State Mu Alpha Theta Contest 2007 Algebra 3&4 Class Test

Transcription

1 State Mu Alpha Theta Contest 00 Algebra & Class Test. Rationalize the denominator: + B. + C. +. On a recent trip, Ellie drove km in the same length of time Carol took to drive 98 km. Ellie s speed was km/h greater than Carol s speed. How many km/h was Ellie driving? 0 B. C.. What is the sum of the slopes of the lines parallel and perpendicular to x + y =? B. C.. Find the distance between, &,.. B.. C... a b c. Simplify: a b c 9b c 9b c B. a b C. c b c a 00 i + i. Simplify: 00 i 00 i B. 0 C. i + i +

2 . Solve the following for t : S = H m( t t ) H Smt mh + Smt B. S C. H + t Sm H + Smt Sm 8. Solve for x: x x x + = B. C. 9. The second angle of a triangle is three times the first and the third is less than twice the first. Find the measure in degrees of the largest angle. 0 B. 9 C.. 0. Find the sum of the series: B. C. 8. Simplify: (9y + y 8) ( y + ) 9 y y + y B. y + y C. 9y + y 0 y + y. Find the units digit of 00. B. C.. A merchant places $ in a jackpot on August, then draws a name of a regular customer. If the customer is present, he or she wins the $ in the jackpot. If the customer is not present, the merchant adds $ to the jackpot on August and draws another name. Each day the merchant adds an amount equal to the day of the month. If the first person to win the jackpot wins $9, on what day of the month was her or his name drawn? August 8 th B. August st C. August th August 0 th. What is the sum of the sequence ?, B.,8 C.,0,8

3 . Solve for x: log( x x x) log( x + ) =. B. C. 0. Jamie can build a computer in hours. Sam can build a computer in hours. How long in hours will it take them to build a computer together? 8 B. 8 C Simplify: B. + C Find the equation of the line containing (-, ) and perpendicular to the line containing (, -) and (-,). y = x B. y = x + C. y = x y = x + 9. Solve: x + 8 > < x < B. x < C. < x < x > 0. Solve: g + g + g + g +... = B. 89 C. 0

4 . Simplify: 9 9 B. C The current in a river is miles per hour. In her motorboat Marissa can travel miles upstream or miles downstream in the same amount of time. What is the speed of her motorboat in still water? 8 mph B. mph C. 0 mph mph. An automobile radiator contains liters of antifreeze and water. This mixture is 0% antifreeze. How much of this mixture should be drained and replaced with pure antifreeze so there will be 0% antifreeze? B. C. 8. The sides of a square are each cm long. A second square is inscribed by joining the midpoints of the sides, successively. In the second square we repeat the process, inscribing a third square. If this process continues indefinitely, what is the sum of areas of all the squares in cm? 8 + B. 0 C.. Diophantos spent of his life as a child, as a young man and as a bachelor. Five years after he was married he had a son who died years before his father at half his father s final age. How many years did Diophantos live? 8 B. 8 C.. Simplify: ( x b x+ b x b b x m n ) ( m n ) x x m n B. m x n x C. m bx n bx m x n x

5 . Find all solutions for x in the following problem x x x x = x + 9 x 9, B. C., 8. A certain fraction, when put in lowest terms, has a value of. If the numerator is decreased by 8 and the denominator is increased by, its value is. Find the original fraction. B. C A farmer buys 00 animals for $00. The animals include at least one cow, one pig, and one chicken. If a cow costs $0, a pig costs $, and a chicken costs $0.0, how many pigs did he buy? B. C. 0. A certain amount of money saved for year at a certain annual interest rate yielded $.0. If the principal had been $ more and the interest rate % less, the interest would have been the same. Find the interest rate. % B. % C. % %. The harmonic mean of two numbers a and b is a number M such that the reciprocal of M is the average of the reciprocals of a and b. Find the formula for the harmonic mean. a + b B. + C. a b + a b ab a + b. What is the sum of and 0? 000 B. 00 C. 00

6 . When the dimensions of a cube are reduced by inches on each side, the surface area of the new cube is 8 square inches. What is the volume of the original cube in square inches? B. 08 C. 09. A ball dropped from a height of 0 feet bounces back 0 9 of that distance. With each successive bounce, the ball continues to reach 0 9 of it s previous height. What is the total vertical distance traveled by the ball when it stops bouncing? 00 B.0 C There are 000 lockers in a high school with 000 students. The day begins with the first student opening all 000 lockers; the second student closes lockers,,, 8, 0 and so on up to locker 000; the third student changes the state (opens closed lockers, closes open lockers) on lockers,, 9,, and so on; the fourth student changes the state of lockers, 8,, and so on. This goes on until every student has had a turn. After the 000 th student, which locker was touched the most? 80 B. 0 C A man goes to the bank and asks for x dollars and y cents. The banker by mistake gives him y dollars and x cents. After spending cents the man realizes that he now has twice the amount he asked for. What was the amount he asked for? Express your answer as an ordered pair ( x, y). (9, ) B. (, ) C. (, ) (, 0). What is the sum of the following sequence? 8,,,,,,,,,, B. C. 8. What is the coefficient of the x y term in the expansion of (x y) 9? B. 888 C. 9099

7 9. How many ordered pairs of positive integer solutions are there (m, n) to the equation? + = m n B. C. 0. What is the sum of all real X such that ( X - ) + ( X - ) = ( X + X - ) B. C.