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

Square area = side length × side length formula S= a×a

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.

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=aaa.

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

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.

Reading comprehension will apply the following formulas that define the properties of theorems.

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× 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? A formula in which the value on the left of the equal sign is equal to the value on the right of the equal sign.

It's called an equation.

The basic properties of the equation: both sides of the equation are multiplied (or divided) by the same number at the same time,

This equation still holds.

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), the score size 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 ... As far as the calculation formula of quantitative relationship is concerned,

1, unit price × quantity = total price 2, single output × quantity = total output.

3, speed x time = distance 4, efficiency x time = total work.

5. 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

Division with remainder: dividend = quotient × divisor+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 cm1cm =10 mm.

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

1 cm2 = 100 mm2

1 m3 = 1000 cubic decimeter

1 cm3 = 1000 cm3

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

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. Such as 3: χ = 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. For example: 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 be divisible by 2, that is, they can be binary.

About integrals. 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 (time is generally in years or months, which should correspond to the unit of interest rate).

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. Such as 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. Example: 3x =(a+b

)*c

Induction of junior high school mathematics knowledge points.

Addition operation of rational numbers

Two numbers with the same sign are added, and the absolute value is added with the same sign.

Different symbols increase or decrease, large numbers determine and symbols.

Add up the opposites of each other, and the result is that zero must be remembered well.

Note that "big" minus "small" refers to the absolute value.

Subtraction operation of rational number

Negative is equal to plus negative, and reducing the burden is equal to plus positive.

Symbolic law of rational number multiplication operation

The sign of the same sign is negative and the product of a term is zero.

Combine similar terms

When it comes to merging similar projects, don't forget the rules.

Only the algebraic sum of the coefficients is found, and the letter index remains unchanged.

Rules for deleting and adding brackets

The key to deleting brackets or adding brackets depends on the connection number.

The expansion symbol is preceded by a plus sign, and the bracket invariant symbol is added.

Parentheses are preceded by a minus sign, and when you add parentheses, they change sign.

solve an equation

Known unknowns lead to separation, and separation must be completed by moving.

Shift addition, subtraction, addition, multiplication, division and multiplication.

formula for the difference of square

The sum of two numbers multiplied by the difference of two numbers is equal to the square of the difference of two numbers.

Product and difference are two terms, and complete square is not it.

Perfect square trinomial

The square of the sum or difference of two numbers has three expansions.

The first and last square, the first and last two in the middle.

The squares of sum are added and connected, and the squares of difference are subtracted and added.

Perfect square trinomial

The first square and the last square, the middle is twice that of the first and the last square.

The squares of sum are added and then added, and the squares of difference are subtracted and then added.

Solve a linear equation with one variable

Remove the denominator first and then the brackets, and remember the sign of the shifted item.

The coefficient "1" is not enough for the merger of similar items.

To obtain the unknown quantity, the value must be checked and replaced.

Solve a linear equation with one variable

Remove the denominator first, then remove the brackets, and merge the items of the same category.

The coefficient of 1 is not ready yet, and the calculation is not in vain.

Factorization and multiplication

The product of sum and difference is multiplication, and multiplication itself is operation.

Product sum and difference are decomposition, and factorization is not operation.

factoring

Don't be afraid of factorization just because the square signs of two formulas are different.

Multiply the sum of two cardinality by the difference of two cardinality, and the decomposition result is it.

The square sign of the two formulas is the same, and the product at the bottom is twice that at the center.

Whether factorization can be done, there is an article on the symbol.

The same difference is squared first and signed.

The sign of the same law is negative, and the difference needs to be added with a power sign.

factoring

One mention, two sets, three sets, cross multiplication is also counted.

None of the four methods works, so we have to split the items and add items to reorganize.

It is hopeless to try to find the root, exchange elements or calculate the remainder in recombination.

A variety of methods can be flexibly selected, and the result of continuous multiplication is the basis.

If the same type of multiplication occurs, this ability means remembering.

Pay attention to mention (common factor formula) two sets (formulas)

factoring

One mention, two episodes, three groups, and the roots of cross multiplication are also counted.

None of the five methods can work, so we have to split and add items to reorganize.

The right medicine, slow and steady, and the result of constant multiplication is the foundation.

Factorization of quadratic trinomial

Think completely flat first, then cross.

Neither method works, so try to find a root decomposition.

Ratio and proportion

The division of two numbers is also called ratio, and the equality of two ratios is also called ratio.

The outer product equals the inner product, and the equal product can be divided into eight proportions.

Internal and external items are exchanged separately, and both items should be called greater than.

The simultaneous exchange of internal and external terms is called inverse ratio.

The ratio before and after the term is constant, which is called the combined ratio.

The difference between the preceding item and the latter item is the ratio.

The sum of two items is not as good as two items, and the proportion is equal.

The sum of the preceding paragraph is equal to the sum of the following items, and the proportion remains unchanged.

Solution ratio

The outer product is equal to the inner product, and the equation is solved.

Find the ratio

There are many ways to find the ratio from the known data.

Flexible use of the nature of the proportion of seven, variable substitution is also very popular.

It's a good idea to destroy Yolanda, and all roads lead to the same goal.

Positive proportion and inverse proportion

The agreed variables are directly proportional and the product variables are inversely proportional.

Positive proportion and inverse proportion

The quotient of the change process is certain, and the two variables are proportional.

The product of the change process is constant, and the two variables are inversely proportional.

Judge that four numbers are proportional.

Whether the four numbers are proportional or not is sorted in ascending and descending order first.

The product of two ends is equal to the intermediate product, and four numbers must be proportional.

Judge that the four formulas are proportional.

Whether the four formulas are proportional or not, the birth or decline of power must be sorted first.

The two-terminal product is equal to the intermediate product, and the four formulas can be proportional.

mean proportional

Among the four proportional terms, the external term is the same.

Sometimes the internal items will be the same, and the intermediate items in the proportion are essential.

The word proportion is very important and will be encountered in many occasions.

Among the four scale projects, many external projects are the same.

Sometimes the internal items will be the same, and the items in the proportion will appear.

The same number, square, different products, there is nowhere to escape in proportion.

Radical and irrational

An algebraic expression represen a square root can be called a radical.

The radical form is different from the irrational form, and its opening mode is not limited.

Only when there are letters in the opened way can it be called unreasonable.

Unreasonable forms are radical forms, which are distinguished by signs.

There are letters on the way to be opened, which can also be called unreasonable.

Find domain name

Four principles should be paid attention to when seeking the domain.

Negative numbers cannot be squared, and zero denominator is meaningless.

Refers to the positive number at the bottom of the fraction, and the number zero has no zero power.

Constraints are not unique and satisfy multiple inequalities.

Four principles should be paid attention to when obtaining the domain through customs clearance.

Negative numbers cannot be squared, and zero denominator is meaningless.

There is a positive number at the bottom of the fractional index, and zero has no zero power.

Constraints are not unique, solve the inequality group.

Solving one-dimensional linear inequality

Remove the denominator first, then remove the brackets, and merge the items of the same category.

The coefficient of "1" is exquisite, and the multiplication and division of the same negative number must change direction.

Remove the denominator first, then the brackets, and don't forget to change the symbol when moving the item.

When similar items are merged, the coefficient is "1".

There is no obstacle to the same multiplication and division, and the same multiplication and division also changes sign.

Solving a system of linear inequalities with one variable

Larger than the head, smaller than the tail, different sizes.

There is no solution to the size, and all four situations are coming.

Take two sides in the same direction and take the middle in the opposite direction.

There is no element in the middle, no solution.

Kindergarten children are responsible, (just like the younger ones)

Nursing homes are proud of being old.

There is no distinction between old and young in the barracks. (Is it big or small)

All schemes, large and small, are empty. (No wow, big and small)