On the Cultivation of Mathematical Logical Thinking in Senior One.
1. Xiaohong's wall clock rings several times, once every half hour. How many times did a * * * ring from 2 pm to 5 pm?
2. Fill the eight numbers of 3, 4, 5, 6, 7, 8, 9 and 10 in the following () respectively (each number can only be used once), so that both formulas are valid.
( )+( )-( )=( )
( )+( )-( )=( )
3. Put the five numbers 2, 5, 6, 8 and 9 into two digits respectively, with the largest two digits being () and the smallest two digits being ().
4. Xiaoming is 6 years old and his sister 13 years old. How old is her sister in five years?
Children line up after school. There are 7 people in front of Ding Ding and 6 people behind him. How many people are there in this team?
6. There are 10 people in this group in Xiao Feng. How many times does he have to shake hands with everyone in the group?
7. Students line up to play games. There are 15 girls. The teacher put a boy between two girls. A * *, how many boys should be inserted?
8. How many times does it take to saw a piece of wood into five sections?
9. A number is between 70 and 90, and the difference between digits is 2. This number may be () ().
10. Mom needs 20 yuan to buy two loaves of bread and two boxes of biscuits, and 24 yuan needs three loaves of bread and two boxes of biscuits. 1 how much is a loaf? How much is a box of biscuits?
1 1, 8 adds 8 continuously, and write the points added each time on the horizontal line. 8, , , , , , , , , 。
12, Xiaohong and Mingming made flowers together. Xiaohong made 16 flowers. After giving Mingming four flowers, they have the same number of flowers. How many more flowers did Xiaohong make than Mingming?
13 and 8 1 subtract 9 successively, and write the number of each subtraction on the horizontal line. 8 1, , , , , , , , 。
14. Three children are comparing their heights. It is known that A is taller than B and C is taller than A. Can you rank the heights of three children?
15, my sister gave Yang Yang and Duoduo 10 five-pointed stars, and then Yang Yang gave Duoduo three five-pointed stars, so how many more five-pointed stars are there than Yang Yang?
16, it takes five minutes for Xiaoli to sing a song, and how many minutes does it take for the whole class to sing this song together?
17, in descending order:17-912-813-6161-614.
& lt& lt& lt& lt& lt& lt& lt
18. A group of children are waiting in line. Lin Ping stood in the middle. There are seven people in front and behind him. How many people are there in this child?
19, a rope folded it in half twice, and then cut it from the middle with scissors, and this rope became ().
20, a * * * There are 16 children lining up to do exercises. There are 6 people in front of Yang Yang. How many people are behind her?
Hong Hong took part in the math contest and shook hands with everyone who took part in the contest. Hong Hong shook hands 19 times. How many people took part in the math contest?
22. Choose three numbers from 3, 6, 9, 12 and 15 and write an equation. Just try it. How many lines can you write?
23, a two-digit number, the number of digits is 3 more than the number of digits. Can such a two-digit number be written?
24. Divide 10 apples into three unequal parts. What's the biggest number?
25. A book has many pages. Lily read 17 pages, and Rhett read 28 pages. Who has more left? How many pages are left?
26. What figures can you fill in the following ()?
50+()& gt； 57 52-()& lt； 46
27. There are 12 male students doing problems. The teacher put a female student between two male students. A * * *, how many female students can you insert?
28. There are 56 students in Class One and Class One and Class Two of Senior High School, with one class transferring to 1 person and the second class transferring to 1 person. Which class is crowded? How many people are there?
29. Xiaolong 14 and Xiaoming 6. After Xiaolong gave Xiaoming a few books, they both had as many books.
30. It was obviously 1 1 birthday, and students from 12 were invited. Five students have come, but how many have not?
3 1, there are 15 birds, three more fly in, and then eight fly away. How many birds are left in the tree?
32, find the law
1 3 6 10 ( )( )( )( )
1 4 9 16( )( )( )( )
33. With the three cards of █▲●, you can arrange them in six ways. For example, please try to arrange them in several other ways.
34. Dad gave Liangliang and Beibei 15 exercise books, of which 7 were for Liangliang and 8 were for Beibei. Who has more exercise books left? How many copies are left?
35. Three children compete for speed. Please guess: Who is the slowest? Who runs fastest?
Xiaoqing said: I am slower than Xiao Bing; Xiao Jing said: I am faster than Xiaoqing; Xiao Bing said I was slower than Xiao Jing; The fastest is (), and the slowest is ().
36. The school organized an autumn outing, and Pingping wanted to take a picture with everyone in the team. It is known that Pingyi * * * took 15 photos, and there are () people in Pingyi's team.
37. A butterfly has six legs, so how many legs do two butterflies have? How many legs do three butterflies have?
There are seven girls and eight boys playing ball games on the playground. After a while, two boys playing football went to play football. How many people are playing on the playground?
39, a circle as required.
(1) Circle ○ greater than ●
○○○○○○○○○
●●●●●
(2) Circle as many parts as χ.
○○○○○○○○○
●●●●●
40. Known: ▲+■ +■ = 7▲+▲+■ =13
Then: ▲ = ()■ = ()
4 1, Duoduo mother bought a pineapple for 4 yuan. With the money for a pineapple, she can buy two sugar cane, and with the money for a sugar cane, she can buy four pears. How much is a pear?
42. A row of students goes from left to right, Xiaohong stands in the fifth place, and from right to left, she stands in the seventh place. How many students are there in this row?
43. Xiaohong has eight balls. After Xiao Ming gave Xiao Hong two, the number of balls was the same. How many balls does Xiaoming have?
44. There are 6 ○ in the first row and 16 ○ in the second row. How much is the second row for the first row, so the number of the two rows is the same?
45, 16 Children stand in a row. There are eight people on the left, and how many people are there on his right?
46. It takes three minutes for three children to eat three apples at the same time, and 10 children to eat 10 apples at the same time takes () minutes.
47. Both Xiao Li and her father collect stamps. After her father gave Xiaoming three stamps, they had the same number of stamps. How many stamps does Dad have than Xiao Li?
48, 70 subtract 7 in succession, and write down the number of each subtraction on the horizontal line:
70、 、 、 、 、 、 、
49. If tomorrow is mom's birthday, you want to buy a birthday present for mom. I have 50 yuan now. How can I buy it? (Expressed by formula): wallet 30 yuan, glasses 35 yuan, silk scarf 26 yuan, hat 15 yuan, gloves 10 yuan, umbrella 18 yuan.
50. My sister has nine fifties, my sister has five fifties, and my sister gave her a few fifties, so their money is the same?
5 1, known as ▲+●= 17 ▲+●+●=20.
Then: ▲ = () ● = ()
52. It takes three matches to make a triangle. Can you build two triangles with five matchsticks? Draw a picture
53. The children lined up to go to the park. There are four people in front of Xiaoli and nine people behind her. Where is Xiaoli? How many children go to the park?
54. It is known that 6+○ =11+△ =12.
Then: ○ = () △ = ()
55. Xiaohong group has 12 people. He shook hands with four people first. How many others didn't?
56. It is clear that there are 12 people in this group. How many times does he have to shake hands with everyone in the group?
57.A * * * has 16 children lined up to do exercises. There are six people in front of Yang Yang. How many people are behind her?
58. Lily and Pumbaa both have some books. After Lily gave Pumbaa six books, they had the same number of books. It turns out that Lily has more books than Pumbaa.
59. My brother and younger brother both have some pencils in their hands. After my brother gave my brother five pens, the number of pens was the same. Then how many pencils does my brother have more than my brother?
60. Xiaohong has 20 balls. After Xiaoming gave Xiaohong two balls, they both had the same number of balls. How many balls did Xiaoming have?
6 1, red everyone shakes hands with the group once, and a * * * shakes hands 13 times. How many people are there in this group?
62. Yang Yang shook hands with five people in the group first, and then shook hands with the remaining seven people. How many people are there in this group?
Mathematics in Grade Three: 12 Comprehensive exercises of logical thinking training questions.
First, the problem of sum and difference
Given the sum and difference of two numbers, find these two numbers.
Formula:
And the sum and the difference are getting bigger and bigger;
Divided by 2, it is big;
And subtract the difference, the smaller the reduction;
Divided by 2, it is small.
Example: It is known that the sum of two numbers is 10, and the difference is 2. Find these two numbers.
According to the formula, large number =( 10+2)/2=6, and decimal number =( 10-2)/2=4.
Second, the problem of chickens and rabbits in the same cage.
Formula:
Suppose all chickens, suppose all rabbits.
How many feet are there? How many feet are missing?
Divided by the foot difference, it is the number of chickens and rabbits.
Example: chickens are free in the same cage, with head 36 and feet 120. Find the number of chickens and rabbits.
When finding rabbits, it is assumed that they are all chickens, so the number of exempted children =( 120-36X2)/(4-2)=24.
When looking for chickens, it is assumed that they are all rabbits, so the number of chickens = (4x36-120)/(4-2) =12.
Third, the concentration problem.
(1) diluted with water
Formula:
Sugar before adding water, sugar water after adding sugar.
Sugar water MINUS sugar water is the amount of sugar added.
Example: There is 20kg of sugar water with the concentration of 15%. How many kilograms of water are added, and the concentration becomes 10%.
Get the sugar before adding water. The original sugar content is 20X 15%=3 (kg).
When the sugar is used up, how much sugar water should there be with the concentration of 10%? 3/ 10%=30 (kg).
Sugar water MINUS sugar water, the amount of sugar water after subtraction is 30-20= 10 (kg).
(2) Sugar concentration
Formula:
Water before adding sugar, syrup after adding water.
If you subtract sugar water from sugar water, you can easily solve the problem.
Example: There is 20kg of sugar water with the concentration of 15%. How many kilograms of sugar are added, and the concentration becomes 20%.
Water needs to be added before sugar is added. The original water content is 20x (1-15%) =17 (kg).
When the water is exhausted, how much sugar water with a concentration of 20% should there be, including 17kg water,17/(1-20%) = 21.25 (kg).
Sugar water minus sugar water, the amount of sugar water minus the original amount of sugar water is 2 1.25-20= 1.25 (kg).
Fourth, the distance problem.
(1) encountered a problem.
Formula:
At the moment we met, the distance disappeared.
Divide by the sum of the speeds and you get the time.
Example: A and B walk in opposite directions from two places with a distance of 120km. Party A's speed is 40km/h and Party B's speed is 20 km/h. How long did they meet?
At the moment we met, the distance disappeared. That is, the distance traveled by Party A and Party B is exactly 120km.
Divide by the sum of the speeds and you get the time. That is, the total speed of Party A and Party B is 40+20=60 (km/h), so the meeting time is 120/60=2 (h).
(2) Traceability problem
Formula:
Slow birds fly first, fast birds chase after them.
The distance to go first, divided by the speed difference,
The time is right.
Brother and sister go to town from home. Big sister walks at a speed of 3 kilometers per hour. After walking for 2 hours, my little brother rode at a speed of 6 kilometers per hour. When will he catch up?
The distance to go first is 3X2=6 (km).
The speed difference is 6-3=3 (km/h).
So the catch-up time is: 6/3=2 (hours).
Verb (abbreviation of verb) and ratio problem
It is known that the whole is divided into parts.
Formula:
Family members want everyone to be together, and separation is also principled.
Denominator ratio sum, numerator's own.
And multiply by the ratio, you deserve it.
Example: The sum of the three numbers A, B and C is 27, A; B: C =2:3:4。 Find the numbers a, b and C. ..
The denominator ratio sum, that is, the denominator is: 2+3+4 = 9;
If the molecule is its own, then the proportions of A, B and C in the total are 2/9, 3/9 and 4/9 respectively.
And the multiplication ratio, so the number A is 27X2/9=6, the number B is 27X3/9=9, and the number C is 27X4/9= 12.
Sixth, the difference ratio problem (difference multiple problem)
Formula:
I am more than you, and multiples are cause and effect.
Actual difference of numerator, multiple difference of denominator.
The quotient is double,
Multiplied by their respective multiples,
You can get two numbers.
For example, the number A is greater than the number B 12, and A: B = 7: 4. Find two numbers.
First, double the amount, 12/(7-4)=4,
So the number A is 4X7=28 and the number B is 4X4= 16.
Seven, engineering problems
Formula:
The total project amount is set to 1,
1 divided by time is work efficiency.
When a person does it, the work efficiency is his own.
When doing it together, the work efficiency is the sum of everyone's efficiency.
1 Subtract what has been done and what has not been done.
What is not completed divided by work efficiency is the result.
Example: A project will be completed in 4 days by yourself and 6 days by yourself. After Party A and Party B do it at the same time for 2 days, how many days will Party B do it alone?
[1-(1/6+1/4) x2]/(1/6) =1(days)
Eight, planting trees
Formula:
How many trees to plant,
How about asking for directions?
Directly subtract 1,
The circle is the result.
Example 1: Plant trees on a road with a length of 120m, with a spacing of 4m. How many trees have been planted?
This road is straight. So species 120/4- 1=29 trees.
Example 2: Plant trees at the edge of a circular flower bed with a length of 120m and a spacing of 4m. How many trees have been planted?
The road is round, so plant 120/4=30 trees.
Nine, profit and loss problem
Formula:
Full profit and loss, greatly reduced;
One profit and one loss, the profit and loss add up.
Divided by the difference in distribution,
The result is the distribution of things or people.
Example 1: Children divide peaches, each peach 10, and 9 peaches are missing; Eight more than seven per person. How many children and peaches do you want?
If one gains and one loses, the formula is: (9+7)/( 10-8)=8 (person), and the corresponding peach is 8X 10-9=7 1 (person).
Example 2: Soldiers carry bullets. 45 rounds, 680 rounds per person; 50 rounds per person is more than 200 rounds. How many soldiers, how many bullets?
The question of total profit. If the big one is subtracted from the small one, the formula is: (680-200)/(50-45)=96 (man), and the bullet is 96X50+200=5000 (rounds).
Example 3: Students distribute books. 10 Each person is missing 90 books; There are eight copies each, and there are still eight left. How many books are suitable for how many students?
Total loss problem. Subtract the big one from the small one. Then the formula is: (90-8)/( 10-8)=4 1 (person), and the corresponding book is 4 1X 10-90=320 (book).
Ten, cattle grazing problem
Formula:
The amount of grass eaten by each cow per day is assumed to be 1.
How much grass did A eat in the first b days?
How much grass did M eat in the first n days?
Subtract the big one from the small one and divide it by the difference of the corresponding days.
The result is the growth rate of grass.
The original amount of grass is correspondingly reversed.
The formula is the amount of grass eaten by A on the first day minus the amount of grass eaten on the second day multiplied by the growth rate of grass.
Cattle with unknown grazing amount are divided into two parts:
A small number eat new grass first, and the number is the proportion of grass;
Divide some grass by the number of remaining cows to get the required number of days.
The grass grows thick and fast all over the pasture. 27 cows can eat grass for 6 days; 23 cows can eat the grass in 9 days. Q 2 1 How many days will it take to finish the grass?
Assume that the daily grazing amount of each cow is 1, the grazing amount of 27 cows for 6 days is 27×6 = 162, and the grazing amount of 23 cows for 9 days is 23×9 = 207.
Subtract the small from the large, 207-162 = 45; The difference between the corresponding two days is 9-6=3 (days)
The result is the growth rate of grass. So the growth rate of grass is 45/3= 15 (cattle/day);
The original amount of grass is correspondingly reversed.
The formula is the amount of grass eaten in B days before A minus B days multiplied by the growth rate of grass.
Therefore, the amount of grass =27X6-6X 15=72 (cattle/day).
Cattle with unknown grazing amount are divided into two parts:
A small number eat new grass first, and the number is the proportion of grass;
That is to say, the required 2 1 cow is divided into two parts, one part is 15 cows eating new grass;
The remaining 2 1- 15=6 eat the original grass,
Therefore, the required number of days is: original grass quantity/allocated surplus cattle =72/6= 12 (days).
XI。 Age problem
Formula:
The precession will not change, when adding and subtracting.
With the change of age, the multiple is also changing.
Grasp these three points and everything will be easy.
Example 1: Xiaojun is 8 years old and his father is 34 years old. A few years later, his father was three times older than Xiaojun.
The precession will not change, this year's age is almost 34-8=26, and it will not change in a few years.
Knowing the difference and multiple, it becomes the problem of difference ratio.
26/(3- 1)= 13. In a few years, dad's age will be 13X3=39, and Xiaojun's age will be 13X 1= 13, so it should be five years later.
Example 2: Sister 13 years old, brother 9 years old. How old should they be when the sum of their ages is 40?
The precession will not change, and the age difference 13-9=4 this year will not change in a few years.
After several years, the age sum is 40, and the age difference is 4, which turns into a sum-difference problem.
Then a few years later, the elder sister's age is (40+4)/2=22 and the younger brother's age is (40-4)/2= 18, so the answer is 9 years later.
Twelve. Residual problem
Formula:
There are (N- 1) residues,
The smallest is 1 and the largest is (N- 1).
When it changes periodically,
Don't look at business,
Just look at Yu.
For example, if the clock now shows 18 o'clock, what time will it be after the minute hand turns 1990?
One revolution of the minute hand is 1 hour, and 24 revolutions is 1 circle of the hour hand, that is, the hour hand returns to its original position. The remainder of 1980/24 is 22, so it is equivalent to the minute hand turning 22 times forward, which is equivalent to the hour hand moving 22 hours forward, which is equivalent to 24-22=2 hours backward, which is equivalent to the hour hand pulling back 2 hours. The instantaneous needle is equivalent to 18-2= 16 (point).
Practice and answer analysis
There are red, yellow and white balls. Red and yellow ball 2 1, yellow and white ball 20, red and white ball 19. How many balls are there in each of the three kinds?
According to the conditions, (2 1+20+ 19) represents twice the total number of three kinds of balls, from which the total number of three kinds of balls can be obtained, and then the number of three kinds of balls can be obtained according to the conditions in the title.
Solutions: Total:
(2 1+20+ 19)÷2=30 (pieces)
White balls: 30-2 1=9 (pieces)
Red ball: 30-20= 10 (piece)
Yellow ball: 30- 19= 1 1 (pieces)
A: There are 9 white balls, red balls 10 and yellow balls 1 1.
2. The cement plant originally planned to complete a task in 12 days, but it completed the task in 10 days due to the production of 4.8 tons of cement every day. How many tons of cement was originally planned to be produced every day?
According to the meaning of the question, the actual cement production in 10 day is (4.8 × 10) tons more than the original plan, and it takes (12- 10) days to complete the extra cement according to the original plan, which means the original plan (10).
Solution: 4.8×10 ÷ (12-10) = 24 (ton)
A: It was originally planned to produce 24 tons of cement every day.
My father is 45 years old. Five years ago, his father was four times as old as his son. How old is his son this year?
Analysis shows that five years ago, the father's age was (45-5) years old, and the son's age was (45-5)÷4 years old, plus 5 is the son's age this year.
Solution: (45-5)÷4+5
= 10+5
= 15 (years old)
A: My son is 15 years old this year.
4. There are 59 students in Class One, Grade Three, 36 students in Chinese competition, 38 students in math competition, and 5 students who have never participated in any subject. How many people attended these two courses?
Think: Some of the 36 people who participated in the Chinese competition took part in the math competition, and some of the 38 people who also participated in the math competition also took part in the Chinese competition. If you add the two together, the number of people who participated in both the Chinese contest and the math contest is counted twice, then the number of people who participated in the Chinese contest plus the number of people who did not participate in one subject MINUS the number of students in the whole class is the number of people who participated in both subjects.
Solution: 36+38+5-59=20 (person)
A: There are 20 participants in both subjects.
5. There are two barrels of oil, and the weight of barrel A is four times that of barrel B. If 18kg of barrel A is poured into barrel B, the weights of the two barrels of oil are equal. How many kilograms is there in a barrel of oil?
Think: "If 18kg is poured from barrel A into barrel B, the oil in both barrels is equally heavy", it can be deduced that the weight of barrel A is (18×2) kg more than that of barrel B. It is known that "the weight of barrel A is four times that of barrel B" and that (18×2) kg is exactly that of barrel B.
Solution:18× 2 ÷ (4-1) =12 (kg)
12×4=48 (kg)
A: Results A barrel oil was 48kg, and B barrel oil 12kg.
6. bright primary school held a math knowledge contest with 20 questions. Answer a question correctly and get 5 points; Answer a wrong question, deduct 3 points; No answer, 0 points. Xiaoli got 79 points in the exam. She got several correct answers, several wrong answers and several unanswered questions.
Analysis: According to the meaning of the questions, all 20 questions were correctly answered 100, 1 questions were incorrectly answered, resulting in a loss of (5+3) points, while those that were not answered only lost 5 points. Xiao Li lost (100-79). Then according to (100-79)÷8=2 (questions), analyze the number of correct, wrong and unanswered questions.
Solution: (5×20-75)÷8=2 (problem)
20-2- 1= 17 (title)
Answer: Correct answer 17, Wrong answer 2, 1 No answer.
7. Train A is 240 meters long and travels 20 meters per second; Train B is 264 meters long and runs at a speed of 16 meters per second. Two cars face each other. How many seconds does it take from the meeting of two heads to the separation of two tails?
Analysis: "From the meeting of two front cars to the separation of two rear cars", the distance traveled by two cars is the sum of their lengths, that is, (240+264) meters, and the sum of their speeds is (20+ 16) meters. According to the relationship between distance, speed and time, the required time can be obtained.
Solution: (240+264)÷(20+ 16)
=504÷30
= 14 (sec)
A: It takes 14 seconds from the time when two cars meet to the time when they leave.
Xiao Ming walks from home to school. If he walks 50 meters per minute, it's time for class. If you walk 60 meters per minute, there are still 2 minutes before class time. How far is it from home to school?
Analysis: If you walk at two speeds with a difference of (60×2) meters and a difference of (60-50) meters per second within the school arrival time of 50 meters per minute, you can find out Xiao Ming's school arrival time of 50 meters per minute.
Solution: 60×2(60-50)= 12 (minutes)
50× 12=600 meters
Xiaoming's distance from home to school is 600 meters.
9. There is a circular runway with a circumference of 600 meters. A and B go in the same direction at the same time. A runs 300 meters per minute, and B runs 400 meters per minute. How many minutes did they meet for the first time?
Analysis: According to the known conditions, when two people meet for the first time, B runs one week more than A, that is, 600 meters. Knowing that B runs (400-300) meters more than A per minute, we can find out the elapsed time when they meet for the first time.
Solution: 600(400-300)
=600÷ 100
=6 (points)
A: It took six minutes for two people to meet for the first time.
10, there is a rectangular cardboard. If the length is only increased by 2 cm, the area will increase by 8 square meters; If the width is only increased by 2cm, the area will increase by 12cm2. What is the original area of this rectangular cardboard?
Analysis: From "only increasing the width of 2cm will increase the area 12cm2", we can find that the original length is (12÷2) cm. Similarly, the original width is (8÷2) cm. If we find out the length and width, we can find out the original area.
Solution: (12÷2)×(8÷2)=24 (square centimeter)
The original area of this rectangular cardboard is 24 square centimeters.
Fourth grade mathematics first volume logical thinking training questions
1 Grade 4 students participating in the broadcast gymnastics competition should be arranged in a square of 1 1 person in each row, * * *1/row. How many students are there in this phalanx?
2. Arrange the chess pieces in a 6×6 square. * * * How many pieces do you need?
3. There are 1764 seedlings to be cultivated in a square nursery (solid square). How many seedlings should be planted on each side of this square nursery?
4.576 people form a solid square. How many people are there on each side of this square?
5. How many pieces can a square with 6 pieces on each side be arranged? What is the total number of pieces? How many pieces are there on the outermost layer?
6. Install colored lights around the square flat roof of the building, one at each corner and 25 at each side. * * * How many colored lights are installed around?
7. The fifth-grade students in a school are arranged in a phalanx, and the outermost number is 60. How many people are there on each side of the outer phalanx? How many fifth-grade students are there in this phalanx?
8. There are 16 students standing around the square, and all four corners are standing 1 person. If the number of people standing on both sides is equal, how many students will stand on both sides?
9. There is a square pond with 1 trees planted on all four corners. If 6 trees are planted on each side, how many trees are planted on each side?
10, 100 Young Pioneers participated in the radio exercise competition, with ten people in a row to form a square team. How many young pioneers are standing around this square?
1 1. On the periphery of a square field, 1 poles are erected at all four corners, and a * * * stands 28 poles. How many columns stand on each side of the square field?
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