Summary and induction of mathematical formulas and knowledge points in senior one.
Summary of mathematical formula knowledge in the first part of senior one.
formulas of trigonometric functions
1, sum of two angles 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)
2. Double angle formula
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
3. 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))
4. 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
Summary of Mathematics Formula Knowledge in Senior One Part II
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 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
Multiplication and factorization 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.
Summary of Mathematics Formula Knowledge in Senior One Part III
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
Reduced power formula
(sin^2)x= 1-cos2x/2
(cos^2)x=i=cos2x/2
General formula of trigonometric function
Let tan(a/2)=t
sina=2t/( 1+t^2)
cosa=( 1-t^2)/( 1+t^2)
tana=2t/( 1-t^2)
How to learn high school mathematics well?
1. Preview before class, listen during class, and review after class is the foundation.
Don't underestimate the content to be explained in this class before class, because it can not only help you quickly integrate into the teacher's classroom, keep up with the teacher's rhythm, but also deepen your understanding of what you have learned. The most important thing is to maintain efficient classroom efficiency. As long as you fully master it in class, you only need to ask the teacher or ask your classmates to answer what you don't understand after class. If you don't have a good grasp of classroom listening, even if you spend ten times time to make up for it after class, you may not be able to achieve the effect of listening carefully in class.
2. Grasping the classroom is the most basic condition.
There is also after-class review, which will make you more efficient. Through review, you can recall your preview and what the teacher said in class, consolidate it through practice, and then read it from time to time. Only in this way can you have a profound understanding of this knowledge and your own unique insights, and firmly grasp it.
3. Skillfully brush the questions, and the questions must be seen.
Brushing questions and mastering a large number of questions are important means to learn high school mathematics well, so we can combine the summary given by the teacher with our own feelings of doing the questions, practice more, skillfully brush the same questions assigned by the teacher, and consolidate the review regularly. Only in this way can we fully digest such problems. For example, in the sequence part, we can divide it into different types, such as grouping summation, parallel summation, flashback summation, dislocation subtraction, cumulative multiplication and so on. We just need to master each question type and correspond to it one by one. So we won't be embarrassed when we don't know how to do it.
4. Master the ingenious method of doing this problem.
Diligence is an indispensable part of our high school mathematics learning process, and we need to brush the questions constantly to pass our calculations. But sometimes in the face of complex calculations, we are very likely to make inevitable mistakes, which will not only affect our time to do the problem, but also lose some unnecessary scores. Therefore, mastering some excellent methods of doing problems can help us answer difficult questions more conveniently and quickly and get all the scores. For example, dislocation subtraction, which contains a large number of high-order addition, subtraction, general score, reduction and other calculations, is undoubtedly the most headache for both ordinary students and academic tyrants, but they just can't get their own satisfactory scores. However, if we remember the fast solution of dislocation subtraction, we can calculate the perfect and correct result within 30 seconds, and only by enriching the process can we get full marks. Similarly, in the substitution equation of conic curve, the method of hardware decoding theorem not only saves us a lot of time, but also brings us confidence in exams, brings us fun in learning high school mathematics, and makes us change from being afraid of math exams to loving math exams. Important subjects of important subjects.