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1 Northern Arizona University Department of Mathematics and Statistics 2010 Math High School Day College Bowl Competition Students, start your brain cells! 2 Evaluate: 1 9 [2] 3 If one box of Froot Nootles will feed three adults, or two teenagers, or five children, how many boxes would be needed to feed a crowd of 30 adults, 30 children and 30 teenagers? [31] 4 What number is three more than half of itself? [6] 5 If x$y stands for (x-1)y, what is (5$3)$2? [22] 6 Sam is two years older than his brother Jim. The sum of their ages is 30. When will the sum of their ages be 40? [2015] 7 What number is three less than half of itself? [-6] 8 How many ways are there to travel from S to F along roads, never visiting the same town twice? S F [4] 9 Simplify: 2 1 1 3 4 [30/13] 10 How many distinct arrangements of the letters MATH are there? [24] 11 What is 20% of 20 plus 30% of 30? [13] 12 How many ways are there to travel from S to F along roads, never visiting the same town twice? S F [9] 13 If a is 2 and b is 3, what is b a a –b ? [-1] 14 Evaluate: 25 81 [4] 15 Compare the two numbers using <, =, or >. 7 5 -1.35 [<] 16 Solve: x 1 5 [x = 24] 17 If half of it is 5 more than a third of it, how much is all of it? [30] 18 What number is 12 more than its square root? [16] 19 How many distinct arrangements of the letters MATT are there? [12] 20 What number is 12 more than twice itself? [-12] 21 Two numbers differ by 3 and their squares differ by 45. What is their sum? [15] 22 Calculate: 1 10 2 3 2 2 [3] 23 The small circle has radius 1 and passes through the center of the big circle. What is the area of the shaded region? [3π] 24 25 16 [3] 25 4 5 7 7 8 10 11 12 ?? [14] 26 x If [email protected] is , y 1 what is ([email protected]) – ([email protected])? [-1] 27 7 1 2 5 1 2 [2] 28 How long is side h of this right triangle? 7 h 5 [√24 or 2√6] 29 If I drive at 30 mph for 20 minutes, then 60 mph for 10 minutes, what is my average speed? [40 mph] 30 Which of these consists of a figure 4 and a reflection of it? A C B E D [D] 31 In a class of 30 students, 8 are blonds, 10 have red hair, and 12 have black hair. If one student is chosen at random, what is the probability that his/her hair is black? [2/5] 32 What is the next number in the sequence below? 192, 96, 48, 24, 12, . . . [6] 33 Ya wanna sandwich? What kinda bread: white, wheat, rye, or pumpernickel? Meat? We got ham, roast beef and chicken. Cheese? Yeah, Swiss, American, or Muenster. How many different sandwiches can you order? [36] 34 What is the area of a circle with radius π? 3 [π ] 35 10 is 20% of what number? [50] 36 Simplify: 3 4 4 2 37 The square is 8 inches on a side, the diagonals meet the sides at midpoints. What is the area of the white band? 8 4 [32 in2] 38 Two numbers differ by 9 and their sum is 7. What are they? [8 and -1] 39 The equation below has exactly two solutions. Both of them can be found without any solving. What are they? (x-1)(x-2)(x-3)(x-4) = 24 [0,5] 40 If x is the first number and y is the second, how do you write the statement “the first number is 5 more than twice the second”? [x = 2y+5] 41 abc bca cab bcd cdb dbc cde dec ?? [ecd] 42 The radius OD is 5, the segment OC has length 3 and is perpendicular to the chord AB. How long is AB? A C B 3 O [8] 5 D 43 The sum of a number and its reciprocal is smaller than the number. How can that be? [The number must be negative] 44 George tells you that the average of 4 consecutive numbers (i.e. positive integers) is 120. What do you deduce? [That George is a liar]