The first volume of Grade Two Mathematics Chapter 1 Summary of Key Knowledge 1 1- 12
Chapter 11 congruent triangles
1. congruent triangles's property: congruent triangles's corresponding edges and angles are equal.
2. congruent triangles's judgment: three sides are equal (SSS), two sides are equal to their included angle (SAS), two angles are equal to their sandwiched edge (ASA), two angles are equal to the opposite side of an angle (AAS), and two right-angled triangles are equal to their hypotenuse and right-angled edge (HL).
3. The nature of the angle bisector: the angle bisector bisects this angle, and the distance from the point on the angle bisector to both sides of the angle is equal.
4. Inference of the bisector of the angle: The point where the distance from the inside of the angle to both sides of the angle is equal is called the bisector.
5. The basic method steps to prove the congruence of two triangles or to prove the equality of line segments or angles with it: ①. Determine the known conditions (including implied conditions, such as common * * * edge, common * * * angle, diagonal, bisector of angle, median line, height, isosceles triangle and other implied angular relations. ); 2. Review the triangle judgment and find out what else we need; ③.
Chapter 12 Axisymmetric
1. If a graph is folded along a straight line and the parts on both sides of the straight line can overlap each other, then the graph is called an axisymmetric graph; This straight line is called the axis of symmetry.
2. The symmetry axis of an axisymmetric figure is the perpendicular bisector of a line segment connected by any pair of corresponding points.
3. The distance from the point on the bisector of the angle is equal to both sides of the angle.
4. The distance between any point on the vertical line of the line segment and the two endpoints of the line segment is equal.
5. The point with equal distance from the two endpoints of a line segment is on the middle vertical line of this line segment.
6. The corresponding line segment and the corresponding angle on the axisymmetric figure are equal.
7. Draw an axisymmetric figure about a straight line: find the key points, draw the corresponding points of the key points, and connect the points in the original order.
8. The coordinates of the point (x, y) about the axis symmetry of X are (x, -y).
The coordinates of the point (x, y) that is symmetric about y are (-x, y).
The coordinates of the point (x, y) that is symmetrical about the origin are (-x, -y).
9. The nature of isosceles triangle: the two base angles of isosceles triangle are equal (equilateral and equiangular).
The bisector of the top angle, the height and the center line of an isosceles triangle coincide, which is referred to as "three lines in one".
10. Determination of isosceles triangle: equilateral and equilateral.
1 1. The three internal angles of an equilateral triangle are equal and equal to 60.
12. Determination of equilateral triangle: A triangle with three equal angles is an isosceles triangle.
An isosceles triangle with an angle of 60 is an equilateral triangle.
A triangle with two angles of 60 is an equilateral triangle.
13. In a right triangle, the right-angled side facing an angle of 30 is equal to half of the hypotenuse.
14. The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.
The first volume of Grade Two Mathematics Chapter 13- 14 Summary of Knowledge Points
Chapter 13 Real Numbers
Arithmetic square root: Generally speaking, if the square of a positive number X is equal to A, that is, x2=a, then this positive number X is called the arithmetic square root of A, and the arithmetic square root recorded as .0 is 0. By definition, A has an arithmetic square root only when a≥0. ※.
Square root: Generally speaking, if the square root of a number X is equal to A, that is, x2=a, then this number X is called the square root of A. ※ 。
A positive number has two square roots (one positive and one negative), which are opposite to each other. 0 has only one square root, which is itself. ※: Negative numbers have no square root.
The cube root of a positive number is a positive number. The cube root of 0 is 0. ※: The cube root of a negative number is a negative number.
The inverse of a is -a, the absolute value of a positive real number is itself, the absolute value of a negative number is its inverse, and the absolute value of 0 is 0.
Chapter 14 Linear Functions
1. General steps for drawing function images: 1. List (one function only needs two points at a time, other functions generally need more than five points, and the listed points are independent variables and their corresponding function values); 2. Draw points (in rectangular coordinate system, draw four points in the table with the value of independent variable as abscissa and the value of corresponding function as ordinate, generally a function only needs two points at a time); 3.
2. Write the resolution function according to the meaning of the question: the key is to find the equivalent relationship between the function and the independent variable, and list the equations, that is, the resolution function.
3. If the relationship between two variables X and Y can be expressed in the form of y=kx+b(k≠0), then Y is a linear function of X (X is the independent variable and Y is the dependent variable). In particular, when b=0, y is said to be a proportional function of x 。
4. General formula of proportional sequence function: y=kx(k≠0), which is like a straight line passing through the origin (0,0).
5. The image of the proportional sequence function y=kx(k≠0) is a straight line passing through the origin. When k >: 0, the straight line y=kx passes through the first and third quadrants, and y increases with the increase of X. When k < 0, the straight line y=kx passes through the second and fourth quadrants, and y decreases with the increase of X. In the linear function y=kx+b, when k >; 0, y increases with the increase of x; When k < 0, y decreases with the increase of x 。
6. Find the resolution function of two known coordinates (resolution function of undetermined coefficient method):
Bring two points into the general formula of the function and list the equations.
Find the undetermined coefficient
Bring the undetermined coefficient value into the general formula of the function and get the analytic function.
7. From the function image, we will find the solution of the linear equation of one variable (i.e. the abscissa value of the coordinate of the intersection point with the X axis), the solution set of the linear inequality of one variable and the solution of the linear equation of two variables (i.e. the coordinate value of the intersection point of two functions).
Summary of Mathematical Knowledge the Next Day Chapter 15
Chapter XV Multiplication, Division and Factorization of Algebraic Expressions
1. Multiplication of the same radix power
Same base powers's multiplication rule: (m, n are all positive numbers) is the most basic rule in power operation. Pay attention to the following points when applying regular operations. ※:
① The preconditions for using this rule are: when the bases of powers are the same and multiplied, the base a can be a specific numeric letter or a term or polynomial;
② When the index is 1, don't mistake it for no index;
③ Don't confuse multiplication with addition of algebraic expressions. Multiplication, as long as the base is the same, the indexes can be added; For addition, not only the radix is the same, but also the exponent needs to be added;
(4) When three or more bases are the same, the rule can be generalized as (where m, n and p are all positive numbers);
⑤ The formula can also be reversed: (M and n are positive integers)
2. Power and product power
1. power law: (m, n are both positive numbers) is derived from the power multiplication law, but the two cannot be confused. ※ 。
※2.。
3. When the base has a negative sign, it should be noted that when the base is a and (-a), it is not the same base, but it can be converted into the same base by power law. ※,
If (-a)3 is replaced by -a3.
4. The base sometimes has different forms, but it can be replaced with the same one. ※ 。
5. Pay attention to the difference between (ab)n and (a+b)n, and don't mistake (a+b) n = an+bn (both a and b are not zero). ※ 。
6. Power law of product: the power of product is equal to each factor of product multiplied by power respectively, that is, (n is a positive integer). ※ 。
7. Power and product power rules can be applied in reverse. ※ 。
3. Multiplication of algebraic expressions
(1). Multiplication rule of monomials: Multiply monomials by their coefficients and the same letters respectively. For a letter contained only in a monomial, together with its exponent, it will be a factor of the product. ※ 。
When applying the monomial multiplication rule, we should pay attention to the following points:
① The coefficient of product is equal to the coefficient product of each factor, so determine the sign first, and then calculate the absolute value. At this time, the common mistake is to confuse coefficient multiplication with exponential addition;
② Multiply the same letters, using the multiplication rule of the same base;
(3) The letters only contained in the monomial should be taken as the factors of the product together with their exponents;
④ The rule of monomial multiplication is also applicable to the multiplication of more than three monomials;
⑤ Single item multiplied by single item, the result is still single item.
(2) Multiplication of monomial and polynomial. ※
Polynomial multiplied by monomial is the distribution law of multiplication and addition, and when it is converted into monomial multiplied by monomial, it is polynomial multiplied by monomial, and then the products are added.
When multiplying a monomial with a polynomial, please pay attention to the following points:
① Multiply a monomial with a polynomial, and the product is a polynomial with the same number of terms as the polynomial;
(2) Pay attention to the sign of the product when operating, and each term of the polynomial contains the previous sign;
③ When mixing operations, pay attention to the operation sequence.
(3). Polynomials are multiplied by polynomials. ※
Multiply polynomials by multiplying each term in one polynomial by each term in another polynomial, and then add the products.
Polynomial multiplication should pay attention to the following points:
(1) Polynomials should be multiplied by polynomials to prevent missing items. The checking method is as follows: before merging similar terms, the number of terms of the product should be equal to the product of the original two polynomial terms;
② Attention should be paid to the similar items in the results of merging polynomial multiplication;
(3) Multiply two linear binomials whose linear coefficient is 1, quadratic coefficient is 1, and the letters are the same. The linear coefficient is equal to the sum of the constant terms in the two factors, and the constant term is the product of the constant terms in the two factors. For two linear binomials (mx+a) and (0) whose linear coefficients are not 1,
4. Variance formula
1.square difference formula: the product of the sum of two numbers and the difference between these two numbers is equal to their square difference.
Namely. ※ 。
(1644) Its structural features are:
① The left side of the formula is the multiplication of two binomials, in which the first term is the same and the second term is the opposite number;
The right side of the formula is the square difference of two terms, that is, the square difference of the same term and the square difference of the opposite term.
5. Complete square formula
1.Complete square formula: the square of the sum (or difference) of two numbers is equal to the sum of their squares, plus (or minus) twice their product.
That is;
Oral decision: the first side, the last side, the middle 2 times product;
2. Structural features:
① The left side of the formula is the complete square of binomial;
② There are three terms on the right side of formula * *, which is the sum of squares of two terms in binomial, plus or minus twice the product of these two terms.
3. When using the complete square formula, we should pay attention to the sign of the item on the right side of the formula to avoid such mistakes.
Rules of parenthesis: The rules of adding positive invariant symbols and negative variable symbols and removing parentheses are the same.
6. Division of the same radix power
1. same base powers's division rule: same base powers divides, the base number is unchanged, and the exponent is subtracted, that is, (a≠0, m, n is a positive number, m >；; n)。
2. Pay attention to the following points when applying. ※:
(1) The prerequisite for using the rule is "divisible by same base powers" and 0 is not divisible, so a≠0 is included in the rule.
② Any number that is not equal to 0, whose power of 0 is equal to 1, that is, if (-2.50= 1), then 00 is meaningless.
(3) The power of any number not equal to 0 is -p (p is a positive integer) which is equal to the reciprocal of the power of this number, that is, (a≠0, p is a positive integer), 0- 1, 0-3 is meaningless; When a>0, the value of a-p must be positive; When a<0, the value of a-p can be positive or negative, for example,
④ Pay attention to the operation sequence.
7. Division in algebraic expressions
1. Single division
Single division, which is divided by the coefficient and the same base, is the factor of quotient. For letters only included in the division formula, it is the factor of quotient together with its index;
2. Polynomial divided by monomial
When a polynomial is divided by a single term, each term of the polynomial is divided by the single term first, and then the obtained quotients are added. It is characterized by dividing a polynomial by a monomial and converting it into a monomial divided by a monomial, and the number of terms obtained is the same as that of the original polynomial. In addition, pay special attention to symbols.
8. Factorization
1. Converting a polynomial into the product of several algebraic expressions is called decomposing this polynomial. ※ 。
2. Factorization and algebraic expression multiplication are reciprocal. ※ 。
Differences and relations between factorization and algebraic expression multiplication;
(1) Algebraic expression multiplication is to multiply several algebraic expressions into polynomials;
(2) Factorization is to multiply a polynomial by several factors.
Extended reading: How to improve the math scores of junior two students 1? There is no necessary connection between cleverness and achievement. Many people with better grades than you must have lower IQ. Good academic performance is not simply determined by IQ, there are many factors, the degree of effort is on the one hand, and more importantly, the method! With the method of getting twice the result with half the effort, you don't have to stay up all night to engage in sea tactics.
Tell your family not to put too much pressure on you, or you will be overwhelmed. Of course, I know that every parent is looking forward to their children being admitted to Peking University Tsinghua, but not all children have that ability. Even if there is such potential, it has not been well tapped and finally buried.
3, parents nag them, don't be affected, follow your plan and your goals. This age depends on ability and strength to eat, not on high education and high diploma, which only shows that nerds are more serious.
4, combined with my experience, talk about ways to improve my grades. (1) First of all, you must have a clear plan, which you know clearly, and you don't have to write it down on paper. For example, what to review today, what you don't understand, how many words to recite, and how many sets of simulation papers to do. (2) I should be good at summing up. I don't think there are as many questions as I did before the middle school entrance examination. I just put the wrong questions and key questions in the papers I have done. After repeated research, you will know which one it is at the last glance. (3) It may be a bit difficult, but it is not impossible to be good at trying to figure out the questioner's ideas. After studying the real questions in recent years several times, you can see some key points. The key point is always the key point, and there is no harm in reviewing it several times. (4) Don't expect too much of yourself, and don't pin your hopes on anything beyond ordinary people. In that case, let's face it frankly.
Everyone's life can only be planned by himself, and others are irreplaceable, because others can never fully understand your thoughts and interests.