Answers to the questions of the 6th Feiyang Cup National Mathematics Knowledge Contest for Primary

I'm only going to be a few really annoying, and a lot more won't

1. Fill in the blanks. 1。China's famous modern mathematician (Hua Luogeng) is self-taught, and he has grown from a young man who only graduated from junior high school to a generation of mathematics masters and educators. His famous work "Theory of Stacked Prime Numbers" is a classic work of mathematical treatises in the 20th century.

2。Than 2003 know that in all nature books, the sum of even numbers is (1003002).

3。Xiaoyun is 23 years older than Xiaoxue this year, and in 2018, Xiaoxue is (23) years older than Xiaoyun.

4。With a 15-meter-long fence on the side of the wall, Wei Chen has a rectangular yard, which can enclose a maximum of (25) square meters of yard.

5。There are 20 questions in the mathematics competition, and each question is 5 points for answering correctly, 1 point will be deducted for mistakes, and 60 points will be passed. If you want several, you need to answer at least 12 questions correctly.

The others think to themselves.

Primary school students have questions that should be solved, not directly to the answer, maybe you throw this question because you can't do it because you don't have the answer to do it, but I checked it and really didn't have this answer, if you can't, you can ask me, my email is happy to help you answer.

Multiple choice questions: c c c c c d b a c

Fill in the blanks: Le Yang Yang Ah Xiang Ah and Ah Ru Ah Yi.

Fill in the blanks: Le Yang Yang Ah Xiang Ah and Ah Ru Ah Yi.

Fill-in-the-blank questions??? Hurry, hurry, hurry, it's going to be handed over tomorrow.

It's all the end of the world, and I'm doing it too.

The answer!! Hurry, hurry!!

Fast!!! Who knows???

Help!!

Annoy, I'm doing it, but I didn't find the answer.

I don't know, but my grandfather watched.

The 12th National "Hua Luogeng Gold Cup" Youth Mathematics Invitational Competition.

Preliminary Round Papers (Primary School Category).

1. Multiple choice questions. (10 marks per question) If only one of the four options in each of the following questions is correct, please write the letter indicating the correct answer in parentheses around each question.

1 Equation. Equal to (

a）3b）2

c）1d）0

2 To fold a batch of paper cranes, it takes half an hour for student A to fold alone, and it takes 45 minutes for student B to fold alone

a) 12 minutes.

b) 15 minutes.

c) 18 minutes.

d) 20 minutes.

3 As shown in the figure below, if four rectangular strips of paper with a length of 16 cm and a width of 2 cm are placed vertically on the table, the area covered by the surface of the table is (

a）72cm2

b）128cm2

c）124cm2

d）112cm2

4 The ratio of land area to ocean area of the earth's surface is 29:71, where three-quarters of the land is in the northern hemisphere, then the ratio of the area of the ocean to the northern hemisphere is (

a）284：29

b）284：87

c）87：29

d）171：113

5 The length, width, and height of a box are exactly 3 consecutive natural numbers, and its volume is equal to 2 times the sum of all its edges, then the surface area of the box is (

a）74b）148

c）150d）154

6 After taking 3 numbers from 10 different non-zero natural numbers whose sum is 55, the sum of the remaining numbers is 55.

then the product of the three numbers taken out is equal to (

a）280b）270

c）252d）216

2. Fill in the blanks. (10 marks per question).

7 As shown in the figure below, there are two sections of road in a park: AB 175 meters and BC 125 meters. To install street lights on these two sections of the road, it is required that a street light be set up at each of the three points A, B and C, and the distance between the two adjacent street lights is equal. At least street lights should be installed on these two sections of the road.

Piece. 8 will 5The product of 42 5 is written in the decimal form.

9 As shown in the figure below, there is a regular triangle with a side length of 1, and for the first time, the regular triangle enclosed by the midpoint of the three sides is removed. For the second time, the three regular triangles left behind are respectively removed from the triangles formed by the connecting lines at their midpoints; ...

After doing it for the fourth time, it was removed.

triangles, the sum of the side lengths of all the triangles removed.

10 When the students were camping, 9 camps were built, and the road connecting the camps is shown in the map. Beibei needs to plant a flag for each camp, and if the flags of the adjacent camps are of different colors, Beibei needs the least.

flags of various colors. If Bei Bei sets out from a certain camp, he doesn't take the same path.

Fill in "can" or "can't") to complete this task.

Answer: 1. Multiple choice questions (10 points per question, out of 60 points) question number.

Answer. bcddb

A2. Fill-in-the-blank questions (10 points per question, 40 points out of 40 points, 5 points per blank question) question number.

Answer. or 40, or.

Or. 3. No, you can't.

If a total of x people participate in the game, each person will play (x-1) and x people will play x(x-1) and score a total of x(x-1) points.

Let the average score of the others be y, then there is:

x(x-1)-16=(x-2)y

y=(x²-x-16)/(x-2)

x+1)-14/(x-2)

So: (x-2) must be a factor of 14, and a factor of 14 has

x-2) probably

So: x .

x(x-1)>16

x>(1+ 65) 2 or x<(1- 65) 2 (undesirable, discarded) x>(1+ 65) 2, i.e., x>

So, x is all up to the question!

Answer: There are 5 or 9 people participating in the competition.

An odd number of players participate in a chess match, each player plays a game against the other players, and the score is 1 point for a win set, a score for each game, and 0 points for a loss. It is known that two of the players scored a total of 8 points, and the average score of the others is a whole number, so how many players are there in the competition?

Solution: If there are x+2 participants, then each person will play x+1 plate.

Then the sum of everyone's scores is (x+1)(x+2) 2, (because, 1 point in a game of chess is equal to two people to score).Then set the score of the rest of the people to y

Therefore, list the equation: (x+1)(x+2) 2=8+xy, (y z)Because x is not equal to 0

Because y is an integer, x must be a divisor of 7, i.e., 1 and 7

Because there are two players scoring 8 points and the number of participants is odd, x can only be equal to 7

After testing, x= is true.

So a total of 9 people participated in the competition.

Solution: integers x1, x2, x3,...,x2008 satisfies: -1 xn 2,n=1,2,...，2008；②x1+x2+…+x2008=2008；③x12+x22+…+x20082=2008，x1=x2=x3=…=x2008=1，x13+x23+…+x20083=2008，x13+x23+…+x20083 has a minimum value of 2008 and a maximum value of 2008

So the answer is: 2008, 2008

Subtract 2 by 2 formulas with 3 formulas to get: x1 2-2x1+...x2008 2-2x2008=-2008 moved to the recipe:

x1-1）^2+（x2-1）^2+..x2008-1) 2=0, so x1=x2=...=x2008=1, so the maximum and minimum values are 2008

①-1≤xn≤2，n=1，2，…，2008；②x1+x2+…+x2008=208；③x12+x22+…+x20082=2008

x1=x2=x3=…=x2008=1

x13+x23+…+x20083=2008，x13+x23+…+x20083 has a minimum value of 2008 and a maximum value of 2008

It's worthy of the Olympiad, which is similar to the high school number series!

Singles: 24 players play first, 2 players play a match, a total of 12 games, 12 people are eliminated, and 12 people remain; The remaining 12 people repeated, played 6 games, eliminated 6 people, and left 6 people; The remaining 6 people will play again, play 3 games, eliminate 3 people, and leave 3 people; In the end, the three people took turns to play, first playing 2 games to evaluate the champion, and finally playing 1 game to evaluate the runner-up and third place.

12 + 6 + 3 + 2 = 23 (field).

Doubles: 32 players divided into 16 groups 8 quarterfinals, 4 semifinals, 2 semifinals, 1 final;

8 + 4 + 2 + 1 = 15 (field).

In short, singles: 12 + 6 + 3 + 2 = 23 (field), doubles: 8 + 4 + 2 + 1 = 15 (field).

Three people see how you get it, two and two battles are 6; The one of the two is the last one, and the big one is 2;

24 people in total, 12 + 6 + 3 + 6 or 12 + 6 + 3 + 232 people, a total of 16 teams.

A total of 1+2+4+8+=15 games.

Column: 24-1=23

Think: The single-game elimination system (i.e., 1 player is eliminated in each game) means that 24 students will compete in the competition, and 23 players will be eliminated in order to produce the champion, so 23 games will be played. 32 Ibid.!

Question 1: SABCD = ab*ad+6*10=60 square centimeters.

sabe=sadf=1 3s abcd=20 cm².

sabe= 1/2ab*be

That is: 20=1 2*6*be

be= 20 3 cm.

EC= BC-BE=10 3 cm.

sadf=1/2 ad*df

df=4 cm.

cf=dc- df=6- 4=2 cm.

secf= 1 2 ec*cf=1 2 *2*10 3=10 3 square centimeters.

SAEF = SAFCD SABE- SADF SECF = 50 3 square centimeters.

Solution 1 of the second problem: original formula = 1 2 1 4 1 8 1 16 1 32 1 64 1 64 1 64 = 1 2 1 4 1 8 1 16 1 32 1 32 1 64=1 2 1 4 1 8 1 16 1 16 1 64=1 2 1 4 1 8 1 8 1 64=1 2 1 4 1 4 1 64=1 2 1 2 1 64=1 1 64=63 64. Solution 2:

Construct a square with side length = 1: then divide it into 2 equal parts, take half of the area, divide the remaining 2 equal parts, take half of the area, and so on, a total of 6 times, and its area sum = 1 1 64 = 63 64

The third question is the original =

1.The triangular AEF area is also one-third of the rectangular ABCD mask, 20 square centimeters.

2.Metamorphosis: 1 + (1-1 2) + (1 2-1 4) + (1 4-1 8) + (1 8 + - 1 16) + (1 16-1 32) + (1 32-1 64).

1+1-1/64=2-1/64=127/643.Original formula = 1 + 1 3 - (1 3 + 1 4) + (1 4 + 1 5) - (1 5 + 1 6) + (1 6 + 1 7) - (1 7 + 1 8) = 1 + 1 8 = 7 8

How do I know if you don't give the question.,There's no question on the Internet.。。。