Math Olympiad 5( Week 26 Mid-Term Exam) 1. If a♣b = |a − 2b|, what is the value of (4♣2)♣3? 2. If a♠b = a2 − ab + b2, what is the value of (5♠4)♠8? 3. If a♥b = a + ab + b2, what is the value of (2♥4)♥3? 4. Josh is 7 times the age of Hillary who is 9 years older than Rene. If the total age of the three is 126, how old is Rene? 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 3 hours 11 minutes? 9. If 3 days before yesterday was Friday, what day of the week will it be 70 days from today? 10. There are 20 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 87, 85, 85, 90, and 90. 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, and 5, 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, 4 and 5 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, 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 even number?
17. A spinner shown in the diagram has 5 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 20x is deducted by 25y, and the difference is then multiplied by , which of the following is the result? 19. Three consecutive multiples of 15 have a sum of 405? What is the smallest number among the three numbers? 20. A complete cycle of a traffic light takes 65 seconds with light in green for 20 seconds, amber for 10 seconds, and red for 35 seconds. What is the probability that the light will NOT be green? |