1)64,48,40,36,34,( )
2)8, 15, 10, 13, 12, 1 1,( )
3) 1、4、5、8、9、( )、 13、( )、( )
4)2、4、5、 10、 1 1、( )、( )
5)5,9, 13, 17,2 1,( ),( )
Second, arithmetic progression.
1. In arithmetic progression, 9 12, 2 1, 30, 39, 48, …
2. Find the sum of all integers between 1 and 100 that are not divisible by 5 or 9.
3. Divide 2 10 by the sum of seven natural numbers, so that after the seven numbers are arranged in a row from small to large, the difference between two adjacent numbers is 5. So, what is the number of 1 and the sixth number?
4. Group all odd numbers starting from 1, where the first number of each group is equal to the number of all numbers in the group, such as (1), (3,5,7), (9,0/1,13,660.
5. Arrange the natural numbers as follows.
1 2 6 7 15 16 …
3 5 8 14 17 …
4 9 13 18 …
10 12 …
1 1 …
…
In this arrangement, the numbers are arranged in the second row 1 column and the third row 13 column. Q: What is the rank of 1993?
Third, the average problem.
1. The average number of 9 known is 72. After removing a number, the average of the remaining numbers is 78, and the removed number is _ _ _ _ _.
There are 40 students in a class, and two students missed the mid-term math exam for some reason. At this time, the average score of the class is 89, and the students who are absent from the exam each get 99 points. The average score of the senior high school entrance examination in this class is _ _ _ _ _ _ _ _.
In the first five months of this year, Xiaoming saved money in 4.2 yuan on average every month. Since June, he has saved 6 yuan every month. Since which month, Xiaoming has saved more money than 5 yuan on average?
4.a, B, C, D, remove one number at a time and average the remaining three numbers. This is calculated four times, and the following four numbers are obtained.
23, 26, 30, 33
What is the average of a, b, c and D 4?
Remove one of the five numbers A, B, C and D4 at a time, and average the remaining three numbers, so that the following four numbers 23, 26, 30 and 33 are counted four times, and the sum of A, B, C and D4 is.
Fourth, simple operations of addition, subtraction, multiplication and division
1) 100-98+96-94+92-90+……+8-6+4-2=( )
2) 1976+ 1977+……2000- 1975- 1976-……- 1999=( )
3)26×99 =( )
4)67× 12+67×35+67×52+67=( )
5)( 14+28+39)×(28+39+ 15)-( 14+28+39+ 15)×(28+39)
Five, the number of arrays.
1, △, □, and zero respectively represent three different numbers;
△+△+△=〇+〇; 〇+〇+〇+〇=□+□+□; △+〇+〇+□=60
Question: △ =△ =□ =
2. Fill in nine consecutive natural numbers in the nine spaces of three rows and three columns, so that the sum of the three numbers in each row and each vertical column is equal to 60.
3. Fill nine consecutive odd numbers starting from 1 into nine spaces in three rows and three columns, so that the sum of three numbers in each row, each column and two diagonal lines is equal.
4 Make a third-order magic square with 9 numbers from 1 to 9, and write all possible results. The so-called magic square refers to filling different numbers in each square of the square grid table, so that the sum of numbers on each row, column and two diagonal lines is equal; Order refers to the number of squares contained in each row and column.
Sixth, the problem of sum and difference times.
1. There are 340 peach trees and apricot trees planted in the orchard, of which the number of peach trees is 20 times more than that of apricot trees. How many trees have been planted?
2. Rectangular, 30cm in circumference, twice as long and wide. Find the area of this rectangle.
3.A and B are two numbers. If A plus 320 equals B, if B plus 460 equals 3 times A, what are these two numbers?
There are two pieces of cloth with the same length. The first piece sells for 25 meters, the second piece sells for 14 meters, and the remaining piece of cloth is twice as long as the first piece. How many meters is each piece of cloth?
There are 150 peach and pear trees in the orchard. There are 20 more peach trees than pear trees. How many fruit trees are there?
6. Two barrels of oil A and B weigh 30 kilograms. If 6 kilograms of oil in barrel A is poured into barrel B, the weight of the two barrels of oil is the same. How much oil do they have?
Seven, the age problem
1. The two brothers are 30 years old this year. When my brother and brother are the same age now, my brother is exactly half his age. How old is my brother this year?
The mother and daughter are 64 years old, and the daughter is three years older than her mother. How old are the mother and daughter?
My brother is older than Xiaoli this year 12 years old. Eight years ago, my brother was four times older than Xiaoli. How old are they this year?
Grandpa is 72 years old and grandson 12 years old. A few years later, grandpa was five times as old as his grandson. A few years ago, my grandfather was 13 times older than my grandson.
Eight. Hypothetical problem
1.42 students participated in tree planting, with an average of 3 trees planted by boys and 2 trees planted by girls, with 56 more trees planted by boys than girls. How many boys and girls are there?
2. A primary school held a math contest with *** 15 questions. He gets 8 points for every right question and 4 points for every wrong question. Xiaoming got 72 points in the exam. How many questions did he get right?
There are 25 questions in a test paper. Answer one question correctly and get 4 points. Answer correctly or not, get 1 point. A classmate will get 60 points. He answered several questions correctly.
4. Xiaohua answers math judgment questions, giving 4 points for a correct answer and 4 points for a wrong answer. She answered 20 true and false questions and got only 56 points. She answered several questions wrong.
5. Yucai Primary School held a math contest in the fifth grade. There are *** 10 questions. She gets 8 points for each correct question, and 5 points for wrong questions. Zhang Xiaoling finally got 4 1 point. How many questions did she answer correctly?
Respondent: fengchenbo 1996- Jianghu rookie level 4 8-27 1 1:20.
◆ Fourth-grade Olympiad Q&A
Reward score: 0- Settlement time: 07: 42 on September 5, 2008.
Fifty students went boating and took 1 1 boat, including 6 in the big boat and 4 in the small boat. How many ships are there?
Questioner: female Liu Xuan-the best answer during the probation period.
The problem of chickens and rabbits in the same cage ... can be solved by equations in junior high school. ...
Primary school Olympic competition ... you have to use the traditional solution of the Chinese nation ...
Number of ships = (11* 6-50)/(6-4) = 8 ... so the number of big ships is 3. ...
Examination questions and answers in the preliminary contest of the sixth mathematics competition.
(in 100)
First, the calculation problem (if it can be calculated by a simple method, a simple algorithm should be used. 4 points for each question, *** 12 points. )
2. 1994+ 199.4+ 19.94+ 1.994
2. Fill in the blanks (5 points for each question from 1 to 7, 7 points for each question from 8 to 10, and 56 points for * * *. )
1. Primary School Mathematics Newspaper is published once a week and on Friday. The issue of 65438+ 10 of 1994 was published on 1 0 of 1995, and the issue of 1995 should be/kloc-0.
2. In arithmetic progression 6, 13, 20, 27, …, the number _ _(shǔ) is 1994 from left to right.
If the number 6 is written after one digit of a number, the new number is increased by 6000. The original number is _ _ _ _.
4. There are seven different prime numbers, the sum of which is 60, and the smallest prime number is _ _ _ _.
5. In the picture on the right, * * * has _ _ _ trapezoids.
6. In the formula "(□-7×□) ÷ 16 = 2", □ "represents the same number and is _ _ _ _.
7. Both Figure 1 and Figure 2 are composed of the same small squares. The circumference of Figure 1 is 22 cm, so the circumference of Figure 2 is _ _ _ _ cm.
8. There are two scores A and B:
Compared with these two scores, _ _ _ is greater than _ _.
9. Let a△b=a×a-2×b, then 5 △ 6 = _ _ _, (5△2)△3=____.
10. There are 25 red chopsticks, 25 black chopsticks, 25 white chopsticks, 25 yellow chopsticks, 25 purple chopsticks and 25 flower chopsticks, all of which have the same shape and length. Look for at least _ _ _ _ pairs of chopsticks in the dark, and make sure there are at least 8 pairs of chopsticks (one pair for every two chopsticks with flowers, or one pair for two chopsticks of the same color).
Three, short answer questions (8 points)
If 26 numbers are randomly selected from 50 numbers of 1, 2, 3, 4, …, 49, 50, then at least two of these 26 numbers are coprime. Q: Why is this?
Fourth, the application problem (write a list of problem-solving processes. 6 points for each question, ***24 points. )
1. Xiaoming leaves home at 6: 50 every morning and arrives at school at 7: 20. The teacher asked him to arrive at school six minutes early tomorrow. If Xiaoming leaves home at 6: 50 tomorrow morning, he must walk 25 meters more than usual every minute according to the teacher's request to get to school on time. Q: How far is Xiaoming's home from school?
2. My daughter is 1994 years old this year. Mother said to her daughter, "When you reach my age, I will be 60 years old!" " "Q: When was Mom 12 years old?
3. Tintin and Ningning each have a box with chess pieces in it, and the chess pieces in both boxes are * * *.
4. There is an isosceles right-angled triangular paper (as shown in Figure 3), AB= 10 cm. Fold its two corners in half to the midpoint o of the hypotenuse, so that both point A and point B coincide with point O (as shown in Figure 4), and then fold Figure 4 with CO as the symmetry axis to obtain a trapezoid (as shown in Figure 5). Find the area of this trapezoid.
Answers and explanations
First, the calculation problem
2. 1994+ 199.4+ 19.94+ 1.994
=(2000-6)+(200-0.6)+(20-0.06)+(2-0.006)
=(2000+200+20+2)-(6+0.6+0.06+0.006)
=2222-6.666
=22 15.334
Description: Questions L and 2 are adapted from two questions in Exercise by Yourself,No. 1 No.287 of Aojiao. The third question is based on the design of the content of the textbook 1 1.
Second, fill in the blanks
1.65438+1October 6th
(24+30+3 1)÷7= 12…… 1 7- 1=6
Description: According to the lecture design of 29 1 "Aojiao".
2. No.285
Multiply 1994=7×284+6 and an(n- 1)×d+a 1.
By comparison, we can get the description of n- 1=284 n=285: adapted from Example 2 of No.293 Austrian School.
3.666
Write 6 after a number, the new number is 10 times more than the original number, and the difference between the new number and the original number (increased by 6000) is 6 times more than the original number.
(6000-6) ÷ (10-1) = 666 Description: Adapted from Teaching You to Think, No.279.
The smallest prime number is 2.
If it is not 2, then all seven prime numbers are odd, and the sum of seven odd numbers is still odd, which can't be 60. Note: According to the conclusion of No.273 of Special Use 2 and the lecture example of No.296 of Austrian School 1.
5.*** has 12 trapezoids.
It is calculated in four categories: (1) the upper bottom is long and the lower bottom is short1; (2) The lower sole is long and the upper sole is short by 5; (3) The bottom is parallel to the left waist; (4) The bottom is parallel to the right waist. Description: adapted from the 309th issue of Clever Solutions to Interesting Problems.
6. This number is 8.
The original formula is (1/kloc-0 /×□-7×□) ÷16 = 2.
4×□÷ 16=2
4×□=32
□=8
Note: According to No.321issue of Austrian School, it was adapted by self-training. 7.33 cm
The perimeter of the graph 1 contains 12 edges, and the perimeter of Figure 2 contains 18 edges. The perimeter of Figure 2 is 18 ÷ 12 = 1.5 times that of Figure 1.
22× 1.5=33
Description: Adapted from No.2865438 +0 of Wonderful Solution to Interesting Problems.
8.b is bigger than a.
Description: The original title of Problem-solving Strategies and Skills No.258.
9. 13; 435
( 1)5△6=5×5-2×6= 13
(2)5△2=5×5-2×2=2 1
2 1△3=2 1×2 1-6=435
Note: adapted from case No.3 1 7 of "Aojiao" (1).
10.2 1 root
There must be a pair of 7, the remaining 5 plus 2, and so on. * * * The root "7×2= 14" should be added. 7+2×7=2 1
On the other hand, if the number of chopsticks is less than 2 1, for example, 20 chopsticks, 5 of which are red,
There are three of them, so there are only seven pairs, so 2 1 is the least.
Description: adapted from the 304th issue of Clever Solutions to Interesting Problems.
Third, short answer questions
Answer: ① There must be two consecutive natural numbers in these 26 numbers;
(2) Because if there can't be two consecutive natural numbers, then the 50 numbers can only take out 25 at most;
③ Any two consecutive natural numbers must be coprime.
Description: adapted from the 299th issue of Clever Solutions to Interesting Problems.
Fourth, the application questions
1. Solution: 25×(30-6)÷6×30.
=3000 meters
Or 25×(30-6)=600 (m) (2 points)
600÷6= 100 (m) (2 points)
100×30=3000 (m) (2 points)
Xiaoming's home is 3000 meters away from school.
Description: Adapted from "Teach You to Think" No.286.
2. Answer: (60- 12) ÷ 2 = 24 ... Age difference (4 points)
1994-24= 1970(2 points)
A: The year is 1970.
Description: adapted from case 2 of the 320th issue of Austrian School.
270- 150= 120 (grain) (1)
(If the number of originals or total pieces of Tintin is regarded as the unit "1", as long as the column answers correctly, score according to the above steps. )
A: Tintin 120, Ningning 150.
Description: Adapted according to the analysis methods of How to Solve Such Problems, No.283, 3rd Edition, and No.3 1 81issue of Olympic School.
4. Option 1: directly substitute into the formula.
Solution 2: Using the area relation, the original largest isosceles right triangle is divided into eight equal small isosceles right triangles, and the trapezoid contains three of them.
Trapezoidal area is:
Description: According to "Teach You to Think" No.265 and No.279, plane natural design.