1, the perimeter of the rectangle = (length+width) ×2 C=(a+b)×2.

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

19, cuboid (cube, cylinder)

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) 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

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.

Respondent: AWM Cloun-Introduction to Jianghu Level 2 4- 16 12:50

1. Know cylinders and cones and master their basic characteristics. Know the bottom, sides and height of a cylinder. Know the bottom and height of the cone. Through the understanding of cylinder and cone, remember the surface area of cylinder, the volume of cylinder and the volume of cone.

2. Explore and master the calculation method of lateral area and surface area of cylinder, as well as the calculation formula of cylinder and cone volume, and use the formula to calculate the volume to solve simple practical problems.

3. By observing, designing and making cylinder and cone models, we can understand the relationship between plane graphics and three-dimensional graphics and develop students' spatial concept.

The area of a square is the square of its side length, and its perimeter is four times its side length.

The area of a rectangle is length times width, and the circumference is 2* (length+width).

The area of a parallelogram is length times height, and its perimeter is twice the sum of adjacent sides.

The area of the trapezoid is (upper bottom+lower bottom) multiplied by the height ÷2, and the perimeter is the sum of all sides.

The area of a triangle is the base times the height divided by 2, and the perimeter is the sum of the sides.

The area of a cylinder is the sum of the area of the side surface plus the area of the two circles at the bottom, which is equal to the perimeter of the bottom multiplied by the height plus 2 π r 2.

The area of the cone is the sector area plus the bottom area, which is equal to the perimeter of the bottom multiplied by the bus length divided by 2, or nπR^2 divided by 360.

Volume and surface area

Area of triangle = base × height ÷2. The formula S= a×h÷2.

Area of square = side length × side length formula S= a2

Area of rectangle = length× width Formula S= a×b

Area of parallelogram = base× height Formula S= a×h

Trapezoidal area = (upper bottom+lower bottom) × height ÷2 Formula S=(a+b)h÷2

Sum of internal angles: sum of internal angles of triangle = 180 degrees.

The surface area of a cuboid = (length× width+length× height+width× height )× 2 Formula: S=(a×b+a×c+b×c)×2.

Surface area of cube = side length × side length ×6 Formula: S=6a2.

Cuboid volume = length× width× height formula: V = abh

Volume of cuboid (or cube) = bottom area × height formula: V = abh.

Volume of cube = side length × side length × side length formula: V = a3.

Circumference = diameter × π formula: L = π d = 2π r

Area of circle = radius × radius× π formula: s = π 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 = π DH = 2π RH.

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+2πr2.

Volume of cylinder: the volume of cylinder is equal to the bottom area multiplied by the height. Formula: V=Sh

Volume of cone = 1/3 bottom× product height. Formula: V= 1/3Sh

arithmetic

1, additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged.

2. Additive associative law: A+B = B+A.

3. Multiplicative commutative law: a× b = b× a.

4. Multiplicative associative law: a × b × c = a ×(b × c)

5. Multiplicative distribution law: a× b+a× c = a× b+c.

6. The nature of division: a ÷ b ÷ c = a ÷(b × c)

7. 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. O is divided by any number that is not O. Simple multiplication: the multiplicand and the end of the multiplier are multiplied by O. 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.

8. Division with remainder: dividend = quotient × divisor+remainder

Equations, Algebras and Equality

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.

Equation: An equation with an unknown number is called an equation.

One-dimensional linear equation: An equation with an unknown number of degree 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.

Algebra: Algebra means replacing numbers with letters.

Algebraic expression: Expressions expressed by letters are called algebraic expressions. For example 3x = AB+C.

mark

Fraction: divide the unit "1" into several parts on average, and the number representing such a part or points is called a fraction.

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.

Addition and subtraction of fractions: add and subtract fractions with the same denominator, only add and subtract numerators, and the denominator remains the same. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.

Fraction multiplied by integer, numerator is the product of fractional and integer multiplication, denominator remains unchanged.

Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.

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 concept of reciprocal: 1 If the product of two numbers is 1, we call one of them the reciprocal of the other. These two numbers are reciprocal. The reciprocal of 1 is 1, and 0 has no reciprocal.

A fraction divided by an integer (except 0) is equal to this fraction multiplied by the reciprocal of this integer.

The basic properties of a fraction: the numerator and denominator of a fraction are multiplied or divided by the same number (except 0), and the size of the fraction.

The law of division of fractions: dividing by a number (except 0) is equal to multiplying the reciprocal of this number.

True fraction: The fraction with numerator less than denominator is called true fraction.

False fraction: Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions. False score is greater than or equal to 1.

With a score: write a false score as an integer, and a true score is called with a score.

The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged.

Calculation formula of quantitative relationship

Unit price × quantity = total price 2, single output × quantity = total output

Speed × time = distance 4, work efficiency × time = total workload.

Appendix+Appendix = and one addend = and+another addend.

Negative-negative = differential negative = negative-differential negative = negative+difference.

Factor × factor = product One factor = product ÷ another factor.

Frequency divider/frequency divider = frequency divider = frequency divider/frequency divider = quotient × frequency divider

Length unit:

1 km = 1 km 1 km = 1000 m

1 m = 10 decimeter 1 decimeter =10 cm1cm =10 mm.

Area unit:

1 km2 = 1 00ha1hectare =10000m2

1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter 1 square centimeter = 100 square millimeter

1 mu = 666.666 square meters.

volume unit

1 m3 = 1000 cubic decimeter

1 cm3 = 1000 cm3

1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter.

Unit right

1 ton = 1 000kg1kg = 1 000g = 1 kg =1kg.

compare

What is the ratio? When two numbers are divided, it 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.

What is proportion? Two formulas with equal ratios are called proportions. For example, 3: 6 = 9: 18

The basic property of proportion: in proportion, the product of two external terms is equal to the product of two internal terms.

Solution ratio: the unknown term in the proportion is called solution ratio. Such as 3: χ = 9: 18.

Proportion: two related quantities, one of which changes and the other 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/x=k( k must be) or kx = y.

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.

per cent

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.

To convert decimals into percentages, just move the decimal point two places to the right and add hundreds of semicolons at the end. 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.

When a fraction is converted into a percentage, the fraction is generally converted into a decimal (three decimal places are generally reserved when it is not used up), 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.

We should learn to decompose fractions into components and fractions into decimals.

Multiplication and divisor

Maximum common divisor: The common divisor of several numbers is called the common divisor of these numbers. There is a finite common factor. The largest one is called the greatest common divisor of these numbers.

Least common multiple: The common multiple of several numbers is called the common multiple of these numbers. There are infinite common multiples. The smallest one is called the least common multiple of these numbers.

Prime number: the common divisor has only 1 two numbers, which is called prime number. Two adjacent numbers must be prime numbers. Two consecutive odd numbers must be coprime. 1 and any number coprime.

Comprehensive score: the difference between scores of different denominators is changed into the same denominator score equal to the original score, which is called comprehensive score. (Common divisor is the least common multiple)

Decrement: divide the numerator and denominator of a fraction by the common divisor at the same time, and the fraction value remains unchanged. This process is called dropping points.

Simplest fraction: The numerator and denominator are fractions of prime numbers, which are called simplest fraction. At the end of the score calculation, the score must be converted into the simplest score.

Prime number (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number).

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.

Prime factor: If a prime number is a factor of a certain number, then this prime number is the prime factor of this number.

Prime factor decomposition: A composite number is represented by the complementary way of prime factors, which is called prime factor decomposition.

Multiple characteristics:

Characteristics of multiples of 2: You are 0, 2, 4, 6, 8.

Characteristics of multiples of 3 (or 9): The sum of the numbers on each digit is multiples of 3 (or 9).

Characteristics of multiples of 5: You are 0, 5.

Characteristics of multiples of 4 (or 25): The last two digits are multiples of 4 (or 25).

Characteristics of multiples of 8 (or 125): the last three digits are multiples of 8 (or 125).

Characteristics of multiples of 7 (1 1 or 13): the difference (big-small) between the last three digits and other digits is a multiple of 7 (1 1 3).

Characteristics of multiples of 17 (or 59): the difference (big-small) between the last three digits and the rest digits is a multiple of 17 (or 59).

Characteristics of multiples of 19 (or 53): the difference (big-small) between the last three digits and other seven digits is a multiple of 19 (or 53).

Characteristics of multiples of 23 (or 29): The difference (big-small) between the last four digits and the other five digits is multiples of 23 (or 29).

Of the two numbers in the multiple relation, the greatest common divisor is smaller and the smallest common multiple is larger.

The coprime relation between two numbers, the greatest common divisor is 1, and the least common multiple is the product.

When two numbers are divided by their greatest common divisor, the quotient is coprime.

The product of two numbers and the least common multiple is equal to the product of these two numbers.

The common divisor of two numbers must be the greatest common divisor of these two numbers.

1 is neither prime nor composite.

A prime number greater than 3 divided by 6 must get 1 or 5.