Summary of Mathematics Knowledge Points in Volume II of Grade One of Beijing Normal University Edition
First, multiplication with the same base.
(m, n is an integer) is the most basic rule in power operation. When applying regular operations, the following points should be noted:
A) The prerequisite for using this rule is that when the bases of powers are the same and multiplied, the base a can be a specific number, letter, monomial or polynomial;
B) When the index is 1, don't mistake it for no index;
C) 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;
Second, the power of power and the power of products.
Third, the division of power with the same base.
(1) The premise of applying the rule is that the cardinality is the same, and this rule can only be used if the cardinality is the same.
(2) Cardinality can be a specific number, or a monomial or polynomial.
(3) Exponential subtraction refers to subtracting the exponent of the divisor from the exponent of the divisor, and the difference is not negative.
Fourth, multiplication of algebraic expressions.
1, the concept of monomial: the algebraic expression composed of the product of numbers and letters is called monomial. A single number or letter is also a monomial. The numerical factor of a single item is called the coefficient of a single item, and the sum of all letter indexes is called the number of times of a single item.
For example, the coefficient of bca22- is 2-, the degree is 4, and the degree of a single nonzero number is 0.
2. Polynomial: The sum of several monomials is called polynomial. Each monomial in a polynomial is called a polynomial term, and the degree of the degree term is called the degree of the polynomial.
Five, the square difference formula
Expression: (a+b) (a-b) = a 2-b 2. The product of the sum of two numbers and the difference of two numbers is equal to the square of the difference of two numbers. This formula is called the square difference formula of multiplication.
Formula application
Can be used for some fractions whose denominator contains the root sign:
1/(3-4 root number 2) Simplification:
Six, the complete square formula
Common mistakes in the complete square formula are:
(1) missed a semester.
② Confusion formula
③ Symbol error in the operation result.
④ Variant application is difficult to master.
VII. Division of algebraic expressions
1, the division rule of monomial
In monomial division, the coefficient and the power of the same base number are separated as a factor of the quotient, and the letter only contained in the division formula, together with its exponent, is taken as a factor of the quotient.
Note: first determine the coefficient of the result (that is, coefficient division), and then divide it by the same base power. If only the letters in the division formula are included, it will be used as the factor of quotient together with its exponent.
Mathematics review materials in the second volume of the seventh grade
similar transformation
1, if two line segments AB are measured with the same length unit, and the length of CD is m and n respectively, then the ratio of these two line segments AB:CD=m:n can be said or written. ※ 。
2. Among the four line segments A, B, C and D, if the ratio of A to B is equal to that of C and D, these four line segments are called proportional line segments for short. ※ 。
※ 3. Precautions:
①a:b=k, which means that A is k times that of B;
(2) Because the lengths of line segments A and B are both positive numbers, k is a positive number;
③ The ratio has nothing to do with the length units of the selected line segments, and the length units of the two line segments should be consistent when solving;
④ Except a=b, a:b≠b:a is reciprocal;
Translation transformation
(1) The shape and size of the graph have not changed before and after translation, but the position has changed;
(2) After the graphic is translated, the line segments connected by the corresponding points are parallel and equal (or on the same straight line).
(3) Multiple translations are equivalent to one translation.
(4) The figure after multiple symmetry is equal to the figure after translation.
(5) Translation is determined by direction and distance.
(6) After translation, the corresponding line segments are parallel (or * * * lines) and equal, the corresponding angles are equal, and the line segments connected by the corresponding points are parallel and equal.
This kind of movement that moves all the points on the graph in a certain direction by the same distance is called the translation movement of the graph, which is called translation for short.
Seven-grade mathematics knowledge points
One-dimensional linear equation
One-dimensional linear equation: an integral equation with only one unknown number, the degree of which is 1, and a one-dimensional linear equation with non-zero coefficient.
The standard form of one-dimensional linear equation: ax+b=0(x is unknown, a and b are known numbers, a≠0).
The simplest form of a linear equation with one variable: ax=b(x is unknown, a and b are known numbers, a≠0).
The general steps of solving a linear equation with one variable: sorting out the equation ... removing the denominator ... dismantling the bracket ... changing the terms ... merging similar terms ... converting the coefficient into 1 ... (testing the solution of the equation).
Common formulas for solving application problems with column equations;
(1) Travel problem: distance = speed time;
(2) Engineering problems: workload = work efficiency and working time;
(3) ratio: part = total ratio;
(4) Downstream problem: Downstream velocity = still water velocity+water velocity, and countercurrent velocity = still water velocity-water velocity;
(5) Commodity price: selling price = pricing discount 0. 1, profit = selling price-cost;
(6) Perimeter, area and volume: C circle =2πR, S circle =πR2, C rectangle =2(a+b), S rectangle =ab, C square =4a, S square =a2, S ring =π(R2-r2), V cuboid =abc, V cube =a3, V cylinder.
Related articles on knowledge point induction in the second volume of junior one mathematics;
★ Summarize the knowledge points in the second volume of Mathematics in Grade One.
★ Summary of basic knowledge points in the second volume of junior high school mathematics
★ Summary of knowledge points in the second volume of junior high school mathematics
★ Summary of mathematics knowledge points in the next semester.
★ Summarize and sort out the knowledge points of Grade One mathematics.
★ Knowledge points in the second volume of Grade One Mathematics
★ Summary of Key Knowledge Points of Mathematics in Volume 2 of Grade 1.
★ Induction and learning methods of mathematics knowledge points in senior one.
★ 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 mathematics knowledge points in the second volume of senior one.