Mathematics formula that junior high school must recite, mathematics is a compulsory subject. With students' familiarity with mathematical formulas, formulas can help us calculate answers more conveniently. There are already many mathematical formulas to learn in junior high school. What are the mathematical formulas that junior high school must recite?
Mathematical formula that junior high school must recite 1 common formula of factorization
1, square difference formula: a05-b05=(a+b)(a-b).
2. Complete square formula: a05+2ab+b05=(a+b)05.
3. Cubic summation formula: a06+b06=(a+b)(a05-ab+b05).
4. Cubic difference formula: a06-b06=(a-b)(a05+ab+b05).
5. Complete cubic summation formula: A06+3A05B+3A05+B06 = (a+b) 06.
6. Complete cubic difference formula: A06-3A05B+3A05-B06 = (a-b) 06.
7. Three complete square formulas: A05+B05+C05+2ab+2bc+2ac = (a+b+c) 05.
8. Cubic summation formula: A06+B06+C06-3abc = (a+b+c) (A05+B05+C05-AB-BC-AC).
2 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
3 triangle inequality
|a+b|≤|a|+|b|
|a-b|≤|a|+|b|
| a |≤b & lt； = & gt-b≤a≤b
|a-b|≥|a|-|b|
-|a|≤a≤|a|
3. The solution of a quadratic equation
-b+√(b2-4ac)/2a -b-√(b2-4ac)/2a
Relationship between root and coefficient
x 1+X2 =-b/ax 1 * X2 = c/a
Note: Vieta theorem.
4. Discrimination
B2-4ac=0 Note: This equation has two equal real roots.
B2-4ac >0 Note: The equation has two unequal real roots.
B2-4ac & lt； Note: The equation has no real root, but a complex number of the yoke.
5. formulas of trigonometric functions
Two-angle sum formula
sin(A+B)= Sina cosb+cosAsinBsin(A-B)= Sina cosb-sinBcosA
cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)
Double angle formula
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
Graphic area formula
Side area of right-angle prism: S=c*h
Side area of oblique prism: S=c*h
Side area of a regular pyramid: s =1/2c * h.
Side area of prism: s =1/2 (c+c) h.
Area of frustum side: s =1/2 (c+c) l = pi (r+r) l.
Surface area of the ball: S=4pi*r2.
Area of cylinder side: s = c * h = 2pi * h
The lateral area of the cone: s =1/2 * c * l = pi * r * l.
Arc length formula: l=a*r.a is the radian number r >； of the central angle; 0
Sector area formula: s =1/2 * l * r.
Cone volume formula: V= 1/3*S*H
Cone volume formula: V= 1/3*pi*r2h.
Oblique prism volume: V=SL Note: where, s is the straight section area and l is the side length.
Cylinder volume formula: V = s * h；; Cylinder V=pi*r2h
Mathematical formula that junior high school must recite 3 junior high school mathematics must recite formula
1 There is only one straight line at two points.
The line segment between two points is the shortest.
The complementary angles of the same angle or equal angle are equal.
The complementary angles of the same angle or the same angle are equal.
One and only one straight line is perpendicular to the known straight line.
Of all the line segments connecting a point outside the straight line with points on the straight line, the vertical line segment is the shortest.
7 Parallel axiom passes through a point outside a straight line, and there is only one straight line parallel to this straight line.
If both lines are parallel to the third line, the two lines are also parallel to each other.
The same angle is equal and two straight lines are parallel.
The internal dislocation angles of 10 are equal, and the two straight lines are parallel.
1 1 are complementary and two straight lines are parallel.
12 Two straight lines are parallel and have the same angle.
13 two straight lines are parallel, and the internal dislocation angles are equal.
14 Two straight lines are parallel and complementary.
Theorem 15 The sum of two sides of a triangle is greater than the third side.
16 infers that the difference between two sides of a triangle is smaller than the third side.
The sum of the internal angles of 17 triangle is equal to 180.
18 infers that the two acute angles of 1 right triangle are complementary.
19 Inference 2 An outer angle of a triangle is equal to the sum of two non-adjacent inner angles.
Inference 3 The outer angle of a triangle is greater than any inner angle that is not adjacent to it.
2 1 congruent triangles has equal sides and angles.
Axiom of Angular (SAS) has two triangles with equal angles.
The corner axiom (ASA) has two corners corresponding to their sides, and two triangles are congruent.
The inference (AAS) has two angles, and the opposite side of one angle corresponds to the congruence of two triangles.
The axiom of 25 sides (SSS) has two triangles with equal sides.
Axiom of hypotenuse and right angle (HL) Two right angle triangles with hypotenuse and right angle are congruent.
Theorem 1 The distance between a point on the bisector of an angle and both sides of the angle is equal.
Theorem 2 is a point with equal distance on both sides of an angle, which is on the bisector of this angle.
The bisector of an angle 29 is the set of all points with equal distance to both sides of the angle.
The nature theorem of isosceles triangle 30 The two base angles of isosceles triangle are equal (that is, equilateral and equiangular).