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San Diego Junior High Math Field Day 2010 Math Wits FINAL ROUND ** indicates a question with a PowerPoint visual. 1. ** L a s V e g a s , N e v a d a was f o u n d e d on May 15, 1 9 0 5, at which time it consisted of 110 a c r e s or 0 . 4 k m2. How many square meters were in the original size of Las Vegas? 2. **Convert 10011110base 2 to base 10. 3. A regular polygon has an interior angle measure of 162 degrees. How many sides are in the polygon? 4. If a 7-inch tall right cylinder has a volume of 56π, how many inches long is the diameter of its base? Express your answer in simplest radical form. 5. A family has three children that are not all boys. What is the probability that all three children are girls? 6. **Triangle ABC is rotated 90 counterclockwise about point A, what are the coordinates of C’? San Diego Junior High Math Field Day 2010 Math Wits FINAL ROUND 7. **What is the greater of the solutions to the equation x2 – 15x – 54 = 0? 8. The measures of two interior angles of a given parallelogram are 10x degrees and 5x degrees. What is the value of x? 9. What percent of the one-digit positive integers is prime? Round your answer to the nearest whole percent. 10. **What is the value of y, to the nearest tenth? 55 y 13 11. **If a # b = b2 + a and a @ b = b – a, what is the value of ((7 # 3) @ 1)? 12. A rectangle has a length of 2x + 3 units, a width of x – 5 units, and an area of 34 square units. What is the value of x? San Diego Junior High Math Field Day 2010 Math Wits FINAL ROUND 13. A book costs $1 plus half of its price. How much does the book cost? 14. **What is the area of the regular hexagon shown here? Express your answer in simplest radical form. 15. What is the value of 1+ 1 4 2 1 2 6 2 1 3 4 ? 2 16. **A point (a, b)is located in the second quadrant of the Cartesian plane. The coordinates are changed according to the functions given: f(a) = 2 – a and g(b) = b2 + 1. In which quadrant is (f(a), g(b)) located? 17. What is the value of y in the arithmetic sequence y + 6, 12, y? 18. **A large square region is divided into four congruent, non-overlapping square regions. If the perimeter of one of these small square regions is 48 cm, what is the area, in square centimeters, San Diego Junior High Math Field Day 2010 Math Wits FINAL ROUND of the large square? 19. Line m contains the points (4, –3) and (8, 5). What is the y-coordinate at the point where line m intersects the y-axis? 20. **What is the ones digit of 32010? San Diego Junior High Math Field Day 2010 Math Wits FINAL ROUND KEY Student: 1. 400,000 (m2) 2. 158 3. 20 4. 4 2 5. 1/7 6. 1 2 3 4 5 Final scores Student 1: Student 2: (4, 2) 7. 18 8. 12 9. 44 (%) 10. 22.7 Student 3: 11. –15 12. 7 13. $2 14. Student 4: 384 3 15. 5 16. 1, I, first 17. 9 18. 576 (cm2) 19. –11 20. 9 Student 5: