sn 5, fnd the value of cos sn. 4 4 A) 7 6 B) 5 6 C) 5 6 D) Whch of the followng dmensons could not be for the fgure they descrbe? A) quadrlateral wth sde lengths, 3, 4, & 7 ft. B) trangle wth sde length 5 m C) trangle wth sde lengths 6, 7, & n. D) trangle wth sde lengths, 7, & 5 dm 4. For ntegers n, k, and r, where n k r, sum of k r? n n. What s the smallest possble k r A) B) 3 C) 4 D) 5 5. Fnd the sum: 5 A) 5 B) 3 5 C) 5 6 D) If, y, and z are non-zero, consecutve ntegers wth y z, whch of the followng yelds a postve odd nteger? A) y z B) y z C) y z D) z y 7. If z log a 3 solves the equaton z z z 4 6 9, fnd the value of a. A) 4 B) C) 3 4 D) 5 4. Whch of the followng statements are true? a c I) If a b c b d, then, where s any non-zero nteger. d II) 3 s a cube root of. III) If y s a negatve number and z s a ratonal number, then number. z y wll be an magnary A) I & II only B) I & III only C) II & III only D) I, II, & III

4 0 MA Natonal Conventon 9. Fnd the vector equaton of the lne of ntersecton of the planes wth equatons y z and 3y 3z 7. 3 A) r d 3 d j d k B) r d 3 d j d k C) r d 3 d j d k D) r d 3 d j d k The fourth roots of 6c s0 correspond to four angles n standard poston n the plane. What acute angle s formed by the second quadrant angle and the -as? A) 0 B) 40 C) 70 D) 0. If,, a b c, where a b c, s the soluton to the system y z y z yz, fnd yz 40 c b a. A) 5 B) 9 C) 4 D) 36. If, s a Cartesan ordered par on the graph of r tan sec, then? A) 4 B) C) 6 D) Fnd the sum of the real values of k that make the matr 4k k 3 k sngular. A) 9 B) 0 C) 9 6 D) 4. How many solutons est for cos cos4 3sn3 for 0? A) 6 B) 5 C) 4 D) 3

5 0 MA Natonal Conventon 5. What s the cotangent of the angle that the dagonal of a cube makes wth one of ts edges? A) B) 3 3 C) D) 3 6. Whch of the followng statements s true? I) A graph through the ponts,09, 3,43, 4,7, 5,4, and 6,305 could defne a lne. II) A graph through the ponts,00, 4,64, 7,, 0,6, and 3,496 could defne a parabola. A) I only B) II only C) I & II D) nether I nor II 7. How many of the followng statements are true? I) The equaton 7 3y 3y 4 y 0 represents a hyperbola. II) The eccentrcty of a crcle s always. III) The dstance from the center of 3y 4 y 4 to a focus s 3. A) 0 B) C) D) 3 f 5 and g 6, fnd the range of f gcos.. If B), A), C) 0, D) 0, 9. For q , y M s the horzontal asymptote, whle Aand O represent, respectvely, the number of vertcal and oblque asymptotes M A O. A) 6 B) 5 C) 3 D) q has. Fnd 30. If M and m are the mamum and mnmum values, respectvely, of P 5 9y, subject to the constrants 3y 9, 5y 5, y, and 5y 5, fnd the value of M m. A) 43 B) 36 C) 3 D) 4