<p> Mu Alpha Theta National Convention: Hawaii, 2005 Gemini Test - Mu Division</p><p>2x- 10 1 7 - 3 z 1. At what point does the graph of =y - = intersect the graph of 3 3 6 7 x+ =1 - 2 y = 2 z - 9 ? 2</p><p>骣3 18 骣 1 骣3 骣 13 A) 琪 ,- ,7 B)琪-, - 2,7 C)琪 ,- 2,2 D)琪-, - 2,7 E)NOTA 桫2 7 桫 2 桫2 桫 2</p><p>2. Which of the following has a vertical line tangent to it at x = 0? </p><p>1 3 1 A) f( x ) = x B) 3 C) f( x ) = D) f( x )= sin x E)NOTA f( x ) = x x</p><p>3. What is the next term of the sequence 1, 7, 4, -17, -29, 22, 109, ____?</p><p>A) 43 B) -49 C) 149 D) -29 E) NOTA </p><p>4. When three points are randomly chosen on a circle, what is the probability that all three of them are within 45 degrees of each other?</p><p>1 1 1 3 A) B) C) D) E) NOTA 64 32 16 64</p><p>5. If A is the least common multiple of 3549 and 4998 and B is their greatest common factor, evaluate A-B. </p><p>A) 844,641 B) 5,912,613 C) 844,620 D) 5,912,592 E) NOTA </p><p>6. Which of the answer choices is closest to the variance of the weight of all rainbow trout in the Hiwassee River based the following sample of 9 rainbow trout with weights rounded to the nearest pound? 3 4 11 6 5 7 6 2 4</p><p>A) 2.7 B) 5 C) 7 D) 5.3 E) NOTA </p><p> x3 +1 7. If f( x) = and g( x) = f( f( x)) , evaluate g (0) . x -1</p><p>1 3 1 3 A) B) C) D) E) NOTA 2 4 8 2</p><p>Page 1 of 5 Mu Alpha Theta National Convention: Hawaii, 2005 Gemini Test - Mu Division</p><p>4 8. Evaluate: ex sin(p x ) dx 1</p><p>-p A) sin(ep x ) + e4 B) (e4 + e) p 2 +1 -p C) (e4 - e ) D) sin(ep x )( e4 + e ) E) NOTA p 2 +1</p><p>2 9. Evaluate: (9x2- 5 x + 3)( 6 x 3 - 5 x 2 + 4 x - 3) dx 1</p><p>3421 17101 856 1145 A) B) C) D) E) NOTA 12 60 3 4</p><p>10. Four numbers are in arithmetic sequence such that the sum of the first two is 35 more than the last and two times the sum of the first and last is 18 more than three times the third. What is the product of the first two terms of the sequence?</p><p>A) 36 B) 144 C) 108 D) not enough information E)NOTA</p><p>11. What is the surface area, in square meters, of a regular octahedron with a volume of 9 2 cubic meters?</p><p>A) 9 2 B) 18 3 C) 33 6 D) 81 E) NOTA </p><p>12. The delivery time for a package sent within the United States is normally distributed with a mean of 4 days and a standard deviation of 1 day. If 300 packages are being sent, which of the following is closest to the number of packages that will arrive in fewer than 3 days? </p><p>A) 96 B) 102 C) 198 D) 48 E) NOTA</p><p>13. Determine the slope of the line normal to the graph of y= ln x at (e2 ,1).</p><p> e2 2 1 A) B) C) -2e2 D) E) NOTA 2 e2 2e2</p><p>14. What is the area of the largest square that can be contained in a regular hexagon with sides measuring 6 cm?</p><p>A) 432- 216 3 B) 27 3 C) 216- 108 3 D) 48 3 E) NOTA </p><p>Page 2 of 5 Mu Alpha Theta National Convention: Hawaii, 2005 Gemini Test - Mu Division</p><p>15. How many integer solutions to the equation x1+ x 2 + x 3 + x 4 =10 exist if xi 1?</p><p>A) 84 B) 126 C) 105 D) 70 E) NOTA</p><p>16. How many three-digit numbers are divisible by 4 and do not contain the digit 2?</p><p>A) 148 B) 124 C) 136 D) 132 E) NOTA </p><p>17. A gambler repeatedly bets $1 that a coin will land on heads when tossed. Each time the coin comes up heads the gambler wins $1; each time the coin comes up tails he loses $1. The gambler decides he will quit playing when either he is ruined (loses all his money) or when he has $100. If he starts with $20, what is his probability of going broke?</p><p>A) 0.80 B) 0.20 C) 0.50 D) 0.75 E) NOTA</p><p>18. Which of the following is equivalent to 1444 in mod 713?</p><p>A) 926 B) 629 C) 713 D) 144 E) NOTA</p><p>19. If the square of a positive two-digit number is decreased by the square of the number formed by reversing the digits, which of the following will not always evenly divide the result?</p><p>A) 9 B) 11 C) the product of the digits of the original number D) the sum of the digits of the original number E) NOTA</p><p> cot x p 20. Consider the function, f, defined on 0 ＃x p by f( x) = for all x . If f were to cos x 2 p 骣p be defined so that it is continuous at x = , determine f 琪 . 2 桫2</p><p>A) 2 B) 1 C) 0 D) -1 E) NOTA</p><p>21. Find the coordinates of the absolute maximum point for the curve y= xe-kx where k is a fixed positive number.</p><p>1 1 1 e 1 1 A) ( , ) B) (- , - ) C) ( , ) D) (0,0) E) NOTA k ke k k k ek</p><p>Page 3 of 5 Mu Alpha Theta National Convention: Hawaii, 2005 Gemini Test - Mu Division</p><p>22. What is the domain of the function log6 (log 6 (log 6 (x ))) ?</p><p>A) {x: x > 0} B) {x: x > 1} C) {x: x > 6} D) {x: x > 36} E) NOTA </p><p>23. A quadrilateral inscribed in a circle has side lengths of 2 5, 5,3 2, and 7 . Find the area of the circle.</p><p>25 25 A) p B) 5p C) 25 D) p E) NOTA 4 2</p><p> n 24. In the expansion of ( x +1) , if n = 97, how many of the coefficients are integral multiples of 97?</p><p>A) 97 B) 96 C) 95 D) 94 E) NOTA</p><p>13 25. Evaluate: 5u u+ 3 du 6</p><p>A) 1200 B) 1196 C) 1188 D) 1192 E) NOTA </p><p>26. Assume x and y are both positive. For what y is ln( x + y) = ln(x) + ln(y)?</p><p>1+ x2 x x2 1+ x2 A) y = B) y = C) y = D) y = E) NOTA 1- x x -1 1+ x2 1- x</p><p>3333+ 667 3 27. Evaluate: 1000</p><p>8341674 A) 667333 B) 334666 C) 343657 D) E) NOTA 25</p><p>Page 4 of 5 Mu Alpha Theta National Convention: Hawaii, 2005 Gemini Test - Mu Division</p><p>28. Farmer Joe wants to build a rectangular enclosure with a dividing fence in the middle of the rectangle. He plans to put some horses on one side and some cows on the other. Also, the Ocoee River will serve as one border of the rectangle so that no fencing is needed there. The fence along the outside costs $6 per foot but the dividing fence costs $12 per foot. If Farmer Joe wants to spend $1200 for this project, what is the maximum area, in square feet, that he can enclose?</p><p>A) 100 sq. ft. B) 1250 sq. ft. C) 2500 sq. ft. D) 25 sq. ft. E) NOTA </p><p>轾4- 2 3 犏8- 3 5 29. Find the inverse matrix of A, if A = 犏 . 臌犏7- 2 4 轾4- 2 7 轾-2 2 - 1 轾4- 2 7 轾1 0 0 犏8- 3 5 犏3- 5 4 犏5 8- 3 犏0 1 0 A) 犏 B) 犏 C) 犏 D) 犏 E) NOTA 臌犏3 4 3 臌犏5- 6 4 臌犏3 4 3 臌犏0 0 1</p><p>30. The formula x(t) gives the position of a particle along the x-axis. The relationship between x and t is given by t� x- x3 5. What is the particle's velocity when it is at position x = 2? </p><p>4 8 21 49 A) B) C) D) E) NOTA 21 49 4 8</p><p>Page 5 of 5</p>