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Grissom Math Tournament Algebra I Test February 25, 2006 1. Evaluate the following: 2[121 – 4(2 + 24 – 12)] – 71 + 25 A. 14 B. 16 C. 71 D. 89 E. 91 2. Bob can type at a constant rate of 50 words per minute and Rob can type at 100 words per minute. If they work together to efficiently type a document with 1500 words, how long will it take them (in minutes) to type the document? A. 6 B. 8 C. 9 D. 10 E. 12 3. Mike is riding his bike around a circular track with a diameter of 36 feet. The radius of each wheel on his bike is 9 inches. How many rotations does each bike wheel make per lap around the track? A. 48 B. 36 C. 24 D. 18 E. 12 4. Steve can eat 5 pies in 6 minutes. Assuming Steve eats at a constant rate, how many pies could he eat in 1½ hours? A. 96 B. 84 C. 75 D. 72 E. 45 5. What is the probability that a card chosen randomly from a standard deck of 52 cards is not a heart or an ace? A. 1 4 B. 4 13 C. 1 2 D. 35 52 E. 9 13 6. Farmer Bob has x chickens and 2x cows. If each chicken has 2 legs and each cow has 4 legs, how many legs (not including Farmer Bob’s) are there on the farm in terms of x? A. 6x B. 10x C. 12x D. 16x E. 20x 7. Which of the following graphs best matches the equation 4x – 5y = 20? A. B. C. D. E. 8. Evaluate: x2 + 2ab + x if x = 2, a = 3, and b = ax. A. 36 B. 40 C. 41 D. 42 E. 46 D. 5 E. 5½ 9. Solve for x: 1 – 2[3 – (x – 3) – 4] = 34 – 2(2x + 8) A. 3½ B. 4 C. 4½ 10. If the graphs of y = 5x – 2 and y = 2x + h have the same x-intercept, what is the value of h? A. 4 5 B. 2 5 C. 2 D. 4 5 E. 5 2 11. Pedro doesn’t remember how many people are on his test writing team. He knows he chose exactly enough people to provide him 20 good questions. Each team member was asked to write 5 questions, but he knows that ½ of the team will not write any questions, and 3/5 of the remaining questions won’t be good ones. How many people are on his team? A. 16 B. 20 C. 24 D. 28 E. 32 12. Find the perimeter of a triangle with vertices at the points (8, 10), (8, 2), and (2, 2). A. 24 B. 25 C. 26 D. 27 E. 28 13. Tony mixed 50 ml of chocolate syrup into 50 ml of milk, and drank 25 ml of chocolate milk. He decided it wasn’t chocolaty enough so he added 25 ml more chocolate syrup to his cup. What percent of the new solution is chocolate syrup? A. 33 1/3 % B. 37.5% C. 50% D. 62.5% E. 75% 14. If ab = 2, bc = 4, and ac = 8, then find the value of abc. A. 16 B. 12 C. 8 D. 7 E. 4 15. If the greatest common factor of 42 and 105 is x and the greatest common factor of 84ab and 112bc is y, then find the least common multiple of x and y. A. 7 B. 28b C. 56b D. 84b E. 168abc 16. John wants to buy an MP3 player for he best friend Kevin. Sadly, the MP3 player costs $600 and John only has $400. One day, he finds the MP3 player on sale for 30% off. He goes to the store and receives a coupon for an additional 15% off of the reduced price. If John gives the cashier his $400 and the coupon, and tax is 10%, how much change will he receive? A. $121.30 B. $53.00 C. $43.10 D. $37.00 E. $7.30 17. If two fair dice are rolled, what is the probability that the sum of the values showing is not prime? A. 11 18 B. 7 12 18. If f(x) = 10x + 7 and g(x) = A. 0 C. 5 12 D. 7 18 E. 5 36 x7 , then find f(g(5)) + g(f(5)). 10 B. 5 C. 10 D. 15 E. 25 19. Find the absolute value of the difference between the solutions to the equation: x 2 4 x 41 0. ? A. 0 B. 4 C. 4 + 6 5 D. 3 5 E. 6 5 20. Find T (I G) (E R ) 2 if T = the number of positive solutions to 2x2 – 11x – 8 = 0 I = The sum of the prime factors of 2310 G = Sum of the prime numbers between 12 and 25 E = 289 2 169 49 4 9 R = The number of real numbers x, such that x3 = x A. 160 B. 161 C. 162 D. 163 E. 164 C. 3 D. 5 E. 7 21. Find the unit’s digit of 72006 - 22006? A. -5 B. 1 22. Peter starts writing down numbers starting with 1, then 2, then 3, and so on. Eventually, he gets tired and stops. If the last number he wrote was 2006, how many digits did Peter write in all? A. 6917 B. 6035 C. 4014 D. 3011 E. 2006 23. If a quadrilateral is formed by the equation xy – 3x – 4y = -12 and the x-axis and y-axis, then what is the area of the quadrilateral? A. 6 B. 8 24. Solve the following for x: A. 9 B. 16 C. 12 D. 16 E. 20 D. 49 E. 225 x 3x 1 11 C. 25 25. If x + y + z = 9 and xy + yz + xz = 21, then find the value of x2 + y2 + z2 ? A. 31 B. 37 C. 39 D. 41 E. 60 TB1. Evaluate: 212 – 202 + 192 – 182 TB2. If Jessica rides to school at a constant rate of 40 mph then returns home on her bicycle at 10 mph, what is her average rate of speed for the round trip (in miles per hour)? TB3. If A = the number of different ways can the letters in the word TEETERTOTTER can be arranged and B = the number of different ways the letters in the word SEESAW can be arranged, then find A/B. Answers: 1. E 2. D 3. C 4. C 5. E 6. A 7. B 8. D 9. A 10. A 11. B 12. A 13. D 14. C 15. D 16. E 17. B 18. C 19. E 20. E 21. D 22. A 23. C 24. B 25. C TB1 78 TB2 16 TB3 462