Addition and subtraction of algebraic expressions 1 Monomial: a formula that represents the product of numbers or letters. A single number or letter is also called a monomial.
2. Coefficient and frequency of single item: the numerical factor in single item is called the coefficient of single item; The sum of all the letter indices in the monomial is called the number of times of the monomial.
3. Polynomial: The sum of several monomials is called polynomial.
4. Number and degree of polynomials: the number of monomials contained in a polynomial is the number of polynomial terms, and each monomial is called a polynomial term; In polynomial, the degree of the term with the highest degree is called the degree of polynomial.
5. Algebraic expression: ① monomial ② polynomial.
6. Similar items: monomials with the same letters and the same letter index are similar items.
7. Rules for merging similar items: When the coefficients are added, the letter index remains unchanged.
8. Rules for deleting (adding) brackets: When deleting (adding) brackets, if there is a "+"sign before the brackets, all items in the brackets remain unchanged; If there is a "-"before the brackets, all items in the brackets should be changed.
9. Addition and subtraction of algebraic expressions:
Found: (underlined);
2 "+":(be sure to start the merger with a+sign);
Trinity: (merger).
10. Ascending and descending order of polynomials: arranging the terms of a polynomial according to the exponent of a letter from small to large (or from large to small) is called ascending order (or descending order) of this letter.
The linear function (1) is one of the functions, and its general form is y=kx+b(k, b is constant, k≠0), where x is the independent variable and y is the dependent variable. Especially when b=0, y=kx+b(k is constant, k≠0), and y is called the proportional function of x.
(B) the three elements of function
1. domain: let x and y be two variables, and the range of the variable x is d. If for each number x∈D, the variable y always has a certain value corresponding to it according to a certain law, it is said that y is a function of x, and it is denoted as y=f(x), x∈D, where x is called an independent variable and y is called a dependent variable.
2. In the classical definition of a function, the range of values changed due to the change of variables is called the range of values of the function, while in the modern definition of a function, it refers to the set of all images corresponding to all elements in the definition domain under a corresponding law. If f(x)=x, then the range of f(x) is the range of function f(x).
3. Correspondence rule: Generally speaking, in the function symbol y=f(x), "f" represents the correspondence rule, and the equation y=f(x) shows that for any value of x in the definition domain, the unique value of y in the value domain can be obtained under the action of the correspondence rule "f".
(3) Representation method of linear function
1. analytic method: the method of expressing a function with independent variable x is called analytic method.
2. List method: The method of tabulating a series of function values y corresponding to x values to express the function relationship is called list method.
3. Image method: the method of expressing functional relationship with image is called image method.
(4) Properties of linear functions
The change value of 1.y is in direct proportion to the change value of x, and the ratio is K. That is, y=kx+b(k≠0)(k is not equal to 0, and k and b are constants).
2. When x=0, b is the intersection point of the function on the Y axis, and the coordinate is (0, b). When y=0, the coordinate of the intersection of the function image on the X axis is (-b/k, 0).
3.k is the slope of the linear function y=kx+b, and k=tanθ (the angle θ is the included angle between the linear function image and the positive direction of the X axis, θ ≠ 90).
4. When b=0 (y=kx), the image of a linear function becomes a proportional function, which is a special linear function.
5. Function image properties: when k is the same and b is not equal, the images are parallel; When k is different and b is equal, the images intersect on the y axis; When k is negative reciprocal, two straight lines are perpendicular.
6. When translating: add top and bottom at the end, and add left and right in the middle.
Angle knowledge point 1. Angle: An angle is a geometric object composed of two rays with a common endpoint.
2. Angle measurement unit: degrees, minutes and seconds.
3. Vertex: An angle consists of two rays with a common endpoint, and the common endpoint of the two rays is the vertex of the angle.
4. Angle comparison:
The angle (1) can be regarded as a ray rotating around its endpoint.
(2) Flat angle and fillet: A ray rotates around its endpoint. When the starting edge and the ending edge are on a straight line, the angle formed is called a straight angle. When it coincides with the starting edge again, the angle formed is a fillet. A right angle is equal to 108 degree, a rounded corner is equal to 360 degree, and a right angle is equal to 90 degree.
(3) bisector: A ray drawn from the vertex of an angle divides this angle into two equal angles, and this ray is called the bisector of this angle.
5. Complementary angle and complementary angle:
(1) Complementary angle: If the sum of two angles is 90 degrees, then these two angles are called complementary angles, which is called "complementation" for short.
Property: The complementary angles of equal angles are equal.
(2) Complementary angle: If the sum of two angles is 180 degrees, these two angles are called "complementary angle" or "remainder" for short.
Property: The complementary angles of equal angles are equal.
Definition of one-dimensional linear equation (1):
One-dimensional linear equation refers to an equation with only one unknown number, the highest order of which is 1, and both sides are algebraic expressions, which is called one-dimensional linear equation. Finding the value of the unknown quantity in the equation is called the solution of the equation.
(2) the steps of solving a linear equation with one variable
(1) Denominator: Turn the coefficient into an integer.
(2) stent removal
③ Shift term: shift the sign of an item on one side of the equation to the other side.
④ Merge similar items.
⑤ The coefficient is 1.
Parallel lines 1. In the same plane, if two straight lines have no intersection point, then the two straight lines are parallel to each other, which is recorded as: a ∨ b.
2. Parallelism axiom: After passing a point outside a straight line, there is one and only one straight line parallel to this straight line.
3. If two straight lines are parallel to the third straight line, then the two straight lines are parallel to each other.
4. The method of judging that two straight lines are parallel:
(1) Two straight lines are cut by the third straight line. If congruent angles are equal, two straight lines are parallel. To put it simply: the same angle is equal and two straight lines are parallel.
(2) Two straight lines are cut by a third straight line. If the internal dislocation angles are equal, two straight lines are parallel. To put it simply: the internal dislocation angles are equal and the two straight lines are parallel.
(3) Two straight lines are cut by a third straight line. If they are complementary to each other, the two straight lines are parallel. To put it simply: the internal angles on the same side are complementary and the two straight lines are parallel.
5. Properties of parallel lines
(1) Two parallel lines are cut by a third straight line and have the same angle. To put it simply: two straight lines are parallel and have the same angle.
(2) Two parallel lines are cut by a third line, and the internal dislocation angles are equal. To put it simply: two straight lines are parallel and their internal angles are equal.
(3) The two parallel lines are cut by the third straight line and complement each other. Simply put, two straight lines are parallel and complementary.