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)

Solve a quadratic inequality in one variable

Firstly, it is transformed into a general formula, which is the second station of the constructor.

If the discriminant value is not negative, the horizontal axis of the curve has an intersection point.

A is opening it. If it is greater than zero, take both sides.

If the algebraic expression is less than zero, the intersection of solution sets.

If the equation has no real root, then the solution of big zero in the mouth is all.

If it is less than zero, there is no solution, and the opening is just the opposite.

Factorization with square difference formula

There is a way to decompose two square terms with different symbols.

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

Factorization of complete square formula

Two square terms are at both ends, and the bottom product is twice that of the middle.

The sum of the same base and the square, the sum of the reciprocal of all negative numbers and the square.

Divided into two base difference squares, the square product should be negative.

Both sides are negative, the middle is positive, and the square of cardinal difference is inverse.

One side after another, the bottom product is twice that of the middle.

Three plus two cardinality and square, all negative and square negative.

Divided into two base difference squares, both ends are positive product negative.

If both sides are negative, the middle is positive, and the square of the base difference is opposite.

Solving quadratic equation with one variable by formula method

To solve an equation with a formula, we must first turn it into a general formula.

Then, adjust the coefficient to make it the simplest ratio.

Determine the parameter abc and calculate the discriminant of the equation.

If there are any real roots, the ratio of discriminant value to zero will be known.

There is a real root setting formula, but there is no real root to talk about.

Solving quadratic equation with one variable by conventional collocation method

First separate the left and right, and then binarize "1".

A series is folded in half and then squared, and the two sides add up.

Divide left and right, and solve the problem directly.

This solution is called a formula, so you should practice more when solving the equation.

Indirect collocation method for solving quadratic equation with one variable

The known unknowns are separated first, and then factorized.

The adjustment coefficient is reciprocal, and the sum-difference product sets the identity.

Complete square constant, indirect formula shows advantages.

Pay attention to identity

Solve a quadratic equation with one variable

The equation has no linear term, so it is ideal to find the root directly.

If there is no constant term, there is no room for discussion on factorization.

B and c are equal to zero, and the root is also zero. Don't forget.

B and c are not both zero, factorization or formula,

You can also set the formula directly and choose a good prescription according to the topic.

Discrimination of positive proportional function

To judge the proportional function, the test is divided into two steps.

One quantity means another quantity, right?

If you have to look at the values again, you need to be all real numbers.

Distinguishing the proportional function, the measurement can be divided into two steps.

One quantity means another quantity, right or wrong.

If there is, it depends on the value. All real numbers must be there.

Images and properties of proportional function

Line, passage and origin of proportional function graph.

K is positive one, three, negative two and four, and the changing trend is in the heart.

K is low on the left and high on the right, climbing in the same direction.

K is negative, the left is high and the right is low, and the mountain is one big and one small.

linear function

Linear function diagram straight line, passing point.

K is low on the left and high on the right, and the higher you climb, the higher you climb.

K is negative, higher left and lower right, and lower and lower.

K is called the slope b intercept, and the zero intercept becomes a positive function.

inverse proportion function

Inverse hyperbola, crossing point.

K is plus one, three, minus two, four, and the two axes are its asymptotes.

K is high on the left and low on the right, and one or three quadrants slide down the mountain.

K is negative, low left and high right, and the second and fourth quadrants are like climbing mountains.

quadratic function

When the quadratic equation changes from zero to y, a quadratic function appears.

All real numbers define the domain, and images are called parabolas.

A parabola has an axis of symmetry, and both sides are monotonous and opposite.

A determines the opening and size, and the intersection of spools is called the vertex.

Vertex is either high or low. Up and down are conspicuous.

If you want to draw a parabola, you can also translate the pursuit point.

Extract formulas and set vertices, and then select them in two ways.

After drawing the list, connect the lines and keep the translation rules in mind.

Add parentheses to the left and right, and add and subtract redundant numbers.

For y, you get a quadratic function.

The image is called parabola, which defines all the real numbers in the domain.

A set the opening and size, with the opening facing upward.

The absolute value is large and the opening is small, and the opening is negative.

Parabola has an axis of symmetry, and the increase and decrease characteristics can be seen in the figure.

The intersection of axes is called the vertex, and the ordinate of the vertex is the most valuable.

If you want to draw a parabola, trace the point and translate two roads.

Select the fixed vertex of the formula and draw all translation points.

After the list is drawn, connect the lines, and three points roughly define the whole picture.

If you want to translate, it is not difficult to draw a basic parabola first

The vertex moves to the new position, and the size of the opening follows the foundation.

Parabola of note cardinal number

Lines, rays and line segments

Linear rays are related to line segments and similar shapes.

The length of a straight line is uncertain and can extend to both sides indefinitely.

The ray has only one endpoint and extends in a straight line in the opposite direction.

The two ends of the line segment are fixed in length and extend in two directions to form a straight line.

The alignment of two points is * * *, and the formation of graphics is the most common.

corner

Starting from a point, two rays form a figure called an angle.

The opposite direction of the * * line is a right angle, and half of the right angle is called a right angle.

A right angle is twice as large as a fillet, and the one smaller than the right angle is called an acute angle.

The straight plane is an obtuse angle, and the flat plane is called the optimal angle.

The sum of two complementary angles and a right angle is the complementary angle of a right angle.

Starting from a point, two rays form a figure called an angle.

A right angle is opposite to a straight line, and half of the right angle is called a right angle.

A right angle is twice as large as a fillet, and the one smaller than the right angle is called an acute angle.

The obtuse angle is between straight and flat, and the flat is called the optimal angle.

Harmony is a right angle called complementarity, a complementary angle and a straight angle.

Prove equal product or proportional line segment

Equal product or proportional line segments can be proved in many ways.

The equal product of the certificate should be changed to equal ratio, and the characteristics should be seen according to the graph.

* * * Points intersect with * * * lines, and parallel sections prove the problem.

The three stereotypes are very similar. Try to prove the similarity.

The graphics are obviously not similar, and the equal line segment ratio replaces the certificate.

After the exchange, the conclusion can be established and the original proposition is proved.

It is really impossible to use the area, and the projection angle can be divided into lines.

As long as you learn to crawl, you can use your hands and brains.

Solve irrational number equation

Everything has two sides, and everything has two sides.

There is no trace of the root sign of the power, and the equation can be solved without burden.

Neither of them is relatively difficult, and it is easy to multiply twice.

Under special circumstances, it is inevitable to exchange elements and get the solution of root test.

Solve fractional equation

Subtract first and then multiply by the common denominator, and the whole equation will be transformed.

Special circumstances can be exchanged, and removing the denominator is the way out.

After the solution, measure the roots, add the original roots, and don't be ambiguous.

Solving application problems with column equations

Use column equation to solve application problems, and use column solution to check and answer.

There are two ways to find the unknown in the exam.

Draw an equation with a list and follow the rules when solving the equation.

The test is accurate and in line with the meaning of the question, and the answer is only known after asking the same question.

Add auxiliary line

Learning geometry is extensive and profound, and success or failure may be a thread.

Decentralization conditions should be concentrated, and auxiliary lines should often be added.

Don't be afraid and then change your mind.

Practice makes perfect, and insight depends on practice.

It is known that there is a middle line in the figure, and the double-length middle line connects the lines.

The rotating structure is conformal, and the angle of equal line segment can be replaced.

The midline can be obtained by connecting multiple midlines with the midpoint.

If the bisector of an angle is known, the two sides can be perpendicular.

It can also be folded along the line to present congruent graphics.

If you add a vertical line to the bisector, you can see an isosceles triangle.

The angular bisector and parallel lines change the angular position of the equal line segment.

The vertical line in the line segment is known, which connects two equal line segments.

The auxiliary line must be dotted, so it will be linked with the original picture.

Formula of distance between two points

Find the distance between two coaxial points and subtract it greatly.

Two points equidistant from the axis, the same is true for distance calculation.

For any two points on the plane, the horizontal and vertical standard deviations should be calculated first.

The difference square plus square, the distance formula should be kept in mind.

Determination of rectangle

Any quadrilateral, three right angles form a rectangle;

Diagonal lines are divided into equal parts, quadrilateral. It is a rectangle.

Known parallelogram, a right angle is called rectangle;

If two diagonal lines are equal, they are naturally rectangles.

Determination of diamond shape

Any quadrilateral, four sides are equal to form a diamond;

The diagonal of the quadrilateral, perpendicular bisector is a diamond.

It is known that a parallelogram with equal adjacent sides is called a rhombus;

If two diagonal lines are perpendicular, it is a diamond in logic.