Analysis and arrangement of mathematics knowledge points in Xiaoshengchu
1-6 grade knowledge system
99 multiplication formula table in the first grade of primary school. Learn basic addition, subtraction, multiplication and division.
In the second grade of primary school, I perfected the multiplication table, learned division and mixing operations, and learned basic geometric figures.
In the third grade of primary school, I learned multiplication and exchange law, geometric area and perimeter, time and unit. Distance calculation, distribution law, fractional decimal.
In the fourth grade of primary school, the natural number of line angle is an integer, the prime factor is trapezoidal symmetry, and the fractional decimal is calculated.
Fractional decimal multiplication and division in the fifth grade of primary school, algebraic equation and average value, comparative size transformation, graphic area and volume.
Proportional percentage probability of sixth grade in primary school, circular fan-shaped cylinder and cone.
Definition, Theorem and Formula of Necessary Memory
Area of triangle = bottom? Tall? 2。 Formula S= a? h？ 2
Area of a square = side length? The side length formula S= a? a
Area of rectangle = length? The broad formula S= a? b
Area of parallelogram = bottom? High formula S= a? h
Area of trapezoid = (upper bottom+lower bottom)? Tall? 2 formula S=(a+b)h? 2
Sum of internal angles: sum of internal angles of triangle = 180 degrees.
Volume of cuboid = length? Wide? High formula: V=abh
Volume of cuboid (or cube) = bottom area? High formula: V=abh
Volume of cube = side length? Side length? Side length formula: V=aaa
Circumference = diameter formula: L=? d=2？ r
Area of circle = radius? Radius formula: S=? r2
Surface (side) area of cylinder: The surface (side) area of cylinder is equal to the perimeter of bottom multiplied by height. Formula: S=ch=? dh=2？ right hand
Surface area of cylinder: the surface area of cylinder is equal to the perimeter of the bottom multiplied by the height plus the area of the circles at both ends. Formula: S=ch+2s=ch+2? r2
Volume of cylinder: the volume of cylinder is equal to the bottom area multiplied by the height. Formula: V=Sh
The volume of the cone = 1/3 bottom? Cumulative height formula: V= 1/3Sh.
Law of fractional addition and subtraction: Fractions with the same denominator are added and subtracted, only the numerator is added and subtracted, and the denominator remains the same. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
The multiplication of fractions is: use the product of molecules as numerator and the product of denominator as denominator.
The law of division of fractions: dividing by a number is equal to multiplying the reciprocal of this number.
First of all, arithmetic.
1, additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged.
2. Law of additive combination: When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and then the third number is added, and the sum remains unchanged.
3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged.
4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied, or the last two numbers are multiplied first and then the third number, and their products are unchanged.
5. Multiplication and distribution law: When two numbers are multiplied by the same number, you can multiply the two addends by this number respectively, and then add the two products, and the result remains unchanged. Such as: (2+4)? 5=2? 5+4? five
6. Nature of division: In division, the dividend and divisor are expanded (or reduced) by the same multiple at the same time, and the quotient remains unchanged. Divide by any number that is not.
Simple multiplication: multiplication of multiplicand and multiplier with O at the end. You can multiply 1 before o first, and zero does not participate in the operation, and add a few zeros at the end of the product.
7. What is an equation? An equation in which the value on the left of the equal sign is equal to the value on the right of the equal sign is called an equation.
Basic properties of the equation: When both sides of the equation are multiplied (or divided) by the same number at the same time, the equation is still valid.
8. What is an equation? A: Equations with unknowns are called equations.
9. What is a linear equation with one variable? A: An equation with an unknown number of degree 1 is called a linear equation with one variable.
Example method and calculation of learning linear equation of one variable. Are there any examples? Formulas and calculations.
10, fraction: divide the unit "1" into several parts on average, and the number representing such a part or points is called a fraction.
1 1, addition and subtraction of fractions: addition and subtraction of fractions with denominator, only numerator addition and subtraction, denominator unchanged. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
12. Comparison of fractional sizes: Compared with the denominator, the numerator is large and the numerator is small. Compare the scores of different denominators, divide them first and then compare them; If the numerator is the same, the denominator is big and small.
13, the fraction is multiplied by the integer, and the product of the multiplication of the fraction and the integer is the numerator, and the denominator remains unchanged.
14. Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.
15, the fraction divided by an integer (except 0) is equal to the fraction multiplied by the reciprocal of this integer.
16, true fraction: the fraction with numerator less than denominator is called true fraction.
17. False fraction: the fraction with numerator greater than denominator or numerator equal to denominator is called false fraction. False score is greater than or equal to 1.
18, with fraction: write the false fraction as an integer, and the true fraction is called with fraction.
19, the basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged.
20. A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.
2 1, the number A divided by the number B (except 0) is equal to the reciprocal of the number A multiplied by the number B. ..
Second, the calculation formula of quantitative relationship
1, unit price? Quantity = total price
2. Single output? Quantity = total output
3. speed Time = distance
4. Work efficiency? Time = total workload
5. Appendix+Appendix = Total
One addend = and+the other addend.
Negative-negative = difference
Subtraction = minuend-difference
Negative = negative+difference
Factor? Factor = product
A factor = product? Another factor
Dividend? Divider = quotient
Dividend = dividend? business
Bonus = business? divisor
Division with remainder: dividend = quotient? Divider+remainder
A number is divided by two consecutive numbers. You can multiply the last two numbers first, and then divide this number by their product, and the result is still the same. For example: 90? 5? 6=90? (5? 6)
6. 1 km = 1 km 1 km =1000m
1 m = 10 decimeter
1 decimeter = 10/0cm
1 cm = 10/0mm
1 m2 = 100 square decimeter
1 square decimeter = 100 square centimeter
1 cm2 = 100 mm2
1 m3 = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cm3 = 1000 cm3
1 ton = 1000 kg
1 kg =1000g =
1 kg = 1 kg
1 hectare = 1 10,000 square meters.
1 mu =666.666 square meters.
1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter.
7. What is the ratio? The division of two numbers is called the ratio of two numbers. Such as: 2? 5 or 3:6 or 1/3
The first and second items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
8. What is proportion? Two formulas with equal ratios are called proportions. For example, 3:6=9: 18
9. Basic properties of proportion: In proportion, the product of two external terms is equal to the product of two internal terms.
10, solution ratio: the unknown term in the ratio is called the solution ratio. Like 3:? =9: 18
1 1, ratio: two related quantities, one changes and the other changes. If the corresponding ratio (i.e. quotient k) of these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. For example: y/x=k( k must be) or kx = y.
12, inverse ratio: two related quantities, one changes and the other changes. If the product of two corresponding numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. Such as: x? Y = k( k must be) or k/x = y.
Percentage: a number that indicates that one number is a percentage of another number, which is called percentage. Percentages are also called percentages or percentages.
13. To convert decimals into percentages, just move the decimal point to the right by two places and add hundreds of semicolons. In fact, to convert a decimal into a percentage, just multiply this decimal by 100%.
To convert percentages to decimals, simply remove the percent sign and move the decimal point two places to the left.
14. When a fraction is converted into a percentage, it is generally converted into a decimal (except for the inexhaustible, three decimal places are generally reserved), and then the decimal is converted into a percentage. In fact, to turn a fraction into a percentage, you must first turn the fraction into a decimal and then multiply it by 100%.
Divide the percentage into components, and rewrite the percentage into components first, so that the quotation that can be lowered can be made into the simplest score.
15, learn decimal component numbers and fractions to decimals.
16, greatest common divisor: several numbers can be divisible by the same number at the same time, and this number is called the greatest common divisor of these numbers. (or the common divisor of several numbers is called the common divisor of these numbers. The largest one is called the greatest common divisor. )
17, prime number: the common divisor is only 1 two numbers, which is called prime number.
18, least common multiple: the multiple shared by several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers.
19. Comprehensive score: dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called comprehensive score. (Common divisor is the least common multiple)
20. Approximation: It is called approximation to change a fraction into a fraction equal to it, but with smaller numerator and denominator. (The greatest common divisor is used for divisor)
2 1, simplest fraction: The fraction whose numerator and denominator are prime numbers is called simplest fraction.
At the end of the score calculation, the score must be converted into the simplest score.
Numbers in units of 0, 2, 4, 6 and 8 can all be divisible by 2, that is, they can be subtracted by 2. A number with a bit of 0 or 5 can be divisible by 5, that is, it can be subtracted by 5. Pay attention to the use of contracts.
22. Even and odd numbers: Numbers divisible by 2 are called even numbers. Numbers that are not divisible by 2 are called odd numbers.
23. Prime number (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number).
24. Composite number: a number. If there are other divisors besides 1 and itself, such numbers are called composite numbers. 1 is neither prime nor composite.
28. Interest = principal? Interest rate? Time (usually in years or months, which should correspond to the interest rate unit)
29. Interest rate: The ratio of interest to principal is called interest rate. The ratio of interest to principal for one year is called annual interest rate. The ratio of interest to principal in January is called monthly interest rate.
30. Natural number: An integer used to represent the number of objects is called a natural number. 0 is also a natural number.
3 1, Cyclic Decimal: a decimal, starting from a certain digit in the decimal part, and one or several numbers appear repeatedly in turn. Such decimals are called cyclic decimals. Like 3. 14 14 14.
32. Acyclic decimals: Decimals that start from the decimal part without one or several numbers appearing repeatedly in turn. Such a decimal is called an acyclic decimal.
Like 3. 14 1592654.
33. Infinitely circulating decimal: a decimal, from the decimal part to the infinite digits, is called an infinitely circulating decimal without one or several numbers appearing repeatedly in turn. Like 3. 14 1592654.
34. What is algebra? Algebra is to replace numbers with letters.
35. What is algebraic expression? Expressions expressed in letters are called algebraic expressions. For example 3x = AB+C.
Third, the general operating rules
Per serving 1? Number of copies = total number
Total? Number of copies = number of copies
Total? Number of copies = number of copies
2 1 multiple? Multiple = multiple
How many times? 1 multiple = multiple
How many times? Multiplication = 1 multiplication
3 speed? Time = distance
Distance? Speed = time
Distance? Time = speed
4 unit price? Quantity = total price
Total price? Unit price = quantity
Total price? Quantity = unit price
5 work efficiency? Working hours = total amount of work
Total amount of work? Working efficiency = working hours
Total amount of work? Working hours = working efficiency
6 addend+addend = sum
And-one addend = another addend
7 minuend-minuend = difference
Negative difference = negative difference+negative = negative.
Eight factors? Factor = product
Product? One factor = another factor
9 dividends? Divider = quotient
Dividend? Quotient = divisor quotient? Divider = dividend
Four, the primary school mathematics graphics calculation formula
1 square
Perimeter area side length
Perimeter = side length? 4 C=4a
Area = side length? Side length S=a? a
2 cubic meters
Volume a: edge length
Surface area = side length? Side length? 6 S table =a? Answer? six
Volume = side length? Side length? Side length V=a? Answer? a
3 rectangle
Perimeter area side length
Circumference = (length+width)? 2 C=2(a+b)
Area = length? Width S=ab
4 cuboid
V: volume s: area a: length b: width h: height.
Surface area (length? Width+length? Height+width? High)? 2 S=2(ab+ah+bh)
Volume = length? Wide? High V=abh
5 triangle
S area a bottom h height
Area = bottom? Tall? 2s = huh? 2
Height of triangle = area? 2? Base triangle base = area? 2? high
6 parallelogram
S area a bottom h height
Area = bottom? High s=ah
7 trapezoid
Height of upper bottom b and lower bottom h in s area a
Area = (upper bottom+lower bottom)? Tall? 2 s=(a+b)？ h？ 2
8 laps
S area c circumference? D= diameter r= radius
Circumference = diameter =2? Radius C=? d=2？ r
Area = radius? radius
Cylinder 9
V: volume h: height s; Bottom area r: bottom radius c: bottom perimeter
Transverse area = bottom circumference? High surface area = lateral area+bottom area? 2
Volume = bottom area? High volume = transverse area? 2? radius
10 cone
V: volume h: height s; Bottom area r: bottom radius
Volume = bottom area? Tall? three
Summary of Error-prone Knowledge Points in Xiaoshengchu Mathematics
1. When calculating the formula, we must pay attention to the difference between division and division: A divided by B or A divided by B. The formula is: A? B, a divided by b, or a divided by b, the formula is: b? a
2. A square with a side length of 100px and a circle with a radius of 50px have different areas and perimeters, so they cannot be compared! It should be expressed as: "The perimeter and area of a square with a side length of 100px are equal".
3. There is a difference between the circumference of a semicircle and that of a semicircle.
4. How many meters does the roller advance at a time? Is to find its circumference. The road surface area rolled by the roller in a cycle is the lateral area of the roller.
5. When calculating the surface area of uncovered buckets, pools, goldfish bowls, sinks, etc. The bottom area must be reduced.
6. How much is a large number larger than a decimal? Decimal)? The quantity unit is "1".
7. Two ropes with the same length, one cuts the rice, the other cuts it, and the remaining lengths cannot be compared; A rope is cut into two sections, the first section is meters long, and the second section is not unparalleled, but the first section is long.
8.0.52? The quotient of 0. 17 is 3, and the remainder is 0.0 1 instead of 1.
9. In the formula for finding the rate or percentage, the last one must be "? 100﹪"。
10. When solving the application problems of total number, total number and whole tree, the results cannot be fractions and decimals.
1 1 Rewrite an exact number. When rounding is not required, be sure to write the number after "10,000" or "100 million" to the decimal part; Only when the mantissa after "10,000" or "100,000,000,000" is approximate or omitted, use "rounding" for approximation, and be sure to write "10,000" or "/at the end.
12. How to read large numbers: the problem of reading a few zeros.
Related example10,0070,0008 How many zeros did you read? Wrong answer 2 Other correct answers
Comment on examples
Reading large numbers is a knowledge point in grade four, especially reading a few zeros, which is easy to make mistakes.
13. Approximation problem
Related examples The approximate value of a number is 10000, and the maximum number is _ _ _ _ wrong answer 9999 correct answer 14999.
Comment on examples
The approximate value obtained by rounding may be not only "five inputs" but also "four inputs".
14. Number size sorting problem: pay attention to the size order required by the topic.
For related examples, put 3. 14,? On 22nd/7th, _ _ _ _ _ _ wrong answers are arranged in descending order. 3. 14.
Comment on examples
Ask any questions you want, and don't fool around. And be sure to write the original number sorting.
15. Scale problem: pay attention to the scale of the area.
Related examples On the sand table with the scale of 1:2000, the ecological park with an actual area of 800,000 square meters is _ _ _ _ square meters. Wrong answer 400, correct answer 0.2.
Comment on examples
Many students directly use 800 thousand? In 2000, I got the wrong answer. Remember, scale = distance on the map: the actual distance is the scale of the length, that is, the length unit of 1 on the map is the actual length unit of 2000. But this problem involves area and needs to be converted into the proportion of area. The ratio of square length is required, that is, the area unit of 1 on the drawing is the actual area unit of 4000000.
16. Positive-negative ratio problem: the meaning of positive-negative ratio is not clear.
True or false: The area of a circle is proportional to its radius. Wrong answer? Correct answer?
Comment on examples
If the product of two quantities is a constant value, it is inversely proportional; If the quotient of two quantities is a constant value, then it is proportional. Strict card definition, the original title changed to "the area of a circle is proportional to the square of the radius", which is correct.
17. Comparison question: Pay attention to the order of the previous items.
Related examples
When the side length of a square increases by 1/3, the ratio of the area of the original square to the area of the new square is _ _ _ _ _ _ _.
Wrong answer 16:9 correct answer 9: 16
Comment on examples
Who is the first item and who is the second item? Be sure to open your eyes and see clearly!
18. Ratio problem: the difference between ratio and ratio
Related examples
When the side length of a square increases by 1/3, the ratio of the area of the original square to that of the new square is _ _ _ _ _.
Wrong answer 9: 16 correct answer 9: 16 example evaluation ratio is a result, a number.
19. Unit problem: Don't leave out the unit.
Related examples
The area of a square with a side length of 4 cm is _ _ _ _ _ _.
Wrong answer 16 correct answer 16 cm2.
Comment on examples
The area problem, the result is correct, but the unit that should be written is not written, just like a traveler in the desert, dying of thirst by the river close at hand. What a pity! Pathetic! Ridiculous! Alas!
20. Unit problem: Pay attention to the consistency of the unit.
Related examples
A flour bag is marked with (25kg plus or minus 50g), and the heaviest weight of this flour is ___kg.
Wrong answer 75 correct answer 25.05
Comment on examples
Many students didn't see that the units of kg and g were inconsistent, and directly gave the wrong answer of 75.
2 1. leap year, flat year problem: the concept of leap year is unclear.
Related examples
1900 is a leap year or a normal year?
Wrong answer leap year correct answer flat year
Comment on examples
Jump in four years, not in a hundred years, and jump again in four hundred years. If a year is a multiple of 4, it is a leap year; Otherwise it will be a normal year. But if it is a whole hundred years (for example,1900,2000), then it must be a multiple of 400 to be considered as a leap year, otherwise it is a flat year.
22. Solve the equation problem: the minus sign is in front of the brackets, and the number should be changed if the brackets are removed! Move the item to change the logo!
Related examples
6? 2(2X？ 3)=4
Wrong answer Other correct answers x=2
Comment on examples
Remove the bracket. If there is a minus sign in front of the bracket, please change it! Move the item (a number moves left and right on both sides of the equal sign) to change the symbol, remember!
23. Calculation problem: Keep in mind the operation order.
Related example 20? 7? 1/7 wrong answer 20 correct answer 20/49
Comment on examples
In the 530 exam, the trend of "de-technicalization" of calculation questions is obvious. This paper focuses on the basic calculation skills such as the operation of four fractions, the operation sequence and the extraction of common factors.
24. The average speed problem
Related examples Xiaoming's climbing speed is 1 m/s, and his downhill speed is 3 m/s, so Xiaoming's average climbing speed is _ _ _ wrong answer (1+3)? 2=2 (m/s) The correct answer is that the whole journey up the mountain is 3 meters, and the average speed is: (3? 2)? (3? 1+3? 3)= 1.5 (m/s)
The definition of average speed is: total distance? total time
25. There are many topics.
Related examples The degree of an angle of an isosceles triangle is 50 degrees, so its vertex angle is _ _ _ _ 80 degrees, which is the wrong answer, and 50 degrees or 80 degrees is the correct answer.
Comment on examples
Many types of problems usually have more than one result. Students must pay attention to the rigor of thinking, sum up more when doing problems at ordinary times, and try to take all the situations into account. Don't give an answer and think you're done.
26. Pay attention to the integrity of expression.
Related examples The ratio of three internal angles of a triangle is 1: 1:2, which is a _ _ _ _ _ triangle. Wrong answer isosceles triangle correct answer isosceles right triangle
Comment on examples
This kind of topic, only when training at ordinary times, think more and summarize more, can ensure that the exam will not make mistakes.