Math Olympiad 5( Week 26 Mid-Term Exam) 1. If a♣b = |a − 2b|, what is the value of (7♣4)♣3? 2. If a♠b = a2 − ab + b2, what is the value of (4♠3)♠5? 3. If a♥b = a + ab + b2, what is the value of (7♥4)♥3? 4. Eric is 7 times the age of Mary who is 4 years older than Richard. If the total age of the three is 50, how old is Richard? 7. If a⊛b = a2 − 2ab + b2, which of the following has the greatest value? 8. There are 24 hours a day, 60 minutes in an hour and 60 seconds in a minute. There are even smaller time units, such as millisecond (10 −3 second), microsecond (10 −6 second), nanosecond (10 −9 second). How many seconds are in 1 hour 41 minutes? 9. If 4 days before yesterday was Monday, what day of the week will it be 30 days from today? 10. There are 12 triangles. Each triangle has exact one shared side with another triangle. How many sides are there in total? 11. There are 6 math exams during the semester. Nick has taken 5 exams so far and the scores were 91, 86, 89, 90, and 93. What will Nick need to score on his final math exam to have an average score of 87 for the semester? 12. Using digits 1, 2, 3, 4, 5, 6, and 7, how many different 3-digit numbers can you make if no digit can be used more than once within a number? 13. Using a die(a cube with number of 1 to 6), what is the probability of throwing a 2, 3 and 6 in the order? 14. The product of 5 consecutive even numbers must be divisible by: 15. What is the least common multiple (LCM) of 2, 3, 4, 5, and 6? 16. A spinner shown in the diagram has 7 equal sections. The probability of the pointer falling into each section is the same (Assume the pointer will never fall on a line between two sections). What is the probability that the pointer falls on an odd number?
17. A spinner shown in the diagram has 8 equal sections. The probability of the pointer falling into each section is the same (Assume the pointer will never fall on a line between two sections). What is the probability that the pointer falls on a number that is a prime?
18. If 8x is deducted by 10y, and the difference is then multiplied by , which of the following is the result? 19. Three consecutive multiples of 20 have a sum of 480? What is the largest number among the three numbers? 20. A complete cycle of a traffic light takes 55 seconds with light in green for 30 seconds, amber for 10 seconds, and red for 15 seconds. What is the probability that the light will NOT be green? |