scr888 ios:scr888,ios,锘,Part,One,New,Curr:锘?p>Part One: New Curriculum Standards High School Mathematics Compulsory 1-5 Formulas Daquan Mathematics Compulsory 1-5 Common Formulas and Conclusions Compulsory 1: First, Set 1, Meaning and Representation: (1) Collection Characteristics

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锘?p>Part One: New Curriculum Standards High School Mathematics Compulsory 1-5 Formulas Daquan Mathematics Compulsory 1-5 Common Formulas and Conclusions Compulsory 1: First, Set 1, Meaning and Representation: (1) Collection Characteristics of the elements: determinism, dissimilarity, disorder (2) classification of sets; finite set, infinite set (3) representation of sets: enumeration method, description method, graphic method 2, relationship between sets: Subset: For any xA, there is xB, then A is called a subset of B.

Record as AB true subset: If A is a subset of B, and at least one element in B does not belong to A, then A is a true subset of B, which is denoted as AB set equal: if: AB, BA, then AB3. Relationship between elements and collections: belonging to not belonging to: empty set: 4, operation of set: union: a set consisting of elements belonging to set A or belonging to set B is called union, and is recorded as AB intersection: by set A and The set of common elements in set B is called intersection, and is recorded as AB complement: in the complete set U, the set consisting of all elements that do not belong to set A is called complement, and is recorded as CUA5. The number of subsets of the set {a1, a2, and an} is 2n; the true subset has 2n鈥?; the non-empty subset has 2n鈥?; 6. The common number set: natural number set: N positive integer set: N Integer set: Z rational number set: Q real number set: R 2. Parity of function 1. Definition: odd function = f(鈥搙)=鈥揻(x), even function = f(鈥搙)=f(x) (Note the definition field) 2. Properties: (1) The image of the odd function is symmetric with respect to the origin; (2) The image of the even function is axisymmetric with respect to the y axis; (3) If the image of a function is about The origin is symmetrical, then this function is an odd function; (4) if the image of a function is symmetric about the y-axis, then this function is an even function. Second, the monotonicity of the function 1. Definition: For the function f(x) whose domain is D, if any x1, x2鈭圖, and x1x21f(x1)f(x2)=f(x1)鈥揻(x2) 0 = f (x) is the increasing function 2f (x1) f (x2) = f (x1) - f (x2) 0 = f (x) is the reduction function 2, the monotonicity of the composite function: the same increase and decrease three, The property of the quadratic function y=ax2+bx+c(a0)*b4acb21, the vertex coordinate formula: 2a, 4a2. The three forms of the analytical expression of the quadratic function 24acb2b, the axis of symmetry: x2a, the maximum (small) value: 4a2 (1) General formula f(x)axbxc(a0); (2) vertex f(x)a(xh)k(a0); (3) two equations f(x)a(xx1)(xx2)(a0 IV. Index and exponential function 1. The algorithm of power: (1) aman=am+n, (2) aaanmnmn, (3) (am)n=amn(4)(ab)n=anbnnnan1ann0m(5) n(6)a=1(a鈮?)(7)an(8)aa(9)ambab1an2, the nature of the root formula (1)a.(2) when na; when n|a|1na,,a04, index The properties of the function y=ax(a0 and a鈮?): (1) Definition domain: R; Value range: (0, +鈭? (2) Image over fixed point (0, 1) 5. Exponential and logarithmic Mutualization: logaNbabN(a0, a1, N0). Five, logarithm and logarithmic function 1 logarithm algorithm: logN(1)ab=N=b=logaN(2)loga1 =0(3)logaa=1(4)logaab=b(5)aa=N(6)loga(MN)=logaM+logaN(7)loga(M)=logaM--logaNNlogbNlogba(8)logaNb=blogaN( 9) Alternate formula: logaN=n(10) inference logamb(11)logaN=nlogab(a0, and a1,m,n0, and m1,n1,N0).m1(12) common logarithm: lgN=log10N( 13) Natural logarithm: lnA = logeAlogNa (where e =) 2, logarithmic function y = logax (a0 and a 鈮?1) properties: (1) domain: (0, + 鈭?; value range: R ( 2) Image over fixed point (1,0) VI, power function y=xa: (1) according to a, for example: y=xy2xxy121x1x 7. Image translation: if the image of function yf(x) is shifted to the right a, move up b units, get the image of the function yf(xa)b; regularity: left plus right minus, upper plus minus eight. average growth rate problem 2 if the original production value is N, the average growth rate For p, then for the total output value y of time x, there is yN1(p). Nine, the zero point of the function: 1. Definition: For yf(x), let the X of f(x)0 be the zero of yf(x) .

is the abscissa of the intersection point when the image of yf(x) intersects the X axis. 2. Function zero existence theorem: If the image of the function yf(x) in the interval a, b is a continuous curve with f(a)f(b)0, then yf(x) is in the interval a There is a zero point in b, that is, there are ca, b, so that f(c)0, this C is the zero point.

3. Steps for finding the zero point of the function by the dichotomy: (given the accuracy) xab2(3) calculates f(x1)1 If f(x1)0, then x1 is the zero point; 2 if f(a)f(x1 0, then zero (1) determines the interval a, b, verifies f(a)f(b)0; (2) finds the midpoint x1x0a of a, b, and x13 if f(x1)f(b)0, then Zero point x0x1, b; (4) to determine whether the accuracy is reached, if ab, the zero point is a or b or a, b any value. Otherwise repeat (2) to (4) compulsory 2: one, straight line and circle 1, the formula of the slope: k = tan 伪 = y2y1 (伪 鈮?90 掳, x1 鈮?x 2) x 2 x 12, the equation of the line (1) oblique cut y=kx+b,k exists; (2) point oblique y鈥搚0=k(x鈥搙0), k exists; (3) two-point yy1xx1xy(x1x2, y1y2); 4) intercept formula 1 (a0) , b0) y2y1x2x1ab (5) general formula AxByc0 (A, B is not 0 at the same time) 4, distance between two points formula: set P1 (x1, y1), P2 (x2, y2), then | P1P2 | = 5, point P(x0, y0) to the straight line l: Ax+By+C=0 distance: dx1x22y1y2222Ax0By0CAB3222 The positional relationship between the point P(x0, y0) and the circle (xa)(yb)r is three. If d, the dr point P is in the circle. Outside; dr point P is on the circle; dr point P is inside the circle. 9. Positional relationship between the line and the circle (the distance from the center of the circle to the line is d) There are three kinds of positional relationships between the line AxByC0 and the circle (xa)(yb)r: 222dr is separated from 0; dr is tangent to 0; the method of judging the positional relationship between two intersecting circles of dr is set to be O1, O2, the radius is r1, r2, O1O2ddr1r2 are separated from 4 common tangent lines; dr1r2 is externally cut 3 Tangent; r1r2dr1r2 intersects 2 common tangent; dr1r2 cuts 1 common tangent; 0dr1r2 contains no common tangent. 11. Circle tangent equation (1) known circle xyDxEyF0. 1 If the tangent point (x0, y0) is known to be on a circle, then there is only one tangent. The equation is 22D(x0x)E(y0y)(x0x)E(y0y) When (x0,y0) is outside the circle, x0xy0yF0 is expressed. The tangent point equation of the two tangent points 22x0xy0y. 2 The tangent equation of the outer circle can be set to yy0k(xx0), and then the tangent condition is used to find k. At this time, there must be two tangent lines. Be careful not to miss the tangent parallel to the y-axis. 3 The tangent equation with the slope k can be set to ykxb, and then the tangent condition is used to find b. There must be two tangent lines. (2) Known circle xyr. 1 The tangent equation of P0(x0, y0) on the circle is x0xy0yr; 2 The tangent equation of the circle with slope k is ykx 2. Stereo geometry (1), line parallel determination theorem: 1. Parallel to the same line The two lines are parallel to each other. 2. The two lines perpendicular to the same plane are parallel. 3. If a line is parallel to a plane, and the plane passing through the line intersects the plane, then the line is parallel to the line of intersection.

4. If two parallel planes intersect at the same time with the third plane, their intersections are parallel.

(2), line parallel determination theorem 1. If a line outside the plane is parallel to a line in this plane, the line is parallel to this plane.

2. If two planes are parallel, any one of the straight lines in one plane is parallel to the other plane.

(3), face parallel determination theorem: If two intersecting lines in one plane are parallel to the other plane, then the two planes are parallel.

(d), line vertical determination theorem: If the line is perpendicular to a plane, then this line is perpendicular to all lines in this plane.

(5), line plane vertical determination theorem 1. If a line and two intersecting lines in a plane are perpendicular, then this line is perpendicular to this plane.

2. If the two planes are perpendicular to each other, the line perpendicular to their intersection in one plane is perpendicular to the other plane.

(6), face vertical determination theorem If a plane passes through a perpendicular line of another plane, then the two planes are perpendicular to each other.

42222 (seven). The way of thinking that proves the parallel line and the straight line is (1) is transformed into the judgment that the coplanar two straight lines have no intersection; (2) the conversion to the two straight lines is parallel to the third straight line; (3) the conversion to the line parallel; (4) the transformation For the line perpendicular; (5) converted to face parallel. (eight). The way of thinking that proves the parallel line and the plane is (1) is transformed into a straight line and the plane has no common points; (2) is converted into parallel lines; (3) is converted into parallel planes. (9). The way to think that the plane parallel to the plane is (1) is transformed into the judgment that the two planes have no common points; (2) the line is parallelized; (3) the line is vertical. (10). Prove that the vertical thinking path of straight line and straight line is transformed into intersecting vertical; (2) transformed into line perpendicular; (3) using three perpendicular theorem or inverse theorem; (11). The way to think that the line is perpendicular to the plane is (1) transformed into the line perpendicular to any line in the plane; (2) transformed into a line perpendicular to the plane intersecting the line; (3) transformed into a line perpendicular to the plane The line is parallel; (4) is converted to the line perpendicular to the other parallel plane; (12). Prove that the plane and the plane's vertical way of thinking (1) are transformed into judging that the dihedral angle is a straight dihedral angle; (2), the spatial geometry (1), the nature of the regular triangular pyramid, the bottom surface is an equilateral triangle, and if the bottom surface is an equilateral triangle If the side length is a, then the bottom surface ABC is O, then O is the center of 鈻矨BC, PO is the height of the pyramid, and the midpoint D of AB is taken. When PD and CD are connected, PD is the oblique height of the triangular pyramid. CD is the height on the AB side of 螖ABC, and point O is on the CD.

鈭次擯OD and 鈻砅OC are both right-angled triangles, and 鈭燩OD=鈭燩OC=90掳(2), the nature of the regular pyramids BEA2, the auxiliary line of the regular pyramid is generally: the bottom surface of the PO鈯BCD is O, Then O is the center of the square ABCD, PO is the height of the pyramid, taking the midpoint E of AB, connecting PE, OE, OA, then PE is the oblique height of the quadrangular pyramid, and point O is on AC.

鈭次擯OE and 鈻砅OA are both right-angled triangles, and 鈭燩OE=鈭燩OA=90掳 (3). The square of one diagonal length of the rectangular parallelepiped is equal to the sum of the squares of the length, width and height of the rectangular parallelepiped.

Specially, if the cube has a length of a, the diagonal of this cube is 3a.

5 Pian II: 1-5 high school mathematics compulsory induction and knowledge formula Daquan Ctrl-click the left mouse to open the first chapter of the video player supporting teacher teaching animation, the set of function concept, a collection of 1, the object of study Collectively.

Collection of three elements:

2, as long as the elements that make up the two sets are the same, the two sets are called equal.

3, common collection: positive integer set: N* or N, :Z,:Q,:, representation of the set: enumeration method, description method, basic relationship between sets 1, generally, for two Set A, B, if any of the elements in set A are elements in set B, then set A is called a subset of set B.

Note, if the set AB, but the element xB, and xA, then the set A is called the true subset of the set B. It is recorded as:, the set without any elements is called. Recorded as: and specified: empty A collection is a subset of any collection. 4. If set A contains n elements, then set A has 2 subsets. Basic operations between sets 1. Generally, consisting of all elements belonging to set A or set B. A collection, called the union of sets A and B. It is written as: In general, a set consisting of all elements belonging to set A and belonging to set B is called the intersection of A and B. It is recorded as: complete set, complement set ? CUA{x|xU, and xU}, the concept of function 1, let A, B be a non-empty number set, if according to a certain correspondence f, make any number x in set A, in set B There is a uniquely determined number fx and its corresponding, then f: AB is a function of set A to set B, denoted as: yfx, the constituent elements of a function are: domain, correspondence, value range. The definition of the two functions is the same, and the correspondence is completely the same, then the two functions are called equal. The representation of the function 1. The three representations of the function: analytical method, image method, list method, monotonicity and Maximum (small) value 1, note the general format of the function monotonic proof: solution: set x1, x2a, b and x1x2, then: fx1fx2 =, parity 1, in general, if any x in the domain of the function fx, has fxfx, then the called function fx image even function symmetric about the y-axis .2, in general, if a function fx x for any defined region, both fxfx, then the called function is an odd function image on fx Origin symmetry. Chapter 2, basic elementary functions (I), exponents and exponential powers

where n1, when n is an odd number, ana; nn When n is an even number, we specify: n(1)amana0,m,nN*,m1;(2)an1ann0;4, the nature of the operation: (1)arasarsa0,r,sQ;(2)arsarsa0, r, sQ; (3) abrarbra0, b0, exponential function and its properties 1, remember image: yaxa0, logarithm and logarithm operation 1, axNlogaNx; 2, loga10, when a0, a1, M0, N0: (1) logaMNlogaMlogaN; (2) logMaNlogaMlogaN; (3), base change formula: logcbabloglogaca0, a1, c0, c1, log1ablogbaa0, a1, b0,., logarithmic function and its properties 1, remember image: ylogaxa0, power function 1, several powers The image of the function: Chapter 3, the application of the function, the root of the equation and the zero of the function, the image of the real root function yfx of the equation fx0 and the intersection function yfx of the x-axis have zero points. 2. Properties: If the function yfx is The image on the interval a, b is a continuous curve, and there is fafb0. Then, the function yfx has zero points in the interval a, b, that is, there are ca, b, so that fc0, this c is the root of the equation fx0. Using the dichotomy to find the approximate solution of the equation 1. Master the dichotomy. Several different types of function models and function models are applied. The conventional method of solving the problem: first draw a scatter plot, then fit it with the appropriate function, and finally test. There are two faces parallel to each other, the other faces are quadrilateral, and the common sides of each adjacent two quadrilaterals are parallel to each other. The polyhedron enclosed by these faces is called a prism.

The projection formed by scattering the light from one point is called the center projection, and the projection line of the center projection is at one point; the projection under the illumination of a parallel beam is called parallel projection, and the projection lines of the parallel projection are parallel.

(1) cylindrical side area; S side 2rl (2) conical side area: S side rl (3) round table side area: S side rlRl (4) volume formula: 1V cylinder Sh; V cone Sh; 31V station S on S S S lower h3 (5) Surface area and volume of the ball: 4S ball 4R2, V ball Chapter 2: Positional relationship between points, lines, planes 1 If two points on a straight line are in one plane, then this line is in this plane.

2 There are three points on a straight line, and there is only one plane.

3 If two non-coincident planes have a common point, then they have one and only one common line passing the point.

4 Parallel to the two straight lines parallel to the same line. In the space of 5, if the two sides of the two corners correspond to each other, then the two angles are equal or complementary.

6 parallel, intersecting, and different faces.

7 lines are in the plane, lines and planes are parallel, lines and planes intersect.

8 parallel, intersect.

9 (1) Judgment: A straight line outside the plane is parallel to a line in this plane, and the line is parallel to this plane.

(2) Properties: A straight line is parallel to a plane, and the intersection of any plane passing through this line with this plane is parallel to the line.

10(1) determines that two intersecting straight lines in one plane are parallel to the other plane, and the two planes are parallel.

(2) Properties: If two parallel planes intersect the third plane at the same time, their intersections are parallel.

11(1) Definition: If a line is perpendicular to any line in a plane, then the line is said to be perpendicular to this plane.

(2) Judgment: A straight line is perpendicular to two intersecting straight lines in a plane, and the straight line is perpendicular to this plane.

(3) Properties: Two straight lines perpendicular to the same plane are parallel.

12(1) Definition: Two planes intersect, and if they form a dihedral angle, they are perpendicular to each other.

(2) Judgment: If one plane passes through a perpendicular line of another plane, the two planes are perpendicular.

鈶?nature: two planes perpendicular to each other, is a plane perpendicular to the straight line of intersection is perpendicular to the other plane.

1ktany2y1x2x12鈶?point inclined straight line equation::

Chapter yy0kxx0鈶?slope-intercept: ykxb鈶?two formula: yy1xx1y2y1x2x1鈶?general formula: AxByC03l1: yk1xb1, l2: yk2xb2 has: 鈶磍k1k21 // l2b1b; 2鈶祃1 and l2 intersect k1k2; 鈶秎k1k21 and l2 coincide; b1b2鈶? A1xB1yC10, l have: 2: A2xB2yC20鈶磍A1B2A2B11 // l2BB; 1C22C1鈶祃1 and l2 intersect A1B2A2B1; Part III: high school mathematics compulsory for all formula 1 finishing high school high school mathematics compulsory 1 all formulas and poor finishing [the plot] 2sinAcosB =sin(A+B)+sin(AB)2cosAsinB=sin(A+B)-sin(AB)2cosAcosB=cos(A+B)-sin(AB)-2sinAsinB=cos(A+B)-cos( AB) sinA+sinB=2sin((A+B)/2)cos((AB)/2cosA+cosB=2cos((A+B)/2)sin((AB)/2)tanA+tanB=sin( A + B) / cosAcosBtanA-tanB = sin (AB) / cosAcosBctgA + ctgBsin (A + B) / sinAsinB-ctgA + ctgBsin (A + B) / sinAsinB [some number of columns of the first n items and] 1 + 2 + 3 + 4+5+6+7+8+9++n=n(n+1)/21+3+5+7+9+11+13+15++(2n-1)=n22+4+6 +8+10+12+14++(2n)=n(n+1)12+22+32+42+52+62+72+82++n2=n(n+1)(2n+1) /613+23+33+43+53+63+n3=n2(n+1)2/41*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 three The radius of the circumscribed circle of the angle is the cosine theorem b2=a2+c2-2accosB Note: the angle B is the arc length of the edge a and the edge c. The formula l=a*ra is the radians of the central angle r0 The fan area formula s=1/2 *l*r multiplication and factorization a2-b2=(a+b)(ab)a3+b3=(a+b)(a2-ab+b2)a3-b3=(ab(a2+ab+b2) Triangle inequality |a+b||a|+|b||ab||a|+|b||a|b=-bab|ab||a|-|b|-|a|a|a|one yuan The solution of the quadratic equation -b+(b2-4ac)/2a-b-(b2-4ac)/2a root and coefficient X1+X2=-b/aX1*X2=c/a Note: Vedic theorem Equation] b2-4ac=0 Note: The equation has two equal real roots b2-4ac0 Note: The equation has no real root, and there are conjugate complex roots [two angles and formula] sin(A+B)=sinAcosB+cosAsinBsin(AB )=sinAcosB-sinBcosAcos(A+B)=cosAcosB-sinAsinBcos(AB)=cosAcosB+sinAsinBtan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(AB)=(tanA-tanB)/( 1+tanAtanB)ctg(A+B)=(ctgActgB-1)/(ctgB+ctgA)ctg(AB)=(ctgActgB+1)/(ctgB-ctgA) [double angle formula] tan2A=2tanA/(1-tan2A ) ctg2A=(ctg2A-1)/2ctgacos2a=cos2a-sin2a=2cos2a-1=1-2sin2a [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+c osA))tan(A/2)=-((1-cosA)/((1+cosA))ctg(A/2)=((1+cosA)/((1-cosA))ctg(A/ 2)=-((1+cosA)/((1-cosA))[Power reduction formula](sin^2)x=1-cos2x/2(cos^2)x=i=cos2x/2銆怳niversal formula 銆?Let tan(a/2)=tsina=2t/(1+t^2)cosa=(1-t^2)/(1+t^2)tana=2t/(1-t^2)銆嬨€?From: Link address: http:///news/ Reprint please keep, thank you! See more related content>>.


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