1. Primary school students' Olympic mathematics thinking training and answers
1, 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, 4 points less than the last two scores, and 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.
Mom goes to the grocery store every four days and 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 ratio of the average of b and c to a is 13∶7. Find the ratio of the average value of a, b and c to a. ..
Solution: If the number of A is 7, then the number of B and C is * * * 13× 2 = 26 (copies).
So the average value of a, b and c is (26+7)/3= 1 1 (copies).
So the ratio of the average of A, B, C and A is 1 1: 7.
2. Pupils' Olympic Mathematical Thinking Training and Answers
1. Dr. Wang just applied to open a small pharmacy. He only has one balance, one weighing 5 grams and the other weighing 30 grams. One day, a customer came to the store and wanted to buy100g of precious powder. If you weigh it three times with a weight of 30 grams, then weigh it twice with a weight of 5 grams, * * * 5 times to weigh out 100 grams of powder. But the pharmacy business is busy, and customers hope that the sooner the better. It is impossible to weigh100g at a time. So, can you think of a quick and good way? Answer: Put 5 grams and 30 grams of weights at one end of the balance, first weigh out 35 grams of powder, and then put these 35 grams of powder and 30 grams of weights at one end of the balance to weigh out 65 grams of powder, so the total powder is * * * 35 = 100 (g).
5. Father-son race: Lao Wang and his son Xiao Wang walked back along the circular runway with a diameter of 100 yards to compete. They started from the same place, but at first Lao Wang didn't move at all, and didn't start until Xiao Wang walked one-eighth of the distance. Lao Wang underestimated his son's walking ability, so he walked slowly until he met Xiao Wang on the way. By this time, Lao Wang had walked one-sixth of the distance.
2. Excuse me: How many times must Lao Wang speed up in order to win this game?
Answer: The diameter of the circular runway has nothing to do with the question. When they met, Lao Wang walked the whole distance of 1∕6, while during his walking time, Xiao Wang walked the whole distance of 16∕4, so his walking speed was four times that of Lao Wang. Lao Wang still has 5∕6 miles to run, while Xiao Wang only has 1∕6 miles. So Lao Wang must be at least five times faster than Xiao Wang.
3. Pupils' Olympic Mathematical Thinking Training and Answers
1, race problem A, B, C race, from A to B, when A runs to the finish line, B is 30 meters away from B and C is 70 meters away from B; When B ran to the finish line, C was still 45 meters away from B. Q: How many meters is there between A and B?
Answer: When B runs the last 30m, C runs (70-45) = 25m, so the speed ratio between B and C is 30: 25 = 6: 5. Because B ran 45 meters more than C at the finish line, A and B separated.
45( 1-5/6)= 270 meters.
This problem mainly investigates the proportional relationship between distance and speed, so that we can find speed from distance and distance from speed.
2. Withdrawal problem
Someone went to the bank to withdraw money. For the first time, he took more than half of his deposit in 50 yuan, and the remaining half was 100 yuan for the second time. At this time, there is 1350 yuan left on his passbook card. Q: How much money does he have on his passbook card?
Answer: We can walk backwards and get the remaining half for the second time, which is less than 100 yuan. We know that "the remaining half exceeds 100 yuan" is 1350, so the remaining half is1350-100 =1250.
The remaining money is: 1250×2=2500 yuan.
Similarly, when I visited the remaining half of 50 yuan for the first time, I knew that the "remaining half is less than 50 yuan" was 2500, so the "remaining half" was 2500+50=2550 (yuan).
The original passbook card is 2550×2=5 100 yuan.
This problem is mainly based on the idea of reduction. The general feature of the reduction problem is that it is known that four operations are performed on a certain number in a certain order, and we usually perform the corresponding inverse operations in the opposite order of operation or increase or decrease.
3. Tricolor ball problem
Red, yellow and white balls 10, mixed in a cloth bag, and at least _ _ _ _ _ balls are taken out at a time to ensure that the colors of the five balls are the same.
Answer: According to the most unfavorable principle, at least 4×3+ 1= 13 needs to be found.
4. Pupils' Olympic Mathematical Thinking Training and Answers
1.Two students, A and B, originally planned to study by themselves at the same time every day. If A increases the self-study time by half an hour every day and B decreases the self-study time by half an hour every day, then the self-study time of B for six days is only equal to that of A for one day. Q: How many minutes did A and B originally plan to study by themselves every day? Analysis: A increases self-study time by half an hour every day, and B decreases self-study time by half an hour every day. A is one hour longer than B, and B's six-day self-study time is only equivalent to A's one-day self-study time, and A is six times as long as B.
Solution: Party B's self-study time after reducing half an hour every day =1(6-1) =1/5 hours = 12 minutes, and Party B's self-study time =30+ 12=42 minutes.
2. A large piece of Di Chin brand chocolate can be divided into several square small pieces with the same size. Xiaoming and Xiao Qiang each have a big piece of Di Chin chocolate, and they start eating the first small piece of chocolate at the same time. Xiao Ming eats 1 cube every 20 minutes, and finally eats 1 cube at 14: 40. Xiao Qiang eats 1 cube every 30 minutes, and eats the last 1 cube on 18. So when did they start eating 1?
Analysis: Xiaoming eats 1 cube every 20 minutes, Xiao Qiang eats 1 cube every 30 minutes, Xiao Qiang eats 10 minutes more than Xiaoming, Xiaoming eats the last 1 cube at 14: 40, and Xiao Qiang eats/kloc-0. Then, 20*20=400 minutes =6 hours and 40 minutes, 14: 40 -6 hours and 40 minutes =8: 00.
Solution: 18-14: 40 =3 hours and 20 minutes =3*60+20=200 minutes, the number of tablets already eaten =200/(30-20)=20 tablets, and it takes Xiaoming 20*20=400 minutes to eat 20 tablets.
5. Primary school students' Olympic mathematical thinking training and answers
1.？ Fill in different prime numbers in □ to make the equation hold. □+□=□×□=□-□
Analysis and answer? If the sum (or difference) of two prime numbers is odd, it must be the sum (or difference) of odd and even numbers, and even numbers are only 2, so repeated filling is required. So this sum can only be an even number. One factor is 2. You can list prime numbers within 100 to select enumeration.
3+7=2×5=23- 133+ 1 1=2×7=37-23
3+7=2×5=7 1-6 13+ 19=2× 1 1=29-7……
2. The unit price of the two Olympic souvenirs is different, both are 0.6 yuan. You can buy two more souvenirs with 36 yuan money than with A, so what is the unit price of A and B?
Analysis and answer? In terms of angles, then
Unit price of 360 =× quantity of A = (unit price of A-6 )× (quantity of A+2).
360= 1×360=2× 180=…= 10×36= 12×30= 15×24= 18×20
It is observed that the unit price of A is 36 cents, that is, 3.6 yuan, and the unit price of B is 3 yuan.
3. A cuboid glass container is 8 decimeters long, 6 decimeters wide, 4 decimeters high and 2.8 decimeters deep. If you put a cubic iron block with a side length of 4 decimeters, how many liters of water will the water tank overflow?
Analysis answers the volume of iron? 4×4×4=64 (cubic decimeter)
The volume of water? 8×6×2.8= 134.4? (cubic decimeter)
The volume of the glass jar? 8×6×4= 192? (cubic decimeter)
Note that the height of the iron block is the same as that of the glass jar, and the sum of the volume of water and iron block is greater than that of the glass jar. What is the volume of overflow water? 64+ 134.4- 192=6.4? (cubic decimeter) =6.4 liters