Summary of junior high school mathematics knowledge points
1, definition of rhombus: A group of parallelograms with equal adjacent sides is called rhombus.
2. The properties of rhombus: (1) rectangle has all the properties of parallelogram;
(2) All four sides of the diamond are equal;
(3) The two diagonals of the diamond are perpendicular to each other, and each diagonal bisects a set of diagonals.
(4) The rhombus is an axisymmetric figure.
Tip: Using the properties of the diamond, it can be proved that the line segments are equal, the angles are equal, and their diagonals are perpendicular to each other, thus dividing the diamond into four congruent right triangles. This can be linked with Pythagorean theorem, and the relationship between diagonal and edge can be obtained, that is, the square of side length is equal to the sum of the squares of half diagonal.
3. Definition of factorization: transforming a polynomial into the product of several algebraic expressions is called factorization of this polynomial.
4. Factorization elements: ① The result must be algebraic expression ② The result must be product form ③ The result is the relationship between factorization of equation ④ and multiplication of algebraic expression: m(a+b+c).
5. Common factor: The common factor of each term of a polynomial is called the common factor of each term of this polynomial.
6. Determination method of common factor: ① When the coefficient is an integer, take the greatest common factor of each item. The product of the greatest common divisor of the same letter and the lowest power of the same letter is the common factor of this polynomial.
7. Common factor extraction: ① Determine the common factor. ② Determine the quotient formula ③ The common factor formula and the quotient formula are written in the form of product.
8. square root representation: the square root of non-negative number a is recorded as, read as positive and negative root number a, and a is the number of prescriptions.
9. The range of the number of square roots: the number of square roots a≥0.
10, square root property: ① A positive number has two square roots in opposite directions. ② The square root of 0 is itself 0. ③ Negative numbers have no square root and square root; The operation of finding the square root of a number is called square root.
1 1, the difference between square root and arithmetic square root: different definitions, different expressions, different numbers and different value ranges.
12, connection: there is a subordinate relationship between them; The existence conditions are the same; The arithmetic square root and the square root of 0 are both 0.
13, meaning of the formula with root sign: it represents the square root of a, the arithmetic square root of a, and the negative square root of a.
14, the method of finding the arithmetic square root of positive number a;
Types of complete squares: ① Whose square is the number A? ② So what is the square root of A? (3) Expressed by formula.
To find the arithmetic square root of a positive number, just ask for a positive number that is equal to A after being squared.
Induction of key knowledge of junior high school mathematics
1, the solution of a quadratic equation;
(1) matching method: (x A)? =b(b≥0) Note: The quadratic coefficient must be changed to 1.
(2) Formula method: aX? +bX+C=0(a≠0) Determine the values of A, B and C, and calculate B? -4ac≥0
If b? -4ac & gt； 0 has two unequal real roots, if b? -4ac=0 has two equal real roots. If b? -4ac & lt； 0 means no solution.
If b? -4ac≥0, then use the formula x =-b √ b? -4ac/2a Note: It must be in general form.
(3) Factor decomposition method
① common factor method: ma+mb=0→m(a+b)=0.
Square difference formula: a? -B? =0→(a+b)(a-b)=0
(2) using the formula method:
Complete square formula: a? 2ab+b？ =0→(a b)？ =0
③ Cross multiplication.
2. Definition of acute angle trigonometric function
The sine (sin), cosine (cos) and tangent (tan), cotangent (cot), secant (sec) and cotangent (csc) of acute angle A are all called acute trigonometric functions of angle A.
Sine: the opposite side is more inclined than the hypotenuse, that is, Sina = a/c;
Cosine (cos): the adjacent side is more inclined, that is, COSA = b/c;
Tangent (tan): the opposite side is greater than the adjacent side, that is, tana = a/b;
Cotangent (cot): adjacent edges compare edges, that is, COTA = b/a;
3, the relationship between products
sinα=tanα cosα
cosα=cotα sinα
tanα=sinα secα
cotα=cosα cscα
secα=tanα cscα
cscα=secα cotα
4. Reciprocal relationship
tanα cotα= 1
sinα cscα= 1
cosα secα= 1
5. Sum and difference formula of two angles
sin(A+B) = sinAcosB+cosAsinB
sin(A-B) = sinAcosB-cosAsinB
cos(A+B) = cosAcosB-sinAsinB
cos(A-B) = cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)
tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
cot(A+B)=(cotA cotB- 1)/(cot B+cotA)
cot(A-B)=(cotA cotB+ 1)/(cot b-cotA)