High school key mathematical formula Daquan multiplication and factorial A2-B2 = (A+B) (A-B) A3+B3 = (A+B) (A2-AB+B2) A3-B3 = (A-B (A2+AB+B2))
Trigonometric inequality | A+B |≤| A |+B||||| A-B|≤| A |+B || A |≤ B < = > -b≤a≤b
|a-b|≥|a|-|b| -|a|≤a≤|a|
The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a
The 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 & lt； Note: The equation has no real root, but a complex number of the yoke.
formulas of trigonometric functions
Two-angle sum formula
sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinb cosa
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
half-angle formula
sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-cosA)/2)
cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
Sum difference product
2 Sina cosb = sin(A+B)+sin(A-B)2 cosa sinb = sin(A+B)-sin(A-B)
2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = cos(A+B)-cos(A-B)
sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)
tanA+tanB = sin(A+B)/cosa cosb tanA-tanB = sin(A-B)/cosa cosb
ctgA+ctgBsin(A+B)/Sina sinb-ctgA+ctgBsin(A+B)/Sina sinb
The sum of the first n terms of some series
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
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
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
Sine theorem a/sinA=b/sinB=c/sinC=2R Note: where r represents the radius of the circumscribed circle of a triangle.
Cosine Theorem b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..
The standard equation of a circle (x-a)2+(y-b)2=r2 Note: (A, B) is the center coordinate.
General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0
Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py
Lateral area of a straight prism S=c*h lateral area of an oblique prism s = c' * h.
Lateral area of a regular pyramid S= 1/2c*h' lateral area of a regular prism S= 1/2(c+c')h'
The lateral area of the frustum of a cone S = 1/2(c+c')l = pi(R+R)l The surface area of the ball S=4pi*r2.
Lateral area of cylinder S=c*h=2pi*h lateral area of cone s =1/2 * c * l = pi * r * l.
The 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
Conical volume formula V= 1/3*S*H Conical volume formula V= 1/3*pi*r2h
Oblique prism volume V=S'L Note: where s' is the straight cross-sectional area and l is the side length.
Cylinder volume formula V=s*h cylinder V=pi*r2h
Summary formula of high school liberal arts mathematics formula 1:
Let α be an arbitrary angle, and the values of the same trigonometric function with the same angle of the terminal edge are equal:
sin(2kπ+α)=sinα (k∈Z)
cos(2kπ+α)=cosα (k∈Z)
tan(2kπ+α)=tanα (k∈Z)
cot(2kπ+α)=cotα (k∈Z)
Equation 2:
Let α be an arbitrary angle, and the relationship between the trigonometric function value of π+α and the trigonometric function value of α;
Sine (π+α) =-Sine α
cos(π+α)=-cosα
tan(π+α)=tanα
cot(π+α)=cotα
Formula 3:
The relationship between arbitrary angle α and the value of-α trigonometric function;
Sine (-α) =-Sine α
cos(-α)=cosα
tan(-α)=-tanα
Kurt (-α) =-Kurt α
Equation 4:
The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3:
Sine (π-α) = Sine α
cos(π-α)=-cosα
tan(π-α)=-tanα
cot(π-α)=-coα
Formula 5:
The relationship between 2π-α and the trigonometric function value of α can be obtained by formula 1 and formula 3:
Sine (2π-α)=- Sine α
cos(2π-α)=cosα
tan(2π-α)=-tanα
Kurt (2π-α)=- Kurt α
Equation 6:
The relationship between π/2 α and 3 π/2 α and the trigonometric function value of α;
sin(π/2+α)=cosα
cos(π/2+α)=-sinα
tan(π/2+α)=-cotα
cot(π/2+α)=-tanα
sin(π/2-α)=cosα
cos(π/2-α)=sinα
tan(π/2-α)=cotα
cot(π/2-α)=tanα
sin(3π/2+α)=-cosα
cos(3π/2+α)=sinα
tan(3π/2+α)=-cotα
cot(3π/2+α)=-tanα
sin(3π/2-α)=-cosα
cos(3π/2-α)=-sinα
tan(3π/2-α)=cotα
cot(3π/2-α)=tanα
(higher than k∈Z)
Formula 7: Sum and difference formula of two angles
Formulas of trigonometric functions of sum and difference of two angles.
sin(α+β)=sinαcosβ+cosαsinβ
sin(α-β)=sinαcosβ-cosαsinβ
cos(α+β)=cosαcosβ-sinαsinβ
cos(α-β)=cosαcosβ+sinαsinβ
tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)
tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)
Formula 8: Double angle formula
Sine, Cosine and Tangent Formulas of Double Angles (Ascending Power and Shrinking Angle Formula)
sin2α=2sinαcosα
cos2α=cos^2(α)-sin^2(α)=2cos^2(α)- 1= 1-2sin^2(α)
tan2α=2tanα/[ 1-tan^2(α)]
Formula 9: Half-angle formula
Sine, cosine and tangent formulas of half angle (power decreasing and angle expanding formulas)
sin^2(α/2)=( 1-cosα)/2
cos^2(α/2)=( 1+cosα)/2
tan^2(α/2)=( 1-cosα)/( 1+cosα)
And tan (α/2) = (1-cos α)/sin α = sin α/(1+cos α).
Formula 10: General formula
sinα=2tan(α/2)/[ 1+tan^2(α/2)]
cosα=[ 1-tan^2(α/2)]/[ 1+tan^2(α/2)]
tanα=2tan(α/2)/[ 1-tan^2(α/2)]
Formula 1 1: Triple angle formula
Sine, cosine and tangent formulas of triple angle
sin3α=3sinα-4sin^3(α)
cos3α=4cos^3(α)-3cosα
tan3α=[3tanα-tan^3(α)]/[ 1-3tan^2(α)]
tan3α=(3tanα-tan^3(α))/( 1-3tan^2(α))
What methods are there to improve senior high school math scores? 1. Activity preview.
Preview is the process of actively acquiring new knowledge, which helps to mobilize the initiative of learning. Before explaining new knowledge, it is an important means to read the teaching materials carefully and develop the habit of previewing actively.
Therefore, we should pay attention to cultivating self-study ability and learning to read. For example, if you teach yourself an example, you should find out what the example is about, what the conditions are, what you want, how to answer it in the book, why you answer it like this, whether there is a new solution and what the steps are.
Grasp these important problems, think with your head, go deep step by step, and learn to use existing knowledge to explore new knowledge independently.
Positive thinking
Many students just listen and can't think actively in the process of listening, so when they encounter practical problems, they don't know how to apply what they have learned to answer them.
The main reason is that you didn't consider the trouble caused in class. In addition to following the teacher's thinking, we should also think more about why we define it like this, and what are the benefits of solving problems like this. Taking the initiative to think can not only make us listen more carefully, but also stimulate our interest in some knowledge and help us learn more.
Rely on the teacher's guidance to think about the way to solve the problem; The answer is really not important; What matters is the method!
3. Be good at summing up laws
Generally speaking, there are rules to follow in solving mathematical problems. When solving problems, we should pay attention to summing up the law of solving problems. After solving each exercise, we should pay attention to reviewing the following questions:
What is the most important feature of this problem?
② What basic knowledge and graphics are used to solve this problem?
How do you observe, associate and transform this problem to achieve transformation?
④ What mathematical ideas and methods are used to solve this problem?
⑤ Where is the most critical step to solve this problem?
Have you ever done a topic like this? What are the similarities and differences between solutions and ideas?
⑦ How many solutions can you find to this problem? Which is the best? What kind of solution is a special skill? Can you sum up under what circumstances?
Put this series of questions through all aspects of problem solving, gradually improve and persevere, so that children's psychological stability and adaptability to problem solving can be continuously improved, and their thinking ability will be exercised and developed.
4. Broaden the thinking of solving problems
Math problem solving should not be limited to this topic, but should be generalized, think more and think more. After solving a problem, think about whether there are other simpler methods that can help you broaden your mind and have more choices in the process of doing the problem in the future.
There must be a book wrong.
Speaking of wrong books, many students feel that they have a good memory and can remember them without wrong books. This is an "illusion", and everyone has this feeling. When the problems increase and the learning content deepens, you will find yourself at a loss.
Wrong questions can record your own knowledge shortcomings at any time, which is helpful to strengthen the knowledge system and improve learning efficiency. Many schoolmasters got high marks because they used the wrong textbooks on their own initiative.