Skills of 40 questions in adult examination mathematics 1. Scoring skills of multiple choice questions
Multiple choice one * * * accounts for 85 points. You must pay attention when you knock on the blackboard. Whether you can get 40 points depends on multiple-choice questions.
When the 1. option is a number, the maximum and minimum values are excluded, and the remaining two items are selected by feeling.
2. When encountering some decisive questions, if there is an absolute word in the option, such as "certain", the answer is generally wrong and excluded.
3. Don't always choose an option. It's not good to choose the same one. Generally, if you can't, it is recommended to choose C or D. ..
4. According to the comparison of the four options, the obviously wrong items are excluded, and the items with big differences are excluded.
In this way, you can generally get 9 questions, with 5 points for each question, which is 45 points. At least 7 questions can be answered correctly, with 35 points.
Second, fill in the blanks scoring skills
Fill in the blanks will be a little more difficult than multiple-choice questions. After all, multiple-choice questions will give several options, so just choose one. And the filler needs to fill in the answer. If the candidates who pass the zero-based mathematics exam must not be empty when doing the fill-in-the-blank questions, they should also write some answers. Fill-in-the-blank questions are difficult to get points, and it is not bad to get 1 for four small questions.
Third, problem-solving skills.
1. Don't leave a blank for solving the problem. Candidates who have no mathematical foundation must remember more mathematical formulas before the exam. When solving math problems, if they can't, write more math formulas. There are steps to solve problems in the exam, and a mathematical formula can get one or two points.
2. The scores of mathematics in the senior high school entrance examination are given according to the steps, so a good score for solving problems is the score of the first step. You just need to write the ellipsis "Solution: Known ……", which is the known condition given in the title. If you write this step, you can get at least 2 points.
3. Space geometry, a compulsory math problem, can't be figured out in the process of solving problems. You can write down the useless conditions directly, and then draw unexpected conclusions, or score.
Parabola of Important Answer Formula in Adult Mathematics (1)
y = ax^2 + bx + c (a≠0)
That is, y equals a times x plus the square of b times x plus C.
Placed in a plane rectangular coordinate system
When a> is 0, the opening is upward.
When a< is 0, the opening is downward.
(a=0 is a linear function of one variable)
C>0, the function image intersects with the positive direction of Y axis.
C<0, the function image intersects with the negative direction of Y axis.
When c = 0, the parabola passes through the origin.
When b = 0, the axis of symmetry of parabola is the Y axis.
(Of course, this function is linear when a=0 and b≠0).
There are also vertex formulas y = a (x+h) * 2+k, (h, k) = (-b/(2a), (4ac-b 2)/(4a)).
That is, y equals a times the square of (x+h)+K.
-h is x of vertex coordinates.
K is y of vertex coordinates.
Generally used to find the maximum, minimum and symmetry axis.
Parabolic standard equation: y 2 = 2px
It means that the focus of parabola is on the positive semi-axis of X, the focal coordinate is (p/2,0), and the directrix equation is x=-p/2.
Since the focus of parabola can be on any semi-axis, * * has the standard equation y 2 = 2px y 2 =-2px x 2 = 2py x 2 =-2py.
(2) circle
Sphere volume = (4/3) π (r 3)
Area = π (r 2)
Perimeter =2πr =πd
The standard equation of a circle (X-A) 2+(Y-B) 2 = R 2 Note: (A, B) is the center coordinate.
General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4f >; 0
(A) ellipse circumference calculation formula
Ellipse circumference formula: L=2πb+4(a-b)
Ellipse circumference's Theorem: The circumference of an ellipse is equal to the circumference (2πb) of an ellipse with the radius of the short semi-axis length plus four times the difference between the long semi-axis length (a) and the short semi-axis length (b) of an ellipse.
(2) Calculation formula of ellipse area
Elliptic area formula: S=πab
Ellipse area theorem: the area of an ellipse is equal to π times the product of the major semi-axis length (a) and the minor semi-axis length (b) of an ellipse.
Although there is no ellipse πT in the above formula of ellipse circumference sum area, these two formulas are all derived from ellipse πT .. Constant is the body, so it can be used.
Calculation formula of ellipsoid volume Long radius * Short radius * π * height of ellipse.
(3) trigonometric function
Sum and difference angle formula
sin(A+B)= Sina cosb+cosa sinb； sin(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)；
cot(A+B)=(cosa cotb- 1)/(cosB+cotA)； cot(A-B)=(cosa cotb+ 1)/(cosB-cotA)；
Double angle formula
tan2a=2tana/( 1-tan^2a)； cot2a=(cot^2a- 1)/2cota；
cos2a=cos^2a-sin^2a=2cos^2a- 1= 1-2sin^2a；
sin2A = 2 Sina cosa = 2/(tanA+cotA)；
In addition: sin α+sin (α+2π/n)+sin (α+2π * 2/n)+sin (α+2π * 3/n)+...+sin [α+2π * (n-1)/n] = 0;
Cos α+cos (α+2π/n)+cos (α+2π * 2/n)+cos (α+2π * 3/n)+...+cos [α+2π * (n-1)/n] = 0 and
sin^2(α)+sin^2(α-2π/3)+sin^2(α+2π/3)=3/2；
tanAtanBtan(A+B)+tanA+tan B- tan(A+B)= 0；
four times the angle formula
sin4a=-4*(cosa*sina*(2*sina^2- 1))
cos4a= 1+(-8*cosa^2+8*cosa^4)
tan4a=(4*tana-4*tana^3)/( 1-6*tana^2+tana^4)
Five-fold angle formula
sin5a= 16sina^5-20sina^3+5sina
cos5a= 16cosa^5-20cosa^3+5cosa
tan5a=tana*(5- 10*tana^2+tana^4)/( 1- 10*tana^2+5*tana^4)
Hexagonal formula
sin6a=2*(cosa*sina)*(2*sina+ 1)*(2*sina- 1)*(-3+4*sina^2))
cos6a=((- 1+2*cosa^2)*( 16*cosa^4- 16*cosa^2+ 1))
tan6a=(-6*tana+20*tana^3-6*tana^5)/(- 1+ 15*tana^2- 15*tana^4+tana^6)
Seven-angle formula
sin7a=-(sina*(56*sina^2- 1 12*sina^4-7+64*sina^6))
cos7a=(cosa*(56*cosa^2- 1 12*cosa^4+64*cosa^6-7))
tan7a=tana*(-7+35*tana^2-2 1*tana^4+tana^6)/(- 1+2 1*tana^2-35*tana^4+7*tana^6)
Octagonal formula
sin8a=-8*(cosa*sina*(2*sina^2- 1)*(-8*sina^2+8*sina^4+ 1))
cos8a= 1+( 160*cosa^4-256*cosa^6+ 128*cosa^8-32*cosa^2)
tan8a=-8*tana*(- 1+7*tana^2-7*tana^4+tana^6)/( 1-28*tana^2+70*tana^4-28*tana^6+tana^8)
Nine-angle formula
sin9a=(sina*(-3+4*sina^2)*(64*sina^6-96*sina^4+36*sina^2-3))
cos9a=(cosa*(-3+4*cosa^2)*(64*cosa^6-96*cosa^4+36*cosa^2-3))
tan9a=tana*(9-84*tana^2+ 126*tana^4-36*tana^6+tana^8)/( 1-36*tana^2+ 126*tana^4-84*tana^6+9*tana^8)
Ten-fold angle formula
sin 10a=2*(cosa*sina*(4*sina^2+2*sina- 1)*(4*sina^2-2*sina- 1)*(-20*sina^2+5+ 16*sina^4))
cos 10a=((- 1+2*cosa^2)*(256*cosa^8-5 12*cosa^6+304*cosa^4-48*cosa^2+ 1))
tan 10a=-2*tana*(5-60*tana^2+ 126*tana^4-60*tana^6+5*tana^8)/(- 1+45*tana^2-2 10*tana^4+2 10*tana^6-45*tana^8+tana^ 10)
General formula of trigonometric function
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)]
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))
cot(A/2)=√(( 1+cosA)/(( 1-cosA))cot(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)+cos(A-B)； -2 sinas inb = cos(A+B)-cos(A-B)；
sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2； cosA+cosB = 2cos((A+B)/2)sin((A-B)/2)；
tanA+tanB = sin(A+B)/cosa cosb； tanA-tanB = sin(A-B)/cosa cosb；
cotA+cotB = sin(A+B)/Sina sinb； -cotA+cotB = sin(A+B)/Sina sinb；
Reduced power formula
Sin? (A)=( 1-cos(2A))/2 = versin(2A)/2；
Because? (α)=( 1+cos(2A))/2 = covers(2A)/2；
Tan? (α)=( 1-cos(2A))/( 1+cos(2A))；
Sine theorem a/sinA=b/sinB=c/sinC=2R Note: where r represents the radius of the circumscribed circle of a triangle.
Cosine Theorem B 2 = A 2+C 2-2 ACCOSB Note: Angle B is the included angle between side A and side C.
(4) Inverse trigonometric function
Arcsine (-x)=- Arcsine
arccos(-x)=π-arccosx
Arctangent (-x)=- arctangent
arccot(-x)=π-arccotx
(5) sequence
General formula of arithmetic progression: an = a1+(n-1) d.
Sum of the top n items in arithmetic progression: sn = [n (a1+an)]/2 = na1+[n (n-1) d]/2.
Geometric series formula: an = a1* q (n-1);
Sum of the first n terms of geometric series: Sn = a1(1-q n)/(1-q) = (a1-a1q n)/(1-q).
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)=n^2
2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1)
1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+…+n^2=n(n+ 1)(2n+ 1)/6
1^3+2^3+3^3+4^3+5^3+6^3+…n^3=(n(n+ 1)/2)^2
1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3
(6) multiplication and factorization
factoring
a^2-b^2=(a+b)(a-b)
a^2 2ab+b^2=(a b)^2
a^3+b^3=(a+b)(a^2-ab+b^2)
a^3-b^3=(a-b)(a^2+ab+b^2)
a^3 3a^2b+3ab^2 b^3=(a b)^3
Multiplication formula
Reversing the left and right sides of the factorization formula above is the multiplication formula.
(7) Trigonometric inequality
-|a|≤a≤|a|
| a |≤b & lt； = & gt-b≤a≤b
| a |≤b & lt； = & gt-b≤a≤b
| a |-| b |≤| a+b |≤| a |+| b | | a |≤b & lt； = & gt-b≤a≤b
|a|-|b|≤|a-b|≤|a|+|b|
| z1|-| z2 |-| Zn |≤| z1+z2+...+Zn |≤| z1|+| z2 |+| zinc |
| z1|-| z2 |-| Zn |≤| z1-z2-...-Zn |≤| z1|+| z2 |+| zinc |
| z1|-| z2 |-| Zn |≤| z1z2 ... Zn |≤| z1| +| z2 |+| Zn |