1. Olympiad math problems and reference answers in the fifth grade of primary school.
1. Among the first 1000 natural numbers, how many natural numbers are neither square nor cube? Solution: Because 3 12 < 1000 < 322, 103 = 1000, there are 3 1 squares in the first 1000 natural numbers,/kloc-0. The natural number * * * is1000-(31+10)+3 = 962.
2. How many different three-digit numbers can be formed by using the numbers 0, 1, 2, 3 and 4 (numbers are allowed to be repeated)?
Solution: 4*5*5= 100.
3. How many different evaluation results are there in choosing an advanced group in learning, physical education and health from six classes in grade five?
Solution: 6*6*6=2 16 species.
4. Known 15 120=24×33×5×7. Q: How many different divisors are there in 15 120 * *?
Solution: The divisors of 15 120 can all be expressed in the form of 2a×3b×5c×7d, where A = 0, 1, 2,3,4, B = 0, 1, 2,3 and C = 0.
2. The second part of the test questions and reference answers of the Olympic Mathematics in the fifth grade of primary school
1. There are two groups of numbers, the sum of the first group of nine numbers is 63, the average value of the second group is 1 1, and the average value of all the numbers in the two groups is 8. Q: How many numbers are there in the second group? Solution: If there are X numbers in the second group, then 63+ 1 1x = 8× (9+x), and x=3.
2. Xiaoming took part in six tests, and the average score of the third and fourth tests was 2 points higher than the previous two tests and 2 points lower than the latter two tests. If the average score of the last three times is 3 points higher than the previous three times, how many points is the fourth time higher than the third time?
Solution: The third and fourth scores are 4 points more than the first two scores, and the last two scores are 4 points less. It can be inferred that the last two scores are 8 points more than the first two scores. Because the sum of the last three times is 9 points more than the sum of the first three times, the fourth time is 9-8 = 1 (points) more than the third time.
Mother goes to the grocery store every four days and to the department store every five days. How many times does mom go to these two stores every week on average? (expressed in decimal)
Solution: Walk 9 times every 20 days, 9÷20×7=3. 15 (times).
3. The fifth grade elementary school olympiad test questions and reference answers.
1, the circumference of the circular runway is 500 meters, and both parties start clockwise from the starting point at the same time. A runs120m per minute, and B runs100m per minute. Both stop every 200 meters 1 minute, so how many minutes does it take for A to catch up with B for the first time? Reference answer:
Solution 1: Because after the line was finished, A walked 500 meters more than B, which means that the rest is 500 ÷ 200 = 2... 100, which is twice. The distance between A and B is 500+ 100×2=700 meters. To chase 700 meters, A needs to walk 700÷( 120- 100)=35 minutes, and A needs to rest 35 × 120 ÷.
Scheme 2: Time ratio of one stop: A is 200: 120 = 5: 3 = 15: 9, B is 200:100 = 2:1=16: 8, A 24. A strike120×15-100×16 = 200m, 500-200× 2 = 100m,100 ÷ (.
2.b is between A and C .. A is from B to A, after departure 1 hour, B is from B to C, after departure 1 hour, C suddenly remembered to inform A and B of something important, so he set off from B to chase A and B by bike. It is known that the speed of A and B is equal, and the speed of C is three times that of A and B. In order to make C spend the least time from B to B, should C chase A first and then return to B, or should C chase B first and then return to A?
Reference answer:
If you chase B first and then return, the time is1÷ (3-1) × 2 =1hour, and then chase A and then return, the time is 3÷(3- 1)×2=3 hours, and * * takes 3+. So, we started after we caught up.
4. The fifth grade elementary school olympiad test questions and reference answers.
A big car and a small car both drive from A to B. The speed of the big car is 80% of that of the small car. It is known that the bus leaves earlier than the car 17 minutes, but it stops at the midpoint of the two places for 5 minutes before continuing to the second place; However, after the bus set off, it didn't stop halfway, and went straight to B. Finally, the bus arrived at B 4 minutes earlier than the bus. It is also known that the bus departs from a place at 10 in the morning. So when did the bus catch up with the bus in the morning? Answer and analysis:
This topic is similar to question 8. But it's more complicated than question 8!
The bus is more than the car 17-5+4= 16 minutes.
Therefore, it takes 16÷( 1-80%)=80 minutes to complete the bus journey.
It takes 80×80%=64 minutes for the car to complete the whole journey.
Since the car has stopped at the midpoint, we have to discuss whether we can catch up at the midpoint.
The bus will reach the midpoint at 80÷2=40 minutes after departure, and leave at 40+5=45 minutes after departure.
The bus starts after 17 minutes, and the bus keeps running 17+64÷2=49 minutes.
It means that when the car reaches the midpoint, the cart has already started again. And then get caught in the second half of the road.
As neither of them had a rest, the bus arrived four minutes earlier than the bus.
Then the catch-up time is 4÷( 1-80%)×80%= 16 minutes ago.
So, after the bus leaves, 17+64- 16=65 minutes.
So the time at this time is 1 1: 05.
5. The fifth grade elementary school olympiad test questions and reference answers.
Given a number 1 1, there must be 6 numbers, and their sum is a multiple of 6. Let 1 1 be a 1, a2, a3, ..., a 1 1. According to the conclusion of [bedding], there must be three numbers in a 1, a2, a3, a4, a5, and the sum is three. There must be three numbers in a4, a5, a6, a7 and a8, and their sum is a multiple of three, so let A4+A5+A6 = 3k2; There must be three numbers in a7, a8, a9, a 10, a 1 1, and their sum is a multiple of three. Let's say a7+a8+a9=3k3. There must be two numbers with the same parity in k 1, k2 and k3. Let the parity of k 1 and k2 be the same, then 3k 1+3k2 is a multiple of 6, that is, the sum of a 1, a2, a3, a4, a5 and a6 is a multiple of 6.