2. The circumference of a square = side length ×4 C=4a.
3. Area of rectangle = length× width S=ab
4. Square area = side length x side length s = a.a = a.
5. Area of triangle = base × height ÷2 S=ah÷2.
6. parallelogram area = bottom x height S=ah
7. trapezoidal area = (upper bottom+lower bottom) × height ÷ 2s = (a+b) h ÷ 2.
8. Diameter = Radius× 2D = 2r Radius = Diameter ÷2 r= d÷2
9. The circumference of a circle = π× diameter = π× radius× 2c = π d = 2π r.
10, circular area = pi × radius× radius? =πr
1 1, the surface area of a cuboid = (length× width+length× height+width× height) × 2.
12, cuboid volume = length× width× height V =abh.
13, the surface area of the cube = side length × side length× ×6 S =6a.
14, volume of cube = side length x side length x side length v = a.a.a = a.
15, lateral area of cylinder = circumference of bottom circle × height S=ch.
16, surface area of cylinder = upper and lower bottom area+side area.
s = 2πr+2πRH = 2π(d÷2)+2π(d÷2)h = 2π(c÷2÷π)+Ch
17, cylinder volume = bottom area × height V=Sh
V=πr h=π(d÷2) h=π(C÷2÷π) h
18, volume of cone = bottom area × height ÷3.
v = sh÷3 =πr h÷3 =π(d÷2)h÷3 =π(c÷2÷π)h÷3
1, number of copies × number of copies = total number of copies/number of copies = total number of copies/number of copies = number of copies.
2. 1 multiple× multiple = multiple1multiple = multiple/multiple = 1 multiple
3. Speed × time = distance/speed = time/distance/time = speed.
4. Unit price × quantity = total price ÷ unit price = total quantity ÷ quantity = unit price
5. Work efficiency × working hours = total workload ÷ work efficiency = working hours ÷ total workload ÷ working hours = work efficiency.
6. Appendix+Appendix = sum, and-one addend = another addend.
7. Minus-Minus = Minus-Minus = Minus+Minus = Minus
8. Factor × factor = product ÷ one factor = another factor.
9. Dividend = quotient dividend = divisor quotient × divisor = dividend
Calculation formula of mathematical graphics in primary schools
1, square c perimeter s area a side length perimeter = side length× 4c = 4a area = side length× side length s = a× a.
2. Cube V: volume A: side surface area = side length × side length× 6s table =a×a×6 volume = side length× side length× side length V = a× a× a.
3. rectangular
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.
(1) Surface area (L× W+L× H+W× H) ×2
S=2(ab+ah+bh)
(2) Volume = length × width × height
V=abh
5 triangle
S area a bottom h height
Area = bottom × height ÷2
s=ah÷2
Height of triangle = area ×2÷ base.
Triangle base = area ×2÷ height
6 parallelogram
S area a bottom h height
Area = bottom × height
S = ah
7 trapezoid
Height of upper bottom b and lower bottom h in s area a
Area = (upper bottom+lower bottom) × height ÷2
s=(a+b)× h÷2
8 laps
Area c perimeter d= diameter r= radius
(1) circumference = diameter ×∏=2×∏× radius
c =∏d = 2r
(2) area = radius × radius×∈
Cylinder 9
V: volume h: height s; Bottom area r: bottom radius c: bottom perimeter
(1) Transverse area = bottom circumference × height.
(2) Surface area = lateral area+bottom area ×2
(3) Volume = bottom area × height
(4) Volume = lateral area ÷2× radius.
10 cone
V: volume h: height s; Bottom area r: bottom radius
Volume = bottom area × height ÷3
Total number ÷ Total number of copies = average value
Sum-difference problem
(sum+difference) ÷ 2 = large number
(sum and difference) ÷ 2 = decimal
And folding problems.
Sum \ (multiple-1) = decimal
Decimal × multiple = large number
(or sum-decimal = large number)
Difference problem
Difference ÷ (multiple-1) = decimal
Decimal × multiple = large number
(or decimal+difference = large number)
Tree planting problem
1 The problem of planting trees on unclosed lines can be divided into the following three situations:
(1) If trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes+1 = total length-1.
Total length = plant spacing × (number of plants-1)
Plant spacing = total length ÷ (number of plants-1)
2 If you want to plant trees at one end of the unclosed line and not at the other end, then:
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
(3) If no trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes-1 = total length-1.
Total length = plant spacing × (number of plants+1)
Plant spacing = total length ÷ (number of plants+1)
The quantitative relationship of planting trees on the closed line is as follows
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
The question of profit and loss
(Profit+Loss) ÷ Difference between two distributions = number of shares participating in distribution.
(Big profit-small profit) ÷ Difference between two distributions = number of shares participating in distribution.
(big loss-small loss) ÷ The difference between two distributions = the number of shares participating in the distribution.
encounter a problem
Meeting distance = speed × meeting time
Meeting time = meeting distance/speed and
Speed Sum = Meeting Distance/Meeting Time
Catch up with the problem
Catch-up distance = speed difference× catch-up time
Catch-up time = catch-up distance ÷ speed difference
Speed difference = catching distance ÷ catching time
Tap water problem
Downstream velocity = still water velocity+current velocity
Countercurrent velocity = still water velocity-current velocity
Still water velocity = (downstream velocity+countercurrent velocity) ÷2
Water velocity = (downstream velocity-countercurrent velocity) ÷2
Concentration problem
Solute weight+solvent weight = solution weight.
The weight of solute/solution × 100% = concentration.
Solution weight × concentration = solute weight
Solute weight-concentration = solution weight.
Profit and discount problem
Profit = selling price-cost
Profit rate = profit/cost × 100% = (selling price/cost-1) × 100%.
Up and down amount = principal × up and down percentage
Discount = actual selling price ÷ original selling price× 1 00% (discount <1)
Interest = principal × interest rate× time
After-tax interest = principal × interest rate × time × (1-20%)
Time unit conversion
1 century = 100 1 year =65438+ February.
The big month (3 1 day) includes:1\ 3 \ 5 \ 7 \ 8 \10 \ 65438+February.
Abortion (30 days) includes: April \ June \ September \165438+1October.
February 28th in a normal year and February 29th in a leap year.
There are 365 days in a normal year and 366 days in a leap year.
1 day =24 hours 1 hour =60 minutes.
1 point = 60s 1 hour = 3600s product = bottom area × height V=Sh.
Part I: Concept.
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× 5
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. That is, an example is given to illustrate that the formula is replaced by χ and calculated.
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. ..
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.
22. What is the ratio? The division of two numbers is called the ratio of two numbers. For example, the first and second terms of the ratio of 2÷5 or 3:6 or 1/3 are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
23. What is proportion? Two expressions with equal ratios are called proportions. For example, 3: 6 = 9: 18
24. The basic nature of proportion: In proportion, the product of two external terms is equal to the product of two internal terms.
25. Solution ratio: Finding the unknown item in the ratio is called solution ratio. Such as 3: χ = 9: 18.
26. Proportion: two related quantities, one of which 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.
27. Inverse proportion: two related quantities, one of which changes and the other changes accordingly. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. For example: x×y = k( k must be) or k/x = y.
28. Percentage: The number that indicates that one number is the percentage of another number is called percentage. Percentages are also called percentages or percentages.
29. To convert decimals into percentages, just move the decimal point two places to the right and add hundreds of semicolons at the back. In fact, to convert a decimal into a percentage, just multiply this decimal by 100%.
30. To convert percentages into decimals, just remove the percent sign and move the decimal point two places to the left.
3 1, the fraction is converted into a percentage, usually converted into a decimal (except infinity, three decimal places are usually reserved), and then 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%.
32, the percentage of the number of components, first rewrite the percentage of the number of components, can be turned into the simplest score.
33. Learn how to divide scores into scores and how to divide scores into scores.
34. 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. )
35. Prime number: The common divisor is only 1, which is called prime number.
36. Least common multiple: the common multiple of several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers.
37. Comprehensive score: Divide scores with different denominators into scores with the same denominator equal to the original score, which is called comprehensive score. (Common divisor is the least common multiple)
38. Approximate fraction: It is called approximate fraction to change a fraction into a fraction that is equal to it, but the numerator and denominator are relatively small. (The greatest common divisor is used for divisor)
39. simplest fraction: The numerator and denominator are fractions of prime numbers, which are called simplest fraction.
40. At the end of the score calculation, the score must be converted into the simplest score.
4 1, numbers with 0, 2, 4, 6 and 8 in the unit can be divisible by 2, that is, can be binary.
42. About integration. 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.
43. Even and odd numbers: Numbers divisible by 2 are called even numbers. Numbers that are not divisible by 2 are called odd numbers.
44. Prime number (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number).
45. 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.
46. Interest = principal × interest rate × time (time is generally in years or months, which should correspond to the unit of interest rate).
47. 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.
48. Natural number: An integer used to represent the number of objects is called a natural number. 0 is also a natural number.
49. Cyclic decimal: a decimal, starting from a certain place in the decimal part, and one or several numbers are repeated in turn. Such decimals are called cyclic decimals. Like 3. 14 14 14.
50. Acyclic decimals: Decimals that start from the decimal part and do not have one or several numbers repeated. Such a decimal is called an acyclic decimal. For example, pi: 3. 14 1592654.
5 1, infinite acyclic decimal: a decimal, from the decimal part to the infinite digits, is called infinite acyclic decimal without one or several numbers repeating in turn. Such as 3. 14 1592654. ...
52. What is algebra? Algebra is to replace numbers with letters.
53. What is algebraic expression? Expressions expressed in letters are called algebraic expressions. For example 3x = AB+C.
Part II: Definition Theorem
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 addition and association: When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and then they are the same as the first number.
Three numbers add up, and the sum remains the same.
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 second two numbers are multiplied first, and then the third number is multiplied, and the product remains 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× 5.
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 0 by any number other than 0 to get 0.
7. Equation: An equation in which the value on the left of the equal sign equals 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. Equations: Equations with unknowns are called equations.
9. One-dimensional linear equation: An equation with an unknown number of 1 is called a one-dimensional linear equation.
Example method and calculation of learning linear equation of one variable. That is, an example is given to illustrate that the formula is replaced by χ and calculated.
10. Score: divide the unit "1" into several parts on average, and the number representing such a part or points is called a score.
1 1. Addition and subtraction of fractions: add and subtract fractions with denominator, only add and subtract numerators, and the denominator remains unchanged. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
12. Comparison of fraction size: Compared with the fraction of 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. Fractions are multiplied by integers, and the product of the multiplication of fractions and integers is a 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. Fraction divided by integer (except 0) equals fraction multiplied by the reciprocal of the 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 score: write the false score as an integer, and the true score is called with score.
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.A divided by b (except 0) equals the reciprocal of a multiplied by b.
Part III: Geometry
1. square
Circumference of a square = side length ×4 Formula: C=4a
Square area = side length × side length formula: s = a× a.
Cubic volume = side length × side length × side length formula: v = a× a× a.
2. Square
The circumference of a rectangle = (length+width) ×2 Formula: C=(a+b)×2.
Area of rectangle = length× width formula: S=a×b
Cuboid volume = length× width× height formula: v = a× b× h.
Step 3: Triangle
Area of triangle = base × height ÷2. Formula: S= a×h÷2
4. Parallelogram
Area of parallelogram = base× height formula: S= a×h
5. trapezoidal
Trapezoidal area = (upper bottom+lower bottom) × height ÷2 Formula: S=(a+b)h÷2.
6. circle
Diameter = radius ×2 Formula: d=2r
Radius = Diameter ÷2 Formula: r= d÷2
Circumference = π× diameter formula: c=πd =2πr
Area of circle = radius × radius× π formula: s = π RR.
7. Cylinder
Transverse area of cylinder = bottom circumference × height. Formula: s = ch = π DH = 2π RH.
Surface area of cylinder = perimeter of bottom × height+area of circles at both ends. Formula: S=ch+2s=ch+2πr2.
Total volume of cylinder = bottom area × height. Formula: V=Sh
8. Cone
Total volume of cone = bottom area × height × 1/3 formula: V= 1/3Sh.
The sum of the internal angles of the triangle = 180 degrees.
Parallel lines: Two straight lines that do not intersect the same plane are called parallel lines.
Perpendicular: Two straight lines intersect at right angles. Two straight lines like this,
Suppose these two straight lines are perpendicular to each other, one of which is called the perpendicular of the other, and the intersection of these two straight lines is called the vertical foot.
Part IV: Calculation formula
Quantitative relationship:
1, number of copies × number of copies = total number of copies/number of copies = total number of copies/number of copies = number of copies.
2. 1 multiple× multiple = multiple1multiple = multiple/multiple = 1 multiple
3. Speed × time = distance/speed = time/distance/time = speed
4. Unit price × quantity = total price ÷ unit price = total quantity ÷ quantity = unit price
5. Work efficiency × working hours = total workload ÷ work efficiency = working hours ÷ total workload ÷ working hours = work efficiency.
6. Appendix+Appendix = sum, and-one addend = another addend.
7. Minus-Minus = Minus-Minus = Minus+Minus = Minus
8. Factor × factor = product ÷ one factor = another factor.
9. Dividend = quotient dividend = divisor quotient × divisor = dividend
Formula of sum and difference problem
(sum+difference) ÷ 2 = large number
(sum and difference) ÷ 2 = decimal
And folding problems.
Sum \ (multiple-1) = decimal
Decimal × multiple = large number
(or sum-decimal = large number)
Difference problem
Difference ÷ (multiple-1) = decimal
Decimal × multiple = large number
(or decimal+difference = large number)
Tree planting problem:
1 The problem of planting trees on unclosed lines can be divided into the following three situations:
(1) If trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes+1 = total length-1.
Total length = plant spacing × (number of plants-1)
Plant spacing = total length ÷ (number of plants-1)
2 If you want to plant trees at one end of the unclosed line and not at the other end, then:
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
(3) If no trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes-1 = total length-1.
Total length = plant spacing × (number of plants+1)
Plant spacing = total length ÷ (number of plants+1)
The quantitative relationship of planting trees on the closed line is as follows
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
The question of profit and loss
(Profit+Loss) ÷ Difference between two distributions = number of shares participating in distribution.
(Big profit-small profit) ÷ Difference between two distributions = number of shares participating in distribution.
(big loss-small loss) ÷ The difference between two distributions = the number of shares participating in the distribution.
encounter a problem
Meeting distance = speed × meeting time
Meeting time = meeting distance/speed and
Speed Sum = Meeting Distance/Meeting Time
Catch up with the problem
Catch-up distance = speed difference× catch-up time
Catch-up time = catch-up distance ÷ speed difference
Speed difference = catching distance ÷ catching time
Tap water problem
Downstream velocity = still water velocity+current velocity
Countercurrent velocity = still water velocity-current velocity
Still water velocity = (downstream velocity+countercurrent velocity) ÷2
Water velocity = (downstream velocity-countercurrent velocity) ÷2
Centralized question:
Solute weight+solvent weight = solution weight.
The weight of solute/solution × 100% = concentration.
Solution weight × concentration = solute weight
Solute weight-concentration = solution weight.
Profit and discount issues:
Profit = selling price-cost
Profit rate = profit/cost × 100% = (selling price/cost-1) × 100%.
Up and down amount = principal × up and down percentage
Discount = actual selling price ÷ original selling price× 1 00% (discount <1)
Interest = principal × interest rate× time
After-tax interest = principal × interest rate × time × (1-20%)
Area and volume conversion
(1)1km =1km =1000m1m =10 decimeter1decimeter =10 cm/kloc.
(2) 1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter 1 square centimeter = 100 square millimeter.
(3) 1 m3 = 1000 cubic decimeter 1 cubic decimeter = 1000 cubic centimeter 1 cubic centimeter = 1000 cubic millimeter.
(4) 1 hectare = 1 ten thousand square meters 1 mu = 666.666 square meters.
(5) 1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter.
Weight conversion:
1 ton = 1000 kg
1 kg =1000g
1 kg = 1 kg
Rmb unit conversion
1 yuan = 10 angle.
1 angle = 10 point
1 yuan = 100 integral.
Time unit conversion:
1 century = 100 1 year =65438+ February.
The big month (3 1 day) includes:1\ 3 \ 5 \ 7 \ 8 \10 \ 65438+February.
Abortion (30 days) includes: April \ June \ September \165438+1October.
February 28th in a normal year and February 29th in a leap year.
There are 365 days in a normal year and 366 days in a leap year.
1 day =24 hours 1 hour =60 minutes.
1 minute =60 seconds 1 hour =3600 seconds.