WASHINGTON STATE MU ALPHA THETA 2009 INDIVIDUAL TEST

Transcription

1 WASHINGTON STATE MU ALPHA THETA 009 INDIVIDUAL TEST ) What is 40% of 5 of 40? a) 9. b) 4.4 c) 36. d) 38.4 ) The area of a particular square is x square units and its perimeter is also x units. What is x? a) b) c) 4 d) 8 3) How many four letter arrangements can be made from the letters A, B, C, D, E, and F, if the first letter must be A and one of the letters must be B and no letter can be used more than once? a) 36 b) 3 c) 4 d) 8 4) MAO city has eight streets, all of which are straight. No street is parallel to another street. One police officer is stationed at each intersection. What is the greatest possible number of police officers needed? a) 4 b) 6 c) 8 d) 30 5) Rank the following in order from largest to smallest: A= 75 B = 4-86 C = a) A, B, C b) B, A, C c) C, A, B d) A, C, B 6) An integer from to 00 inclusive is chosen at random. What is the probability that the integer is a perfect square or a perfect cube, but not both? a) b) 0 c) 9 d) 00

2 7) All positive integers whose digits add up to are listed in increasing order: 9, 38, 47,. What is the product of the digits of the eleventh number in that list? a) b) 8 c) 4 d) 6 8) The mean, median, unique mode and range of a set of positive integers are all 8. What is the largest possible value of any element? a) b) 3 c) 4 d) 5 9) Rank in order from largest to smallest: A = The volume of a right circular cylinder with radius cm and height cm B = The volume of a sphere with radius cm C = The volume of a cube with edge 3cm a) B,C,A b) A,B,C c) B,A,C d) A,C,B 0) The least integer of a set of consecutive even integers is 30. If the sum of the set of these integers is 66, how many integers are in this set? a) 3 b) 33 c) 34 d) 35 ) The probability of an unfair coin landing heads is 5 3 and a probability of landing tails is 5. If the coin is tossed 5 times what is the probability it will land tails 4 times and heads once? 8 a) b) 35 7 c) d) 35 ) I traveled from Bellingham to Seattle at a constant rate of 50mph. On the exact same trip back I traveled at a constant rate of 70 mph. What was my average rate in mph of the entire trip? a) 60 b) 6 3 c) 58 d) 58 3

3 3) Each of the circles in the figure has a radius of. If a point within the square is chosen at random, what is the probability the point is in the shaded region? a) 6π b) π 4 c) 4 π 4 d) 64 6π 4) How many cubic inches are there in two-thirds of a cubic foot? a) 8 b) 96 c) 5 d) 54 5) The product of a number M and six less than M is 5. What is the sum of all possible values of M? a) 6 b) 9 c) d) 7 e)nota 6) What is the sum of this following series? a),683 b) 486 c) 56 d),84 7) Given the following addition problem, with digits A, B, and C: AB + AB = CC, and A B C, how many distinct ordered triples (A, B, C) exist? a) b) c) 3 d) 4 8) How many equilateral triangles can be formed using the grid below if at least of the vertices of the triangle must be on points of the grid? a) 4 b) 30 c) 36 d) 4

4 9) In the figure shown below, AC = CD = DE = EB, and AE = 4 5 inches. What is the number of square inches in the area of triangle ADB? A C D E B a) b) 5 c) 6 d) 6 5 0) Given that 3 n divides 5!, what is the greatest possible integral value of n? a) 7 b) 8 c) 9 d) 0 ) What is the sum of all possible values of n satisfying the following equation? 3(n ) 4(n + ) 6(n 3) = (n ) - 8 a) 5 b) 7 c) d) φ ) What is the tenth term of the arithmetic sequence a n, with a = 3 and a = 73? a) 70 b) 59 c) 49 d) 66 3) This mathematician named the number e, claiming that it stood for the word exponential, instead of his name. a) Euclid b) Euler c) Erdös d) Eratosthenes

5 4) Simplify: ( 5)( log 7)( log 04)( log 40) log3 7 5 a) + log 896 b) 896 c) 360 d) ) What is the largest possible product of a set of positive integers whose sum is 0? a),458 b),68 c),96 d) greater than,800 6) Stephanie remembers that her 5-digit zip code contains only the digits 7, 8, and 9, and each digit is used at least once. How many different zip codes are possible? a) 75 b) 00 c) 5 d) 50 7) If two integers -40 inclusive are randomly selected, what is the probability that exactly one of the two integers selected is divisible by 4? a) 4 9 b) 5 c) 5 3 d) 8 3 8) Express as a fraction: % + 3,33 a) b) 440,84 c) 44,94 d) 440 9) What is the area of the region bounded by the graphs of the following? y = - x + 4 and y = x - 4 a) 4 b) 8 c) 6 d) 3 30) Evaluate: a) 0 9 b) 0 c) 5 3 d) 5

6 3) A pentagonal number is a number that can be represented in a pentagonal array. The first pentagonal number is, the second is 5 and the third is. What is the tenth pentagonal number? = a) 0 b) 3 c) 4 d) 45 3) In a trivia game, there are two types of questions: an easy question and a hard question. A player receives 3 points for answering an easy question and 7 points for answering a hard question. What is the largest integer that cannot be a contestant s total score for the game? a) 3 b) 3 c) 43 d) greater than 50 33) There are four baskets numbered from to 4 and four balls numbered from to 4. Each basket is allowed to have at most two balls. How many ways can the balls be placed in the baskets such that no ball has the same number as the basket it's in? a) 63 b) 66 c) 69 d) 7 34) After performing an ordinary arithmetic addition, a man replaced each digit with a unique letter. TAKE + MORE MONEY What digit does E represent in the above problem? a) 4 b) 5 c) 6 d) 7 35) How many positive 3-digit numbers have an even number of even digits? a) 5 b) 360 c) 450 d) 900

7 36) Four friends (Curtis, Tamara, David, and Tiffany) are sitting around a circular table talking about their respective sports of expertise (tennis, golf, swimming, or jogging). The following information is known: Curtis is sitting across from the tennis player. David is sitting across from the golfer. Tamara is sitting on Tiffany s left. The jogger is sitting on the swimmer s right. There is a boy sitting on Curtis right. Who is the golfer among the four? a) Tamara b) Tiffany c) Curtis d) David 0 37) Find x, if =. x a) x = - b) x = 0 c) x = d) x = 38) What is the equation of a line in slope/intercept form that passes through the origin and is perpendicular to the line x 3y = 4? 3x a) y = b) y = 3x 3x 3x c) y = + d) y = - 39) A right circular cone is inscribed in a hemisphere of radius 6 such that the base of the cone is the base of the hemisphere. What is the volume of the hemisphere that is not contained in the cone? a) 36π b) 48π c) 64π d) 76π 40) How many ordered pairs of positive integers (x, y) are solutions to the equation 5x + 3y = 9? a) b) c) 3 d) 4 or more