Rectangular perimeter = (length+width) × 2 c = 2 (a+b)
Square perimeter = side length × 4 c = 4a
Circumference = π× diameter c = π d c = 2 π r
The circumference of a semicircle = half of the circumference+diameter c = π r+d
Area formula:
Rectangular area = length× width s = ab
Square area = side length x side length s = A2
Parallelogram area = base × height s = ah
Triangle area = base × height ÷ 2s = ah ÷ 2
Height of triangle = area × 2 ○ base h = S2 ○ a.
Triangle base = area ×2÷ height b = S2 ÷ h
Trapezoidal area = (upper bottom+lower bottom) × height ÷ 2s = (a+b) ÷ 2.
Trapezoidal height = area ×2÷ (upper bottom surface+lower bottom surface) H = s × 2 ÷ (+b)
Trapezoid (upper bottom+lower bottom) = area ×2÷ height (a+b) = s × 2 ÷ h
Trapezoid (upper bottom+lower bottom) = area ×2÷ height-lower bottom a=s×2÷h-b
Area of circle = π× square of radius s = π R2
Side area of cylinder = bottom circumference × height S=ch.
Surface area formula:
Rectangular surface area = (length+width+height) 2s = (AB+AH+BH) × 2.
Surface area of cube = side length × side length× 6s = 6a2
Side area of cylinder = bottom circumference x height s = ch.
Surface area of cylinder = side surface area+bottom surface area × 2s = S side +2s bottom.
Volume formula:
Cuboid volume = length× width× height v = abh
Cube volume = side length x side length x side length v = a3
Cylinder volume = bottom area × height v = sh
(Square the approximate cuboid to get:
Cylinder volume = half of lateral area × radius v = ch ÷ 2× r = 2π r ÷ 2× r.
Cone volume = bottom area × height ÷ 3 v = sh ÷ 3 or 1/3.
Relationship:
Fraction application problem:
Number of single house "1"× score (percentage) = corresponding number.
Known quantity ÷ corresponding score (percentage) = quantity in "1"
Comparison Quantity ÷ Quantity in "1" = score (percentage)
Engineering problems:
Work efficiency × working hours = total workload.
Total workload ÷ working time = working efficiency
Total amount of work ÷ work efficiency = working hours
Encountered problems:
Speed sum × meeting time = distance
Sum of distance/speed = meeting time
Distance ÷ Meeting time = speed and
Standardization issues:
Single quantity × quantity = total quantity
Total ÷ single quantity = quantity
Total Quantity ÷ Quantity = Single Quantity
Proportion:
Distance on the map: actual distance = scale
Map distance = actual distance × scale
Actual distance = distance on map/scale.
Average value:
Total number ÷ Total number of copies = average value
Positive proportional relationship:
Y = k (definite) Inverse ratio: xy = k (definite)
General operating rules:
(1) Appendix+Appendix = sum
(2) One addend = and-another addend and-one addend = another addend
(3) minuend-minuend = difference
(4) Negative = negative difference
(5) Minus = Minus+Difference
(6) Factor × factor = product
(7) One factor = product ÷ another factor
(8) Dividend = quotient
Divider = dividend quotient
(10) Divider = quotient × divisor
(1 1) Division with remainder: dividend = quotient × divisor+remainder.
(12) per share × number of shares = total
(13) Total ÷ Each copy = number of copies
(14) Total number of copies/number of copies = number of copies.
(15) 1 multiple × multiple = multiple
(16) What multiple ÷ 1 multiple = multiple
(17) Multiply by Multiply = 1 Multiply
(18) speed × time = distance
(19) distance/time = speed
(20) Distance/Speed = Time
(2 1) unit price × quantity = total quantity
(22) Total price/unit price = quantity
(23) Total Price/Quantity = Unit Price
Unit conversion
unit of length
1 km =1000m1m =10 decimeter1decimeter = 10cm.
1m = 100cm 1cm = 10mm
Square area system
1 km2 = 1 00ha1hectare =10000m2
1 m2 = 100 square decimeter 1 square minute = 100 square centimeter
1 cm2 = 100 mm2
Volume (solution) unit
1 m3 = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cubic decimeter = 1 liter
1 cm3 = 1 ml
1 m3 = 1000 liter
Unit right
1 ton = 1000 kg
1 kg =1000g
1 kg = 1 kg
1 kg = 2 kg
1 kg = 500g
Rmb exchange
1 yuan = 10 angle.
1 angle = 10 point
1 yuan = 100 integral.
The transformation of time
1 century = 100 year
1 year = 65438+ February.
The big month (3 1 day) has1/3/5/7/8/10/65438+February.
Abortion (30 days) occurred in 4/6/9/ 1 1 month.
The normal year is February 28th, and the operation year is February 29th.
The average annual duration is 365 days and the annual duration is 366 days.
1 day = 24 hours
1 = 60 points
1 min = 60 seconds
1 = 3600 seconds
Mathematics defines meaning and reason.
1, additive commutative law:
The position where two numbers are added to exchange addends. The sum remains the same.
2, additive associative law:
Add three numbers. Add up the first two numbers first. Or add the last two numbers first and then the third number. The sum remains the same.
3. Multiplicative commutative law;
When two numbers are multiplied, the position of the exchange factor remains unchanged.
4. Multiplicative associative law
When three numbers are multiplied, the first two numbers are multiplied, or the last two numbers are multiplied and then multiplied by the third number, their products remain unchanged.
5. Law of Multiplication and Distribution
Multiply two numbers with the same number, you can multiply two addends with this number respectively, and then add the two products, and the result remains the same.
Such as: (2+4) × 5 = 2× 5+4× 5
6, the nature of the division of labor
In division, the dividend and divisor are expanded (or reduced) by the same multiple at the same time. Quotient remains unchanged. Divide 0 by any number that is not 0 to get 0.
7. 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:
Both sides of the equation are multiplied (or divided) by the same number at the same time, and the equation still holds.
8. Equation
Equations with unknowns are called equations.
9. One-dimensional linear equation
An equation with an unknown number and an uncountable number is called a linear equation with one variable.
10, score
Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction.
1 1, the law of addition and subtraction of fractions
Add and subtract the fraction of the bisector, only add and subtract the numerator, and the denominator remains the same.
Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
12, comparison of scores
Compared with the fraction of denominator, the numerator is large and the numerator is small.
Compare scores of different denominators, divide them first and then compare them. If the numerator is the same, the denominator is big and small.
13, integer part
The numerator is the product of the numerator of a fraction multiplied by an integer, and the denominator remains the same.
14, fraction by fraction
Use the product of molecular multiplication as the numerator and the product of denominator multiplication as the denominator.
15 fraction divided by integer (except 0)
Is equal to the fraction times the reciprocal of this integer.
16, true score
Numbers with numerator less than denominator are called true fractions.
17, false score
Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions, which are greater than or equal to 1.
18, with score
Writing a false score as an integer and a true score is called scoring.
19, Basic Properties of Fractions
The numerator and denominator of a 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 times b.
Calculation formula of quantitative relationship
1, ratio
The division of two numbers is called the ratio of two numbers.
For example: 2÷5 or 3: 6 or 1/3. The first and second terms of the ratio are multiplied or divided by the same number at the same time. (except 0) The proportion remains unchanged.
2. Proportion
(1) definition
Two expressions with equal ratios are called proportions.
Such as: 3: 6 = 9: 18
(2) Basic nature
In proportion, the product of two external terms is equal to the product of two internal terms.
(3) solution ratio
The unknown term in finding the proportion is called the solution ratio.
For example: 3: x = 9: 18
(4) Positive proportion
Two related quantities, one quantity changes and the other quantity changes, if the ratio (i.e. quotient k) corresponding to these two quantities is constant. These two quantities are called proportional quantities, and the relationship between them is called proportional relationship.
For example: y/k = k (k must) kx = y
(5) Inverse proportion
Two related quantities, one of which changes and the other changes with it. If the product of the corresponding two numbers in these two quantities is certain. These two quantities are called inverse proportional quantities, and the relationship between them is called inverse proportional relationship.
For example: xy = k (k must be) or k/x = y.
6. Percentage
A number that represents a percentage of one number or another is called a percentage, and a percentage is also called a percentage or percentage.
3. Decimals, fractions and percentages
(1) To convert a decimal into a percentage, just move the decimal back two places and add hundreds of semicolons. In fact, to convert a decimal into a percentage, just multiply this number by 100%.
(2) Fractions and percentages are usually divided into decimals (except three decimal places) and then into percentages. Fraction percentage is actually divided into decimals and then multiplied by 100%.
(3) To convert fractions into decimals, just remove the percent sign and move the decimal point to the left by two places.
(4) the percentage of the number of components, first rewrite the percentage of the number of components, can be turned into the simplest fraction.
4, the greatest common divisor
Several numbers can be divisible by the same number at the same time. This number is called the greatest common factor of these numbers, or the common factor of several numbers is called the common factor of these numbers. The largest one is called the greatest common divisor)
5, prime number
The common divisor is only 1, which is called a prime number.
6. 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.
7. Comprehensive score
Convert scores with different denominators into scores with the same denominator equal to the original score. It is called general division (general division uses the least common numbers)
8. About integration
Changing a fraction into a fraction that is equal to it, but with smaller numerator and denominator, is called divisor (divisor is a common number).
9. The simplest score
A fraction whose numerator and denominator are prime numbers is called simplest fraction.
At the end of (1) score calculation, the score must be the simplest score.
(2) Numbers with digits of 0, 2, 4, 6 and 8 can be divisible by 2. That is, you can use 2 to subtract points.
(3) A number with 0 or 5 digits can be divisible by 5, that is, it can be divisible by 5.
(4) The sum of the numbers on each digit is a multiple of 3. That is, it can be divided by 3.
10, even and odd numbers
Numbers that are divisible by 2 are called even numbers, and numbers that are not divisible by 2 are called odd numbers.
1 1, prime number (prime number)
A number (such as 1 1), if there are only two factors: 1 and itself (1 1). Such numbers are called prime numbers.
12, composite number
A number (such as 12) is called a composite number if it has other factors besides 1 and itself (12), and 1 is neither a prime number nor a composite number.
13, interest
Interest = principal interest rate time (time is usually in months or months, which should correspond to the unit of interest rate)
14, interest rate
The ratio of interest to principal is called interest rate, the ratio of interest to principal in one year is called annual interest rate, and the ratio of interest to principal in January is called monthly interest rate.
15, natural number
Integers used to represent the number of objects are called natural numbers. It can also be divided into prime numbers and even numbers. 0 is also a natural number.
The unit of a number is 1, 3, 5, 7 or 9, which is an odd number. The prime numbers within 20 are 2,3,5,7,9, 1 1, 13, 17, 19.
The number of digits is 0, 2, 4, 6 or 8, and this number is even.
16, cyclic decimal
A decimal, starting from somewhere in the decimal part, and one or several numbers are repeated in turn. Such decimals are called cyclic decimals.
Such as: 3. 14 14 14
17, acyclic decimal
A decimal, starting from the decimal part, without one number or several numbers appearing repeatedly, is called a non-decimal.
Such as: 3. 14 1592654
18, infinite cycle decimal
A decimal, from the decimal part to the infinite digits, is called an infinite acyclic decimal without one number or several numbers appearing successively and repeatedly.
Such as: 3. 14 1592654 ...
19, algebra
Is to replace numbers with letters.
20. algebraic expressions
Do algebra with formulas expressed by letters.
For example 3x = AB+C.
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 time = working efficiency
6. Appendix 1+ Appendix 2 = sum-Appendix 1 = Appendix 2- Appendix 2 = Appendix 1.
7. Minus-Minus = Minus-Minus = Minus+Minus = Minus
8. Factor 1× factor 2 = product/factor 1 = product/factor 2 = factor 1.
9. Dividend = quotient dividend = divisor quotient × divisor = dividend
Calculation formula of mathematical graphics in primary schools
1 square (c perimeter, s area and a side length)
Perimeter = side length× 4c = 4a Area = side length× side length s = a× a.
2 cubic meters (V volume A side length)
Surface area = side length × side length× 6 s table = a× a× 6 volume = side length× side length× side length v = a× a× a.
3 rectangle (c perimeter, s area and a side length)
Circumference = (length+width) × 2c = 2 (a+b) Area = length× width S = AB
4 cuboid (volume v area a length b width h height)
(1) surface area = (length× width+length× height+width× height )× 2s = 2 (AB+ah+BH)
(2) volume = length× width× height v = abh
5 triangle (s area, a base and h height)
Area = bottom × height ÷ 2s = ah ÷ 2
Height of triangle = area ×2÷ base of triangle = area ×2÷ height
6 parallelogram (s area, a base and h height)
Area = bottom × height s = ah
7 trapezoid (s area a, upper bottom b, lower bottom h high)
Area = (upper bottom+lower bottom) × height ÷ 2s = (a+b )× h ÷ 2.
8 circle (s area c perimeter π ππππππd = diameter r = radius)
(1) circumference = diameter×π = 2×π× radius C=πd=2πr
(2) Area = radius × radius× π
9 cylinder (v volume h height s bottom area r bottom radius c bottom circumference)
(1) lateral 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
Formula of sum and difference problem
(sum+difference) ÷ 2 = large number (sum-difference) ÷ 2 = decimal.
And folding problems.
Sum ÷ (multiple- 1) = decimal × multiple = large number
(or sum-decimal = large number)
Difference problem
Difference ÷ (multiple-1) = 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 nodes = total length/distance between plants = distance between plants × 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 ÷ plant spacing-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 nodes = total length/distance between plants = distance between plants × 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%)
65438+ 0× number of copies per copy = total
Total copies/number of copies = number of copies
Total copies/number of copies = number of copies
2 1 multiple × multiple = multiple
Multiply1Multiply = Multiply
Multiply/Multiply = 1 Multiply
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 workload.
Total amount of work ÷ work efficiency = working hours
Total workload ÷ working time = working efficiency
6 addend+addend = sum
And-one addend = another addend
7 minuend-minuend = difference
Negative difference = negative
Difference+Minus = Minus
8 factor × factor = product
Product ÷ One factor = another factor
Dividend = quotient
Dividend = divisor
Quotient × Divider = Divider
Calculation formula of mathematical graphics in primary schools
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×a×6
Volume = side length × side length × side length
V=a×a×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.
(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) lateral 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
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
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%)
Perimeter formula:
Rectangular perimeter = (length+width) × 2 c = 2 (a+b)
Square perimeter = side length × 4 c = 4a
Circumference = π× diameter c = π d c = 2 π r
The circumference of a semicircle = half of the circumference+diameter c = π r+d
Area formula:
Rectangular area = length× width s = ab
Square area = side length x side length s = A2
Parallelogram area = base × height s = ah
Triangle area = base × height ÷ 2s = ah ÷ 2
Height of triangle = area × 2 ○ base h = S2 ○ a.
Triangle base = area ×2÷ height b = S2 ÷ h
Trapezoidal area = (upper bottom+lower bottom) × height ÷ 2s = (a+b) ÷ 2.
Trapezoidal height = area ×2÷ (upper bottom surface+lower bottom surface) H = s × 2 ÷ (+b)
Trapezoid (upper bottom+lower bottom) = area ×2÷ height (a+b) = s × 2 ÷ h
Trapezoid (upper bottom+lower bottom) = area ×2÷ height-lower bottom a=s×2÷h-b
Area of circle = π× square of radius s = π R2
Side area of cylinder = bottom circumference × height S=ch.
Surface area formula:
Rectangular surface area = (length+width+height) 2s = (AB+AH+BH) × 2.
Surface area of cube = side length × side length× 6s = 6a2
Side area of cylinder = bottom circumference x height s = ch.
Surface area of cylinder = side surface area+bottom surface area × 2s = S side +2s bottom.
Volume formula:
Cuboid volume = length× width× height v = abh
Cube volume = side length x side length x side length v = a3
Cylinder volume = bottom area × height v = sh
(Square the approximate cuboid to get:
Cylinder volume = half of lateral area × radius v = ch ÷ 2× r = 2π r ÷ 2× r.
Cone volume = bottom area × height ÷ 3 v = sh ÷ 3 or 1/3.
Relationship:
Fraction application problem:
Number of single house "1"× score (percentage) = corresponding number.
Known quantity ÷ corresponding score (percentage) = quantity in "1"
Comparison Quantity ÷ Quantity in "1" = score (percentage)
Engineering problems:
Work efficiency × working hours = total workload.
Total workload ÷ working time = working efficiency
Total amount of work ÷ work efficiency = working hours
Encountered problems:
Speed sum × meeting time = distance
Sum of distance/speed = meeting time
Distance ÷ Meeting time = speed and