1, multiplication and factorization a2-B2 = (a+b) (a-b) a3+B3 = (a+b) (a2-ab+B2) a3-B3 = (a-b (a2+ab+B2))
2. Trigonometric inequality | A+B |≤| A |+B||||| A-B|≤| A |+B |||| A |≤ B < = >-B≤ A ≤ B.
|a-b|≥|a|-|b| -|a|≤a≤|a|
3. The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a.
4. Relationship between root and coefficient X1+x2 =-b/ax1* x2 = c/a Note: Vieta theorem.
discriminant
B2-4ac=0 Note: This equation has two equal real roots.
B2-4ac > 0 Note: The equation has two unequal real roots.
B2-4ac < 0 Note: This equation has no real root, but is a complex number of the yoke.
5. formulas of trigonometric functions
Two-angle sum formula
6、sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinBcosA
7、cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
8、tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
9、ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)
10, double angle formula
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
1 1、cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
12, half-angle formula
sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-cosA)/2)
13、cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)
14、tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
15、ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
Sum difference product
16、2 Sina cosb = sin(A+B)+sin(A-B)2 cosa sinb = sin(A+B)-sin(A-B)
17、2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = cos(A+B)-cos(A-B)
18、sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)
19 、+ tanB = sin(A+B)/cosAcosB tanA-tanB = sin(A-B)/cosAcosB
20、ctgA+ctgBsin(A+B)/Sina sin B-ctgA+ctgBsin(A+B)/Sina sinb
The sum of the first n terms of some series
2 1、 1+2+3+4+5+6+7+8+9+…+n = n(n+ 1)/2 1+3+5+7+9+ 1 1+ 13+ 15+…+(2n- 1)= N2
22、2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6
23、 13+23+33+43+53+63+…n3 = N2(n+ 1)2/4 1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3
24. Sine Theorem a/sinA=b/sinB=c/sinC=2R Note: where R represents the radius of the circumscribed circle of a triangle.
25. Cosine Theorem b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..
26. The standard equation of a circle (x-a)2+(y-b)2=r2 Note: (A, B) is the coordinate of the center of the circle.
27. General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0.
28. Parabolic standard equation y2 = 2 pxy 2 =-2 pxy 2 = 2 pxy 2 =-2py.
29, straight prism side area S=c*h oblique prism side area s = c' * h.
30. lateral area of a regular pyramid S= 1/2c*h' lateral area of a regular prism S= 1/2(c+c')h'
3 1, the side area of the frustum S = 1/2(c+c')l = pi(R+R)l The surface area of the ball S=4pi*r2.
32. Cylindrical lateral area S=c*h=2pi*h Cone lateral area S =1/2 * c * l = pi * r * l.
33. the arc length formula l=a*r a is the radian number of the central angle R > 0. Sector area formula S = 1/2 * L * R
34. Cone volume formula V= 1/3*S*H Cone volume formula V= 1/3*pi*r2h
35. The volume of oblique prism V=S'L Note: where s 'is the straight cross-sectional area and l is the side length.
36. Cylinder volume formula V=s*h Cylinder V=pi*r2h
Extended data
Partial basic 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.
References:
Baidu encyclopedia-junior high school formula