The Questions, Answers and Analysis of the Fifth Grade Olympic Mathematics in a Primary School
30 beads are strung into a circle in the order of 8 red, 2 black, 8 red and 2 black ... A grasshopper jumps down from the second black bead, jumping six beads at a time and landing on the next one. This grasshopper has to jump at least a few times before it lands on the black beads again. Answer and analysis:
These beads are strung in a circle according to the order of 8 red, 2 black, 8 red and 2 black, so for every 10 bead, we can infer that when these 30 beads count to the ninth and 10, 19 and 20, 29 and 30, 39 and 40, 49 and 50, they will be just right, I ..
The Test Questions, Answers and Analysis of Olympiad Mathematics in Grade 5, Grade 2.
The annual interest rates of lump-sum deposit and withdrawal in the bank are: two years 1 1.7%, three years 12.24% and five years 13.86%. Both Party A and Party B deposit RMB 10000 at the same time. Party A deposits it for two years, and then deposits it with interest for three years. B for five years. Five years later, both of them are taken out at the same time, so who has more income and how much more? Answer and analysis:
If A is kept for two years, the interest earned after two years is:/kloc-0 /×1.7 %× 2 = 0.234 (ten thousand), and after three years it is (1+23.4% )×12.24 %×.
If B is stored for five years, after five years, 1× 13.86%×5=0.693 (ten thousand yuan) will be obtained.
So b is greater than a, 0.693-0.453=0.24 (ten thousand yuan).
Problems, Answers and Analysis of the Fifth Grade Olympiad Mathematics in the Third Primary School
A string of numbers are arranged in a line, and their law is like this. The first two numbers are 1. Starting from the third number, each number is the sum of the first two numbers, namely 1, 1, 2, 3, 5, 8, 13, 2 1, 34, 55, … Q. Answer and analysis:
If you look at the written numbers, you will find that every two odd numbers have an even number. If you count a few more figures, you will find that this rule still holds. This rule is not difficult to explain: because the sum of two odd numbers is an even number, two odd numbers must be followed by an even number. On the other hand, the sum of odd number and even number is odd number, so the even number is followed by odd number, and the latter is still odd number. In this way, an even number must be followed by two consecutive odd numbers, which must be followed by an even number, and so on. Therefore, even numbers appear in the third, sixth, ninth ... 99th seats. So the number of even numbers is equal to the number of multiples of 3 in 100, which is equal to 99/3=33.
Problems, Answers and Analysis of Olympiad Mathematics in Grade Four and Grade Five of Primary School
A ship goes upstream on the river at a speed of about per hour 1000 meters. At noon, a passenger's hat fell into the river. The passengers asked the boatman to return to chase the hat, when the ship was already sailing upstream at a distance of 0/00 meters from the hat/kloc-. As we all know, the speed of this ship in still water is 20 meters per minute. Suppose you start chasing hats right away, regardless of the time of turning around, and ask when you should get them back. Answer and analysis:
The idea is that the ship's speed in still water is 20m per minute. Given that the ship's speed in still water is hourly 1200m and the conditional water speed is hourly 1000m, the upstream speed of the ship is 1200- 1000 = 200m, and the downstream speed of the ship is 65440. From the time when the hat falls into the water under the condition 12 to the time when the ship leaves the hat 100 meters, this cycle actually goes in the opposite direction, and the time is:100 ÷ (200+1000) =1/kloc-.
Detailed explanation of ship's still water speed: 20× 60 = 1200m.
Ship countercurrent speed:1200-1000 = 200m.
Ship speed along the water: 1200+ 1000 = 2200m.
Time from the hat falling into the water to leaving the hat 100 m:100 ÷ (2200-1000) =112 hours =5 minutes.
The catching-up time is100 ÷ (2200-1000) =112 hours =5 minutes.
The total time for the hat to fall into the water at 12 is: 5+5= 10 minute.
A: The recovery of hats should be 12 and 10.
The Problems, Answers and Analysis of Fifth Grade Olympiad Mathematics in Fifth Primary School
Two cars, A and B, set off from A and B at the same time and walked in opposite directions. The two cars met for the first time at a distance of B 64 kilometers ... After the encounter, the two cars continued to drive at the original speed and immediately returned along the original road after reaching the starting point of the other side. On the way, the two cars met for the second time at a distance of 48 kilometers. What is the distance between A and B? Answer and analysis:
When A and B cars, * * *, completed a journey of AB together, B car walked 64 kilometers. As can be seen from the above picture, when they met for the second time, they took three AB journeys. Therefore, we can understand that the car B * * * walked three 64 kilometers. From the above picture, subtracting 48 kilometers is exactly equal to an AB trip. The distance between AB is 64× 3-48 = 144 (km).