Knowledge points in the second volume of junior one mathematics
Multiplication and factorization of algebraic expressions.
First, multiplication and division of algebraic expressions.
Multiply the monomial with the monomial, respectively by their coefficients and the same letters. For letters contained only in the monomial, they are used as a factor of the product together with its index. bc2=(a？ b)？ (c5？ C2)=abc5+2=abc7 Note: The operation sequence is multiplication first, then multiplication and division, and finally addition and subtraction.
In monomial division, the coefficient and the same base are divided by the factor of quotient, and only the letter contained in the divided formula, together with its index, is used as the factor of quotient.
Multiplying a polynomial by a monomial is to multiply each term of the polynomial by a monomial, and then add the products, m(a+b+c)=ma+mb+mc Note: neither weight nor leakage, in order, pay attention to the constant term and the negative sign. The essence is the law of multiplication and distribution.
Polynomial divided by monomial, first divide each term of this polynomial by this monomial, and then add the obtained quotients.
Multiply each term of one polynomial by each term of another polynomial, and then multiply the product by (a+b)(m+n)=am+an+bm+bn.
Multiplication formula: square difference formula: the product of the sum of two numbers and the difference between these two numbers is equal to the square difference between these two numbers. (a+b)(a-b)=a2-b2。
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. (A B) 2 = A2 2AB+B2。
Factorization: turning a polynomial into the product of several algebraic expressions is also called decomposing this polynomial.
Factorization method:
1, common factor method Key: find the common divisor.
The common factor formula consists of three parts: ① coefficient (number)-the common divisor of each coefficient; 2 letters-the same letters contained in each item; (3) Index-the lowest number of the same letter; Step 1, finding the common factor; The second step is to extract the common factor and determine another factor. It should be noted that after extracting the common factor, the number of terms of another factor is the same as that of the original polynomial, which can be used to check whether there are any missing terms.
Note: ① After extracting common factors, each factor should be in the simplest form, that is, decomposed to the "bottom"; ② If the coefficient of the first term of the polynomial is negative, a "-"sign should be put forward to make the coefficient of the first term in brackets positive.
2. Formula method. 1A2-B2 = (a+b) (a-b) The square difference of two numbers is equal to the product of the sum of these two numbers and the difference of these two numbers. A and b can be numbers or the formula 2a2AB+B2 = (ab) 2. The sum of squares of two numbers plus or minus the product of these two numbers is equal to the sum of these two numbers [
③ the cubic difference formula of x3-y3 = (x-y) (x2+xy+y2)
The first day of the second book mathematical triangle knowledge points
I. Objectives and requirements
1. Know the triangle, know the meaning of the triangle, know the sides, internal angles and vertices of the triangle, and express the triangle in symbolic language.
2. Experience the practical activities of measuring the side length of a triangle and understand the unequal relationship among the three sides of the triangle.
3. Know how to judge whether three line segments can form a triangle, and use it to solve related problems.
4. The interior angle theorem of triangle can be deduced from the properties of parallel lines.
5. Some simple practical problems can be solved by applying the triangle interior angle sum theorem.
Second, the main points
Theorem of sum of interior angles of triangle;
In order to understand the concept of triangle, three bars can be expressed in symbolic language.
Third, difficulties.
The reasoning process of triangle interior angle sum theorem;
Identify all triangles without repetition or omission in specific graphics;
Judging whether three line segments can form a triangle by the unequal relationship of three sides of a triangle.
Fourth, the knowledge framework.
Verb (abbreviation of verb) summary of knowledge points and concepts
1. triangle: A figure composed of three line segments that are not on the same line and are connected end to end is called a triangle.
2. Classification of triangles
3. Trilateral relationship of triangle: the sum of any two sides of triangle is greater than the third side, and the difference between any two sides is less than the third side.
4. Height: Draw a vertical line from the vertex of the triangle to the line where the opposite side is located, and the line segment between the vertex and the vertical foot is called the height of the triangle.
5. midline: in a triangle, the line segment connecting the vertex and the midpoint of its opposite side is called the midline of the triangle.
6. Angular bisector: The bisector of the inner angle of a triangle intersects the opposite side of this angle, and the line segment between the intersection of the vertex and this angle is called the angular bisector of the triangle.
7. Significance and practice of high line, middle line and angle bisector.
8. Stability of triangle: The shape of triangle is fixed, and this property of triangle is called stability of triangle.
9. Theorem of the sum of interior angles of triangle: the sum of three interior angles of triangle is equal to 180.
It is inferred that the two acute angles of 1 right triangle are complementary;
Inference 2: One outer angle of a triangle is equal to the sum of two non-adjacent inner angles;
Inference 3: One outer angle of a triangle is larger than any inner angle that is not adjacent to it;
The sum of the inner angles of a triangle is half of the sum of the outer angles.
10. External angle of triangle: the included angle between one side of triangle and the extension line of the other side is called the external angle of triangle.
1 1. The Properties of the Exterior Angle of Triangle
(1) Vertex is the vertex of a triangle, one side is one side of the triangle, and the other side is the extension line of one side of the triangle;
(2) An outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it;
(3) The outer angle of a triangle is greater than any inner angle that is not adjacent to it;
(4) The sum of the external angles of the triangle is 360.
12. Polygon: On the plane, a figure composed of end-to-end line segments is called a polygon.
13. Interior angle of polygon: The angle formed by two adjacent sides of a polygon is called its interior angle.
14. Exterior angle of polygon: the angle formed by the extension line of one side of polygon and its adjacent side is called the exterior angle of polygon.
15. Diagonal line of polygon: the line segment connecting two non-adjacent vertices of polygon is called diagonal line of polygon.
16. Classification of polygons: it can be divided into convex polygons and concave polygons. Convex polygons can also be called plane polygons and concave polygons can also be called space polygons. Polygons can also be divided into regular polygons and non-regular polygons. Regular polygons have equal sides and equal internal angles.
17. Regular polygon: A polygon with equal angles and sides in a plane is called a regular polygon.
18. plane mosaic: covering a part of a plane with some non-overlapping polygons is called covering the plane with polygons.
Important knowledge points of seventh grade mathematics
real number
Knowledge point classification-real number
1. Classification by definition: 2. Classification by natural symbols:
Note: 0 is neither positive nor negative.
Knowledge point 2 Related concepts of real numbers
1. Inverse
Algebraic meaning of (1): There are only two numbers with different signs, and we say that one of them is opposite to the other. The antonym of 0 is 0.
(2) Geometric meaning: On both sides of the origin on the number axis, two points with the same distance from the origin represent two opposite numbers, or on the number axis, the points corresponding to two opposite numbers are symmetrical about the origin.
(3) The sum of two opposites is equal to 0.a and B are opposites a+b=0.
2. Absolute value |a|≥0.
3. The reciprocal (1)0 has no reciprocal. (2) Two numbers whose product is 1 are reciprocal. A and b are reciprocal.
4. Square root
(1) If the square of a number is equal to a, it is called the square root of a, a positive number has two square roots, and the two square roots are in opposite directions. 0 has a square root, and the square root itself is 0; Negative numbers have no square root. The square root of a(a≥0) is written as.
(2) The positive square root of a positive number is called the arithmetic square root of a, and the arithmetic square root of a(a≥0) is recorded as.
5. Cubic root
If x3=a, then x is called the cube root of a, and positive numbers have positive cube roots; Negative numbers have negative cubic roots; The cube root of zero is zero.
Knowledge point 3 Real number and axis
Definition of number axis: the straight line defining the origin, positive direction and unit length is called number axis, and the three elements of number axis are indispensable.
Comparison of real numbers of knowledge point four
1. For any two points on the number axis, the point on the right represents a larger number.
2. Positive numbers are all greater than 0, negative numbers are all less than 0, and two positive numbers, the greater the absolute value, the greater the positive number; Two negative numbers; The absolute value is large but small.
Related articles on knowledge points in the second volume of junior one mathematics:
★ Knowledge points in the second volume of Grade One Mathematics
★ Summary of basic knowledge points in the second volume of junior high school mathematics
★ Summarize the knowledge points in the second volume of Mathematics in Grade One.
★ Summary of knowledge points in the second volume of junior high school mathematics
★ People's Education Edition, Grade One Mathematics, Book Two, review and summarize knowledge points, and prepare for the senior high school entrance examination.
★ Summary of seventh grade mathematics knowledge points
★ Knowledge points of next semester in senior one mathematics.
★ Summary of mathematics knowledge points in the second volume of senior one.
★ Summary of mathematics knowledge points in the next semester.
★ Summary of knowledge points in junior high school mathematics textbooks