Math Olympiad 5( Week 26 Mid-Term Exam) 1. If a♣b = |a − 2b|, what is the value of (8♣6)♣12? 2. If a♠b = a2 − ab + b2, what is the value of (3♠2)♠1? 3. If a♥b = a + ab + b2, what is the value of (2♥1)♥3? 4. Ed is 4 times the age of Jane who is 7 years older than Ben. If the total age of the three is 71, how old is Ben? 7. If a⊛b = a2 − 2ab + b2, which of the following has the smallest 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 4 hours 33 minutes? 9. If 4 days before yesterday was Saturday, what day of the week will it be 80 days from today? 10. There are 14 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. Smith has taken 5 exams so far and the scores were 85, 89, 85, 81, and 91. What will Smith need to score on his final math exam to have an average score of 84 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 3, 5 and 6 in the order? 14. The product of 5 consecutive natural numbers must be divisible by: 15. What is the least common multiple (LCM) of 2, 3, 4, 5, 6, and 7? 16. A spinner shown in the diagram has 10 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 6 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 multiple of 3?
18. If 12x is deducted by 16y, and the difference is then multiplied by , which of the following is the result? 19. Three consecutive multiples of 30 have a sum of 900? 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 35 seconds, amber for 5 seconds, and red for 15 seconds. What is the probability that the light will NOT be green? |