1. Test questions and answers of Olympic mathematics in the fourth grade of primary school
Xiao Wang and Xiao Li usually love playing cards, and they have strong reasoning ability: one day, they and Professor Hu played cards around the table, and Professor Hu gave them a reasoning question. Professor Hu draws the following 18 playing cards from the table: hearts: a, q, 4.
Spades: J, 8, 4, 2, 7, 3, 5.
Cao Hua: k, q, 9, 4, 6, 10.
Diamonds: a, 9
Professor Hu draws a card from 18, tells Xiao Wang the number of points in this card and tells Xiao Li the color of this card. Then, Professor Hu asked Xiao Wang and Xiao Li, "Can you infer what this card is from the known points or colors?
Xiao Wang: "I don't know this card."
Xiao Li: "I know you don't know this card."
Xiao Wang: "Now I know this card."
Xiao Li: "I know, too."
Excuse me: What kind of card is this?
According to Xiao Wang's I don't know this card, the number of points to push this card is a repeated number, including A, Q, 4 and 9.
According to Xiao Li's "I know you don't know this card", the number of cards in this deck is repeated, including hearts and diamonds.
According to Xiao Wang's "Now I know this card", the introduction of this card can only be Q of hearts, 4 of hearts or 9 of diamonds.
Finally, according to Xiao Li's "I know", the card is 9 diamonds.
2. Question and answer of the fourth grade Olympiad.
1. A school has 100 students who participated in the math contest, with an average score of 63, including 60 for boys and 70 for girls. More boys than girls (). There is a pile of black and white debris, in which the number of sunspots is twice that of Bai Zi. If four sunspots and three Bai Zi are taken out of this pile at the same time, after taking out () times, there are 1 albino and 18 sunspots.
The school spent 185 yuan to buy four basketballs and five volleyballs. A basketball is more expensive than a volleyball, and the unit price of basketball is () yuan.
Reference answer:
1, solution: there are x boys and (100-X) girls.
[60x+70 (100-x)] ÷100 = 63, X=70, female students have 100-70=30 (person).
So there are more boys than girls: 70-30=40 (people)
2. Solution: Let x times have 1 albino stars and 18 sunspots.
4X+ 18=2(3X+ 1), and the solution is X=8.
So after 8 times, there were 1 albinism and 18 sunspots.
3. Solution: Let the basketball be X yuan and the racket ball be X-8 yuan.
4X+5(X-8)= 185，X=25。
So 25 yuan is a good basketball player.
3. Questions and answers about Olympic mathematics in the fourth grade of primary school.
Question 1. It takes 1 minute to boil water and make tea, 1 minute to boil water, 2 minutes to wash teapot, 2 minutes to wash teacups and1minute to fetch tea. How can I arrange tea as soon as possible? Analysis: Wash the kettle first, then boil the water. When boiling water, wash the teapot, wash the teacup and get tea. * * * Need1+10 =11min.
Question 2: The cargo transported from place A to place B is 137 tons, the load capacity of large trucks is 5 tons, and the load capacity of small trucks is 2 tons. The fuel consumption of large trucks and small trucks per train is 10 liter and 5 liter respectively. How to choose vehicles to minimize fuel consumption in transportation? How many liters of oil does * * * need to consume at this time?
Analysis: According to the meaning of the question, the fuel consumption per ton of large trucks is 10÷5=2 (liters); The fuel consumption per ton of minivan is 5÷2=2. 5 (liters). In order to save gasoline, trucks are selected to transport goods as much as possible, and because 137=5×27+2, the transportation scheme is: 27 trucks and 1 truck can be selected to transport all goods, and at this time, the fuel consumption is the least, and only10× 27+5×1is needed.
Question 3. Bake the cake in a pan. Only two cakes can be put on the pan. Bake the cake for 2 minutes on one side and 4 minutes on both sides. It takes at least a few minutes to bake three cakes now.
Analysis: The general practice is to bake two cakes at the same time, which takes 4 minutes, and then bake the third cake, which takes 4 minutes and * * * takes 8 minutes. However, we noticed that when baking the third cake alone, the position of the other cake was empty, which indicated that it might be a waste of time. How to solve this problem?
We can bake the first side of the first and second cakes first. After two minutes, we can take the first cake, put the third cake and turn the second cake over. Two minutes later, the second cake was baked. At this time, we can take down the second cake, turn the third cake over and put the unburned side of the first cake on it. Two minutes later, the first and third cakes were baked, and the whole process took 6 minutes.
4. Question and answer of Olympic Mathematics in the fourth grade of primary school
1, trip questions a and b practice running. If A lets B run first 10 meter, A can catch up with B in 5 seconds; If A lets B run for 2 seconds first, A can catch up with B in 4 seconds. Q: What are the speeds of A and B respectively?
Answer: The analysis shows that if A lets B run10m first, then10m is the distance difference between A and B, and 5 seconds is the catching-up time. Based on this, we can find that their speed difference is 10÷5=2 (m/s); If A lets B run for 2 seconds first, A can catch up with B in 4 seconds. In this process, the catching-up time is 4 seconds, so the distance difference is 2×4=8 (meters), that is, B ran 8 meters in 2 seconds, so the speed of B can be calculated, and the speed of A can also be calculated. The comprehensive formula is calculated as follows:
Solution: The speed of B is: 10÷5×4÷2=4 (m/s).
The speed of A is: 10÷5+4=6 (m/s).
A: A's speed is 6 meters per second, and B's speed is 4 meters per second. ..
2. Travel issues
At 8: 08 in the morning, Xiaoming set off from home by bike. Eight minutes later, his father came after him on a motorcycle and caught up with him 4 kilometers away from home. Then my dad went home immediately. When he got home, he went back to chase Xiao Ming and caught up with him. Just 8 kilometers from home. What time is it now?
Answer: During the period from the first time my father caught up with Xiaoming to the second time, Xiaoming walked 8-4=4 (km), while my father walked 4+8= 12 (km), so the speed ratio of motorcycle and bicycle was 12: 4 = 3: 1. Xiaoming rode 8 kilometers, and his father rode 4+ 12= 16 (kilometers) back and forth. Because he started late, it took 8 minutes less. Judging from the speed ratio calculated above, Xiao Ming rides a bike for 8 kilometers. If he starts at the same time, his father should ride 24 kilometers. Now it takes 8 minutes to ride, and 24- 16=8 (km) less, so the speed of the motorcycle is calculated to be 1 km per minute. Dad always rides 16 km, which takes 16 minutes, and 8+ 16=24 (minutes). At this time, it is 8: 32.
5. Question and answer of Olympic Mathematics in the fourth grade of primary school
1. My son is 10 years old this year. My mother was six times his age five years ago. How old is her mother this year? Analysis: My son is 10 years old this year, and he was 5 years old five years ago, so his mother was 5×6=30 years old five years ago, so his mother is 30+5=35 years old this year.
2. To build a highway, it was originally planned that 60 people would work and it would be completed in 80 days. I've been working for 20 days now, and I've added 30 people. How many days can I work for the rest?
Analysis and solutions:
(1) How many working days (total) will it take to build this highway?
60×80=4800 (Labor Day).
(2) After 60 people work for 20 days, how many working days are left?
4800-60×20=3600 (Labor Day).
(3) After adding 30 people, how many days will it take to complete the remaining projects?
3600÷(60+30)=40 (days).
Solution: (60×80-60×20)÷(60+30)=40 (days).
A: It will be finished in 40 days.