Junior high school must memorize 88 mathematical formulas to sort out the common formulas of factorization;
1, square difference formula: a2-b2=(a+b)(a-b).
2. Complete square formula: a2+2ab+b2=(a+b)2.
3. Cubic summation formula: a3+b3=(a+b)(a2-ab+b2).
4. Cubic difference formula: a3-b3=(a-b)(a2+ab+b2).
5. Complete cubic summation formula: a3+3a2b+3ab2+b3=(a+b)3.
6. Complete cubic difference formula: a3-3a2b+3ab2-b3=(a-b)3.
7. Three complete square formulas: a2+b2+c2+2ab+2bc+2ac=(a+b+c)2.
8. Cubic summation formula: a3+b3+c3-3abc = (a+b+c) (a2+b2+c2-ab-bc-ac).
Square root calculation formula:
The numbers in the radical sign can be changed into the same or the same ones can be added or subtracted, and the different ones can't be added or subtracted.
If the numbers in the root sign are the same, they can be added or subtracted; If the numbers in the root sign are different, you can't add or subtract; If you can simplify it to numbers with the same root sign, you can add and subtract.
Examples are as follows:
(1)2√2+3√2=5√2 (all the numbers in the root sign are 2 and can be added).
(2)2√3+3√2 (one of the radicals is 3 and the other is 2, which cannot be added)
(3)√5+√20=√5+2√5=3√5 (although the numbers in the radical symbols are different, they can be replaced by the same ones and added).
(4)3√2-2√2=√2
(5)√20-√5=2√5-√5=√5
Multiplication and division of root sign:
√ AB = √ A √ B (A ≥ 0B ≥ 0), such as √ 8 = √ 4 √ 2 = 2 √ 2.
√a/b=√a÷√b
Triangle inequality
|a+b|≤|a|+|b|
|a-b|≤|a|+|b|
| a |≤b & lt； = & gt-b≤a≤b
|a-b|≥|a|-|b|
-|a|≤a≤|a|
Area formula of common figures:
Area of rectangle = length× width S = ab
Area of a square = side length × side length S = a2
Area of triangle = base × height ÷2 S=ah÷2.
Area of parallelogram = base × height S=ah
Trapezoidal area = (upper bottom+lower bottom) × height ÷2 S=(a+b)h÷2.
Area of circle = π× radius× radius
Formulas that must be remembered in solving equations:
Multiplication and factorization
a2-b2=(a+b)(a-b)
a3+b3=(a+b)(a2-ab+b2)
a3-b3=(a-b)(a2+ab+b2)
Solution of quadratic equation in one variable;
-b+√(B2-4ac)/2a-b-b+√(B2-4ac)/2a
How to learn junior high school mathematics 1 Actively preview.
Preview is a general understanding of the relevant knowledge of the course to be studied, which is convenient for you to easily keep up with the teacher's teaching chapters in class.
Doing so not only makes passive lectures become active lectures, but also strengthens the effect of lectures and improves learning efficiency. Have a general understanding of the knowledge learned in the next lesson, such as texts, laws, formulas and so on.
Positive thinking
Most students just listen mechanically in the process of listening to the class and can't think on their own initiative. In this way, when facing the questions in the exam, they will have no way to start and don't know how to apply what they have learned to answer them.
3. Be good at summing up laws
Mathematics is a discipline that can grasp the law through thinking, simplify the complex and solve mathematical problems with rules to follow.