Reprinted Mathematics 【 High School, all , the formula 】

 High School Mathematics
all, the formula】 sealed, never
Mathematics 【High School, all, the formula】

sin2α = 2sinαcosα
cos2α = cos2α -sin2α = 2cos2α-1 = 1-2sin2α
2tanα
tan2α =-----
1-tan2α
sin3α = 3sinα- 4sin3α
cos3α = 4cos3α-3cosα
3tanα-tan3α
tan3α =------
1-3tan2α
trigonometric functions and the difference of the plot formula of the product of trigonometric functions and differential equations
α + β α-β
sinα + sinβ = 2sin --- · cos --- < br> α + β α-β
sinα-sinβ = 2cos --- · sin ---
α + β α-β
cosα + cosβ = 2cos --- · cos ---
α + β α-β
cosα-cosβ =- 2sin --- · sin ---
sinα · cosβ =- [sin (α + β) + sin (α-β)]
cosα · sinβ =- [sin (α + β)-sin (α-β)]
cosα · cosβ =- [ ,],[angle in the form of a trigonometric function (auxiliary angle trigonometric formulas
collection, a collection of simple logic functions

any x ∈ A x ∈ B, denoted by A B
AB, BAA = B
AB = x
AB = x ∈ A, or x ∈ B ;
card (AB) = card (A) + card (B)-card (AB)
(1) the original proposition if the proposition p is
q
converse, if not q then p
if p then q
proposition against any proposition, if q, then p
(2) the four propositions relationship
(3) AB, A sufficient condition is established B
BA, A is a necessary condition for the establishment of B
AB, A is B established necessary and sufficient condition
Functions Logarithmic
(1) domain, range, corresponding to the rule
(2) monotonicity ;
For any x1, x2 ∈ D
if x1
x1 f (x2), called f (x) in D is a decreasing function
(3) parity
the function f (x) of within the definition of any one of x, if f (-x) = f (x), say f (x) is even function
if f (-x) =- f (x), called f ( x) is an odd function
(4) periodic
for the function f (x) within the definition of any one of x, if there exists a constant T, so f (x + T) = f (x), called f (x) is a periodic function (1) Score Index Score Index of the power
is the meaning of power indices
negative score is the meaning of power ;
(2) of the nature and number of algorithms
loga (MN) = logaM + logaN
logaMn = nlogaM (n ∈ R) < br> exponential function logarithmic function
(1) y = ax (a> 0, a ≠ 1) is called exponential function
(2) x ∈ R, y> 0
image through the (0,1)
a> 1 时, x> 0, y> 1; x <0,0
<1>0 < a <1 时, x> 0,0 <0, x <1;>1
a> 1 时, y = ax is an increasing function of
0 < is a function y="ax" (a (1) decreasing 1,>0, a ≠ 1) is called the logarithmic function
(2) x> 0, y ∈ R
After Image (1,0)
a> 1 时, x> 1, y> 0; 0
<0 <1,>0 <1 x 时,>1, y <0; 0 <1,>0
a> 1 时, y = logax is an increasing function of
0
<1 y="logax" decreasing 时,>exponential equations and logarithmic equations
basic
logaf (x) = bf (x) = ab (a> 0, a ≠ 1)
with the bottom type
logaf (x) = logag (x) f (x) = g (x)> 0 (a> 0, a ≠ 1)
substitution type f (ax) = 0 or f (logax) = 0
series
the basic concepts of arithmetic series, series
(1) Number Sequence formulas an = f (n)
(2) series recurrence formula
(3) series with a general formula of n items and the relationship between < br> an +1- an = d
an = a1 + (n-1) d
a, A, b into the arithmetic 2A = a + b
m + n = k + l am + an = ak + al
commonly used geometric series sum formula
an = a1qn_1
a, G, b into the geometric G2 = ab
m + n = k + l aman = akal
inequality
important inequalities of the basic properties of inequalities
a> bb < a
a> b, b> ca> c
a> b a + c> b + c
a + b> ca> c-b
a> b, c> d a + c> b + d
a> b, c> 0 ac> bc
a> b, c <0 ac
a> b> 0, c> d> 0 ac
a> b> 0 dn> bn (n ∈ Z, n> 1)
a > b> 0> (n ∈ Z, n> 1)
(a-b) 2 ≥ 0
a, b ∈ R a2 + b2 ≥ 2ab
| a | - | b | ≤ | a ± b | ≤ | a | + | b | the basic method of Inequality
comparison
(1) To prove the inequality a> b (or a
a-b> 0 (or a-b <0 = can
(2) If b > 0, to permit a> b, only need to prove that,
to permit a
synthesis method is the synthesis method known or has been proven from the inequality , the realities of the nature of inequality derived want to permit inequality (from the fruit by derivative) method.
analysis method is a sufficient condition for concluding the establishment of start, step by step for the establishment of the necessary and sufficient conditions conditions, until the desired conditions are known correctly so far, apparent in c, b = d
(a + bi) + (c + di) = (a + c) + (b + d) i
(a + bi) - (c + di) = (a-c) + (b-d) i
(a + bi) (c + di) = (ac-bd) + (bc + ad) i
a + bi = r (cosθ + isinθ)
r1 = (cosθ1 + isinθ1)? r2 (cosθ2 + isinθ2)
= r1? r2 〔cos (θ1 + θ2) + isin (θ1 + θ2)
〕 〔r (cosθ + sinθ)〕 n = rn (cosnθ + isinnθ)
k = 0,1, ... ..., n-1 < br> Analytic Geometry
1, line
distance between two points, will score points straight line equation
| AB | = | |
| P1P2 | =
y-y1 = k (x-x1)
y = kx + b
angle between two lines of the location and distance
or k1 = k2, and b1 ≠ b2
l1 and l2 coincidence
or k1 = k2 and b1 = b2
l1 and l2 intersect ;
or k1 ≠ k2
l2 ⊥ l2
or k1k2 =- 1 l1 to l2 corner angle
l1 and l2
point to a line distance
2.
conic
ellipse standard equation of circle (x-a) 2 + (y -b) 2 = r2
center for the (a, b), radius R
general equation x2 + y2 + Dx + Ey + F = 0
where the center is (),
radius r
(1) with a straight-line distance from the center to the radius r d and the judge or the discriminant to determine the location of straight lines and circular relationship
(2) two-round relationship between the position of the radius with the center distance and difference d with the ellipse
determine the focus of F1 (-c, 0), F2 (c, 0)
(b2 = a2-c2)
eccentricity alignment equation

focus radius | MF1 | = a + ex0, | MF2 | = a-ex0
hyperbolic parabola
hyperbolic
focus F1 (-c, 0), F2 (c, 0)
(a, b> 0, b2 = c2-a2 )
eccentricity alignment equation

focus radius | MF1 | = ex0 + a, | MF2 | = ex0-a parabola y2 = 2px (p> 0 )
focus F
alignment axis translation equation

here (h, k) is the origin of the new coordinate system in the original coordinate system of coordinates.
1. a collection of elements each with the opposite sex ① ② ③ deterministic randomness
2. collection representation ① description of enumeration method
③ ② ④ Wayne graph the number of axis method
3. collection operations
⑴ A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
⑵ Cu (A ∩ B) = CuA ∪ CuB
Cu (A ∪ B) = CuA ∩ CuB
4. a collection of the nature of the
⑴ n element subset of the set number: 2n
subset number: 2n-1; non-empty subset number: 2n-2
High School Summary
four mathematical concepts, inequalities
1, if n is a positive odd number, can be introduced by the it? (can)
n is a positive even if it? (non-negative only when)
2, the same can be subtracted to the inequality, divide up (can not)
can add it? (can)
can multiply it? ; (energy, but conditional)
3, two positive numbers mean inequality is:
three positive numbers mean inequality is:
n a positive mean inequality is:
4, the harmonic mean of two positive numbers, geometric mean, arithmetic mean, root mean square is the relationship between the
6, two-way inequality is:
the left of the equal sign in time to obtain the right to obtain equal in time.
five series
1, etc. Arithmetic general formulas, the former n items and formula: =.
2, the general term geometric series formula,
ago n items and the formula is:
3, When the common ratio of geometric series q satisfy <1, = S =. In general, if the infinite series and limits of the former existence of n items, put the limit of the known and the series (or all items and), with S, ie S =.
4, if m, n, p, q ∈ N, and, then: when the series is the arithmetic progression, there; when the series is the geometric sequence, there .
5, arithmetic sequence, if Sn = 10, S2n = 30, then S3n = 60;
6, geometric sequence, if Sn = 10, S2n = 30, then S3n = 70; < br> VI complex
1, how to calculate? (n is 4, except the first request from the remainder,)
2, is one of the two imaginary cube root, and:
3, the complex is set within the triangle inequality:, where the left side in the complex z1, z2 corresponding vector collinear and opposite (in the same direction) is taken equal sign, right in the complex z1, z2, and the corresponding vector collinear with the (reverse) to take equal time.
4, Di Mo Buddha theorem is:
5, if not zero complex number, z n has n-th root, namely:
them in the complex plane the corresponding point in the distribution of any special relationship?
are located in the center of the circle at the origin, radius of the circle and this circle n equal portions.
6, if, complex z1, z2 are corresponding points A, B, then △ AOB (O as the coordinate origin) of the area is.
8, the complex plane z corresponds to the complex a few basic tracks:
① track as a ray. < br> ② path as a ray.
③ trajectory is a circle.
④ trajectory is a straight line.
⑤ There are three possible trajectories circumstances: a) At the time, oval track; b) At the time, track is a line segment; c) At the time, path does not exist.
⑥ track there are three possible cases: a) time, the trajectory is hyperbolic; b) At the time, for the two-ray path; c) At the time, path does not exist.
seven, permutations and combinations, binomial theorem
1, addition principle, multiplication principle applies to what the situation? What are the characteristics?
additive category, class, class of independence; multiplication step, step by step related.
2, Permutation formula is: = =;
arrangement number and the relationship between the number of combinations:
combinations formula is: = =;
; combination of several properties: = + =
3, the binomial theorem: expansion of two general formulas:
eight, analytic geometry
1, Shull formula:
2, number line distance between two points formula:
3, rectangular coordinate plane distance formula between two points:
4, if the point P divided into a fixed ratio to the line λ, then λ =
5, if the points, point P is divided into a fixed ratio to the line λ, is: λ = =;
If, then △ ABC the coordinates of the center of G is.
6, Line Slope was defined as k =, two formula k =.
7, several forms of linear equations:
point slope form:, inclined cutting:
two-point: the intercept-type:
; general formula:
the intersection of two lines through the linear system equation is:
14, of circular and linear relationship between the location of the most commonly used in two ways , that is:
① discriminant method: Δ> 0, = 0, <0, equivalent to a straight line and circle intersect, tangent, Deviation;
; ② examine the center of the circle to the line between distance and size of the radius: the distance is greater than the radius, equal to the radius, smaller than the radius, equivalent to phase away from the straight line and circle, tangent, intersect.
15, the four parabolic form of the standard equation:

16, the focus of the parabolic coordinates are:, quasi-line equation is:.
If the point is a point on the parabola, the focal point of the distance to the parabola (called the focal radius) is:, over the focus of the parabola and the parabola symmetry axis perpendicular to the string ( known as Path) in length are:.
17, ellipse standard equation of the two forms are: and
.
18, the focus of elliptical coordinates, the quasi-line equation is that eccentricity is the long path is. Them.
19, if the point is elliptic on the point is that its left and right focus, the focal point P and the radius length is.
20, the standard hyperbolic equations in two forms: and
.
21, the focus of the hyperbolic coordinates, the quasi-line equation is that eccentricity is a long path, the asymptotic line equation is. Them.
22, with a total of asymptote hyperbola hyperbolic equation system is. And hyperbolic equations were the focus of the hyperbolic system is.
23, if the straight lines and conic curves intersect at two points A (x1, y1), B (x2, y2), then the string length;
If the straight lines and conic curves intersect at two points A (x1, y1), B (x2, y2), then the string length.
24, the focal conic geometric parameter p is the significance to the reference line of the focus distance, the ellipse and hyperbola are:.
25, translation axis, the origin of the new coordinate system in the original coordinate system coordinates (h, k), if the point P in the original coordinate system the coordinates of the coordinate system in the new coordinates is then = =.
second, composite second radical simplification of
When is a completely square, on the shape of the radical reduction using the above formulation is more convenient.
⑵ and set the number of elements:
n (A ∪ B) = nA + nB-n (A ∩ B)
5. N natural numbers or non-negative integers
Z set of integers Q R rational real numbers
6. Simple logic truth table
p consistent with the proposition true or false
non-p
false true
in the definition domain, if, for the dual function; if it was odd function.
1 had two points and only a straight line the shortest line between two points
2
3 of the supplementary angle with the same angle or isometric angle or isometric
4 with the complementary angle equal to
5 had a little one and only one straight line and known point outside a straight line perpendicular to
6 points connected with straight line segments in all, the vertical section of the shortest
7 point outside a straight line through the parallel axiom, and only one straight line and this line if the two lines parallel to
8 and the third line are parallel, these two lines are parallel to each other
9 Tong Weijiao equal, the two straight lines parallel to the wrong
10 equal angles, two straight lines Parallel
11 complementary with the adjacent angles, two straight lines parallel to the two parallel
12, Tong Weijiao equal
13 two parallel lines, alternate angles are equal within the two lines parallel
14, with the next complementary angles
15 on both sides of the triangle theorems and inference than the third side
16 on both sides of the triangle is less than the third side
17 angles of a triangle and the theorem of the three angles of a triangle and is equal to 180 °
18 Corollary 1 right angle more than two acute triangles each triangle
19 Corollary 2 and it is not an exterior angle is equal to two adjacent interior angles
20 Corollary 3 the triangle exterior angle is greater than any one and it is not adjacent angles
21 corresponding sides congruent triangles, corresponding angles are equal
22 corner edge axiom (SAS) has two sides and their corresponding angles equal two triangles congruent
23 angle corners axiom (ASA ) he had two horns and their corresponding folders sides congruent two triangles of equal
24 Corollary (AAS) which had two horns, and the corresponding corner on the edge of two triangles of equal side of justice congruent
25 Collage (SSS) with the corresponding three sides of equal triangles congruent
26 hypotenuse of two right-angled edge of axioms (HL) and a right-angle bevel edge with the corresponding two triangles congruent equivalent of Theorem 1 in the corner
27 point to divide equally the angle of the line equidistant from both sides of Theorem 2-1
28 angle from both sides of the same points in the angle bisector of angle bisector
29 is the angle equidistant points on both sides of the set of all the nature
30 isosceles triangle isosceles triangle theorem of the two bottom corners are equal (that is, on the other side isometric)
31 Corollary 1 lines equally divide equally angle isosceles triangle bottom and perpendicular to the bottom of the
32 isosceles triangle the angle bisector, the bottom edge of the middle and the bottom edge of the high overlap each other
33 Corollary 3 corners of an equilateral triangle are equal, and each a corner of the isosceles triangle is equal to 60 °
34 Judgement Theorem If a triangle has two angles equal, then the two angles are equal the right side (equiangular, equilateral)
35 Corollary 1, three corners are equal is equilateral triangle
36 Corollary 2 has an angle equal to 60 ° isosceles triangles are equilateral triangles
37 in a right triangle, if one acute angle is 30 ° so it right right-angle bevel edge is equal to half the hypotenuse of a right triangle
38 the center line on the hypotenuse is equal to half the
39 Theorem on the axis line segment point and the two ends of this segment are equidistant
40 inverse and a line equidistant from the two end points in this segment of the vertical split line
41 perpendicular bisector of line segment and the segment end points can be regarded as equal to all the points from the set of
42 Theorem 1 in a straight line on the symmetry of the two figures are congruent shape
43 Theorem 2 If two graphics symmetrical about a straight line, then the corresponding point of the axis of symmetry is the axis connecting Theorem 3 Two
44 symmetrical about a straight line graph if their corresponding intersection line or extension cord, then the intersection of the inverse of the axis of symmetry
45 points if the two corresponding connection graph is a straight line with the axis, then the two graphics on the this line of two symmetrical
46 Pythagorean triangle edge at right angles a, b and the square is equal to the square of the hypotenuse c, ie a ^ 2 + b ^ 2 = c ^ 2
47 Pythagorean Theorem If the triangle triangular inverse long a, b, c has a relationship a ^ 2 + b ^ 2 = c ^ 2, then the triangle is right triangle quadrilateral theorems
48 equal angles and 360 °
49 quadrilateral exterior angle equal to 360 °
50 angles and the theorem of n sides polygon-shaped interior angles is equal to (n-2) × 180 °
51 deduction equal to any multilateral exterior angle and 360 °
52 parallelogram properties Theorem 1 parallelogram equal
53 diagonal parallelogram parallelogram nature of Theorem 2 on the opposite side in the same folder
54 inference between two parallel lines, parallel line segments are equal
55 parallelogram parallelogram nature of Theorem 3 diagonal to each other equally
56 Theorem 1 determine the two parallelogram angles are equal to the quadrilateral is a parallelogram parallelogram
57 Theorem 2 to determine the respective groups on the same side of a quadrilateral is a parallelogram
58 Theorem 3 diagonal parallelogram to determine each split quadrilateral is a parallelogram parallelogram
59 Theorem 4 to determine a set of parallel sides equal quadrilateral is a parallelogram
60 rectangular nature of Theorem 1, the four corners of the rectangle are rectangular Cartesian
61 rectangular diagonal nature of Theorem 2 is equal
62 has three rectangular determine the angle of Theorem 1 is at right angles to rectangular quadrilateral is a rectangle
63 Theorem 2 to determine the diagonal of the parallelogram is a rectangle equal to < br> 64 diamond Diamond Theorem 1 the nature of the four sides are equal
65 diamond diamond diagonal nature of Theorem 2, perpendicular to each other, and each diagonal split a diamond-shaped area on the corner
66 = diagonal half of the product, ie S = (a × b) ÷ 2
67 diamond-shaped sides are equal Theorem 1 determine a quadrilateral is a rhombus diamond
68 Theorem 2 to determine the diagonal of the parallelogram are perpendicular to each other diamond
Theorem 1 69 square nature of the four corners of a square are right angles, four sides are equal
70 square nature of Theorem 2, the two diagonal squares are equal, and perpendicular to each other equally, and each diagonal a diagonal split
71 Theorem 1 on the center of symmetry of the two graphs are congruent
72 Theorem 2, the two graphics on the center of symmetry, symmetry point connection have been the center of symmetry and is symmetric against the center divide
73 Theorem If two graphs have been a corresponding point of the connection point, and is it equally, then the two graphics on this point the nature of symmetry
74 isosceles trapezoid isosceles trapezoid theorems in the same two corners on the bottom isosceles trapezoid are equal
75 two diagonals are equal decision theorem
76 isosceles trapezoid in the same two corners on the bottom of the ladder are equal isosceles trapezoid
77 diagonal is equal to the trapezoidal isosceles trapezoid
78 equal portions parallel segments Theorem If a set of parallel lines cut in a straight line segment obtained
equal, then the other straight line intercepted the line are equal
79 Corollary 1 through trapezoidal the midpoint of the waist and bottom of a parallel line, the other will be shared equally by the waist
80 Corollary 2 side of the midpoint of the triangle parallel with the other side of the line, will split the third side
81 triangle triangle median line of Theorem the median line parallel to the third side and equal to its half of the
82 trapezoid trapezoid theorem of the median line median line parallel to the two end and two equal to half of the bottom and L = (a + b) ÷ 2 S = L × h
83 (1) If the proportion of the basic properties of a: b = c: d, then ad = bc
if ad = bc, then a: b = c: d wc / S ?
84 (2) the nature of cooperation than if a / b = c / d, then (a ± b) / b = (c ± d) / d
85 (3) If the geometric properties of a / b = c / d = ... = m / n (b + d + ... + n ≠ 0), then
(a + c + ... + m) / (b + d + ... + n) = a / b
86 parallel line segments proportional to the theorem of three sub-parallel lines cut two lines from the corresponding line segments proportional reasoning
87 side of the line parallel to the triangle cut other side (or both sides of the extension cord), which is proportional to the corresponding segment < br> 88 Theorem If a line cut on both sides of the triangle (or both sides of the extension cord) from the corresponding line segments proportional, then this line parallel to the triangle's third side
89 parallel to the side of the triangle, and the other side intersecting lines, triangles intercepted by the triangular sides of a triangle corresponds to the original proportional
90 Theorem side of the line parallel to the triangle and the other side (or both sides of the extension line) intersects the triangle composed of the original triangle Similar
91 corners of similar triangles to determine the corresponding equivalent of Theorem 1, the two triangles similar to the (ASA)
92 high on the hypotenuse of a right triangle is divided into two right triangles and similar triangles of the original decision theorem 2
93 proportional to the corresponding sides and angles equal, the two triangles similar to the (SAS)
94 to determine the corresponding proportion trilateral Theorem 3, the two triangles similar to the (SSS)
95 Theorem If the hypotenuse of a right triangle and a right-angle edge hypotenuse of another right-angle side and a corresponding proportion, then the two triangles similar to the nature of Theorem 1
96 higher than the corresponding similar triangles, corresponding to the center line than the corresponding angle bisector is equal to the ratio nature than
97 similar similar triangles theorem 2 ratio is equal to the circumference of the nature similar to Theorem 3 than
98 similar similar triangles is equal to the area than the square
99 than the sine of any acute angle equal to its complementary angle of the cosine, any acute angle equal to its complementary angle cosine sine
100 tangent of any acute angle equal to its complementary angle cotangent value, the value of any acute angle equal to its complementary angle cotangent tangent of < br> 101 round is a distance equal to the fixed-length fixed-point set of points inside the circle
102 can be seen as the distance is less than the radius of the center point of the set
103 can be seen as outside the circle from the center of the circle greater than the radius of the set of points such
104 circle with the radius of a circle or equal
105 a distance equal to the fixed point of the trajectory of fixed length, is the point of a circle, a circle of radius length
106 and the distance between the two endpoints are known to line the locus of points equal to, is the perpendicular bisector of line segments to a known angle
107 equidistant points on both sides of the track, is the angle bisector
108-2 equidistant parallel lines locus of points, and it is these two parallel lines parallel and equidistant Theorem is not a straight line
109 three-point line has been identified with a circle.
110 vertical diameter perpendicular to the chord diameter of Theorem equally split this string by string and the two arcs
111 of Corollary 1 ① split string (not diameter) perpendicular to the string diameter, and equally the right chord arc
② two perpendicular bisector of string through the center of the circle, and the strings are split on the two strings of the arc
③ split an arc of diameter, the vertical split string, and split the string by another pair Corollary 2 arc
112 round clip of two parallel strings are equal
113 circle arc is the center of the center as the center of symmetry theorem of symmetry
114 or so in the same round in the circle, central angle equal The equivalent of the arc, the equivalent of the string, the string on the heart strings of inferences from the same
115 round or so in the same round, if the two central angle, two arcs, two string or two strings heart strings in a set amount of distance equal to that they correspond to the amount of the other groups are equal
116 theorem of an arc on the circumference of the angle of the central angle is equal to its half
117 Corollary 1 with the arc or other arc of the circumference of the equal angles; the same circle or other circular, the equivalent of the circumferential angle of the arc are equal
118 Corollary 2 semicircle (or diameter) of the angle of the circle at right angles; 90 ° circumferential angle The diameter of the string is
119 Corollary 3 If the center line on the side of the triangle is equal to half the side, then the triangle is right triangle within the circle theorems
120 quadrilateral diagonal complementary, and any exterior angle is is equal to its angle within
121 ① ⊙ O line L and intersects d
② ⊙ O line L, and d = r
③ tangent line L and ⊙ O phase from the d> r?
After 122 Tangent Theorem to determine the radius of the outer end and perpendicular to the radius of this circle tangent line is tangent to the nature of the Theorem
123 round after a cut perpendicular to the tangent point of radius
124 1 through the center of the circle and the inference will be perpendicular to the tangent line through the tangent point
125 Corollary 2 points after a cut perpendicular to the tangent line through the center
126 will be a long tangent point theorems introduced from outside the circle of the two tangent circles, their appearance and so the tangent , center, and split the connection that the angle between two tangents
127 quadrilateral circumscribed circle on the side of the two groups and equal
128 Xian Qiejiao Theorem Xian Qiejiao arc is equal to its folder circumferential angle
129 inference that if two Xianqie Jiao folder arc equal, then the two are equal
130 Xian Qiejiao intersection of the two strings intersect circle theorem of string, was divided into two intersection equal to the product of a long line
131 deduction if the chord and the diameter of vertical intersection, then the string by half its diameter into two sub-segments in the proportion of items
132 cutting line from the circle theorems point outside the circle tangent cited and the secant, tangent length is the secant and the circle to the intersection point of two line segments in the proportion of long-term
133 inferences that lead from outside the circle round the two secant, which is the secant and the circle of each the intersection of the product of two equal length segments if the two circles tangent
134, then the cutoff point must be in line with the heart outside the two circles
135 ① from the d> R + r ② d = exterior of two circles R + r
③ two circles intersect Rr r)
④ two circles inscribed d = Rr (R> r) ⑤ two circles containing d r)
136 two-circle theorem of intersecting lines with the axis of two circles the heart of public * String
137 into the circle theorem of n (n ≥ 3):
⑴ points followed by links from each polygon is The circle inscribed n-gon
⑵ points for each round after the tangent to the intersection of the tangent to the adjacent vertices of this polygon is a circle circumscribed n-gon theorem of any regular polygon
138 has a circumcircle and an inscribed circle, the two circles are concentric
139 regular n-gon of each interior angle is equal to (n-2) × 180 ° / n
140 theorems are n edge Heart-shaped edge radius and n from the regular 2n-gon into two congruent right triangle
141 n-gon is the area of ​​Sn = pnrn / 2 p n-gon that is the perimeter of an equilateral triangle
142 area of ​​√ 3a / 4 a side said
143 around if a vertex k-regular n-gon angle, and these angles should be 360 ​​°, so k × (n-2) 180 ° / n = 360 ° into the (n-2) (k-2) = 4
144 arc length formula: L = n Wu R/180
145 fan-shaped area formula: S fan = n Wu R ^ 2 / 360 = LR / 2
146 within the common tangent length = d-(Rr) grandfather tangent length = d-(R + r)
multiplication and factoring
a ^ 2-b ^ 2 = ( a + b) (ab)
a ^ 3 + b ^ 3 = (a + b) (a ^ 2-ab + b ^ 2)
a ^ 3-b ^ 3 = (ab (a ^ 2 + ab + b ^ 2)
triangle inequality | a + b | ≤ | a | + | b | | ab | ≤ | a | + | b | | a | ≤ b <=>-b ≤ a ≤ b
| ab | ≥ | a | - | b | - | a | ≤ a ≤ | a |
the solution of a quadratic equation-b + √ (b ^ 2-4ac) / 2a-b- √ (b ^ 2-4ac) / 2a
relationship between roots and coefficients X1 + X2 =- b / a X1 * X2 = c / a Note: Whyte Theorem
discriminant
b ^ 2 - 4ac = 0 Note: The equation has two equal real roots
b ^ 2-4ac> 0 Note: The equation has two unequal real roots
b ^ 2-4ac <0 Note: The equation has no real root, root
a conjugate trigonometric formulas
corners and formulas
sin (A + B) = sinAcosB + cosAsinB
sin (AB) = sinAcosB-sinBcosA
cos ( A + B) = cosAcosB-sinAsinB
cos (AB) = cosAcosB + sinAsinB
tan (A + B) = (tanA + tanB) / (1-tanAtanB)
tan (AB) = (tanA -tanB) / (1 + tanAtanB)
cot (A + B) = (cotAcotB-1) / (cotB + cotA)
cot (AB) = (cotAcotB +1) / (cotB-cotA).

Jun , thus far from the truth

 Wang does not know which Autumn, is still the clear and bright. Do not know what a darling, is still a delicate and exquisite fragrance. War scattered the pain has already memorable collection, interpretation of the fragments can not get into a fuzzy frame by frame, while a burst of sad, leaving only look forward eagerly to look back.
frown a smile back, everything is a hatchback situation, season of blooming, dying of the Sansei's watch. Moment ten years in strangers to each other behind, and only soul Jieao debauchery. Totally into, whether still, who are willing to open ze endured Hin window.
in that place, under the light touch of quiet, the faint scent of ink released into the atmosphere. Like to hear your voice in the quiet read, lovely clean surface shallow worry, long hair and drooping posture, Ning Mei's Zi Yan subtle fragrance. Off lightly, and in the corner, as you, the heart is young and reclusive.
in that place, quiet corner, and the rest quietly larvae, tired body is no longer loud. A chair across the still quiet, the rhythm of the rest of the rhyme accompanied slowly flowing. On the visual has become a luxury, clean quarter alone keep down, as I have, to a good time.
in that place, snow mountains and meandering Man Juan, Wang Zhou Qifeng cold river crossing. Play each other each sleeve, further and further away with each other attention, the boat between cliffs, offer all kinds of attachment, All kinds of care. Boat dead, sent by a sigh, Gu Fan Yuan shadow blue sky to make, you and I read a sigh in vain.
may be looking for a vacant in love is perhaps the fate of the picking in the ethereal romantic loss. Recent times, can not you smell the fragrance wan quiet, well, when they tore up the horizon of the bags traveled.

snow, Fen Yang, fog, into the cream off a Mang Ai gray, is the winter of the net, Ling into , decorated with cold equipment.
How many times in the text in search of your old Mo Yang, Do not dream vaguely window just before dawn. How many times, traveling alone, but is accountable to the landscape, but why the fascination with the color screen and wandering. Wine Lin Feng, Jun from discretion, and is delighted where.
that 是,
roots of disease-free sigh Ho Yin, Fang Fei driving into the distance desolate bone cold. Huan proud of what to do in life, only the shortage of film-shaped single-dig graves.
sigh but,
worship, read the text the word sacrifice Iraqis, terraced rice paddies Ling who left singing. Net empty string Laji color alone, Chan Yu harmony martyrdom field.

ancients read, friend is easier lost by key from the cliff against the king since far from the truth, Yin is the separation desolate
bitter sigh, a dream every horizon far away, chanting the Yanzi driving into the distance to the heart from the Autumn cold. Autumn season dyed brilliant, but it is, is blowing colorful leaves one place.
leave may be eternal elegance poor, how happy silly monsters, raw minced conditions, plants in the word, waving sleeves, staring eyes, why do not be despair, yin and yang are two different worlds. Chuang Meng-Ho
vain, free map students complain, for one would like to read.
and both, Hugh laughed at me, kind of crazy dream love love the roots, the word down into martyrs, who read this volume?
the course, how amazing Abas Mexico Qin cuddle peace of mind, loose sentence into a poem, but Yin Cipian!

out the window, Fen Yang snow, dark gray past the gorgeous autumn day. When the bitter cold, Review your summer warmth. Only so much to think about thoughts of inspiration with engraved reproduction. Dream, love is not far.
pro! Jun, thus far wrong.
with Xiaokan reincarnation of the brilliant!

Women should dead pixels

 Happy

in woman's goodness can be the era of cheap mortgage, trust in the woman's age can be used in women sincere emotion that can be played in the era of free men and women must be . Because the woman Aesthetic prone to fatigue in men age, women and but the total poor in 1 cm. For men, the less easy to get, the more worthy of care.

as to Because the

Second, the A beautiful woman, the love of many will be confused and not know which were which were true love false love. May have been the most heart love you, but in the end is a cruel joke.

woman enjoy, and that really love their people, looked at each other grow old!

three Lantie. Woman if the shoes.

woman Moment to lose their personality, but do not lose IQ.

Fourth, the They will not live in someone else's eyes, and did not live in someone else's comments, chic to do: go their own way, others are willing to drive to drive it!

woman

Five, Had not a thing, where can the dust alight. Woman

trouble to yourself, sad is inevitable. Want to open is happy, satisfied is happy! Their students have not great, so Biequ Why live? Life is more than twenty thousand days, a day less one day, today is the most authentic woman, the most important, want to do have to do, no need to worrying about not aware or not tomorrow!

six, Get yourself a little sunshine, brilliant point. Do not do it deliberately, but to live out the absolute self. No pretense, no affectation, simply refreshing cool to live out the true self.

woman AC Elegance and recent communication patterns one after another, less whining like a country girl and less of a Jour-like family gossip, it is easy to own. Who does not welcome such a woman?

seven, If you can Life is their own happiness is life Benxiang. Is not difficult for their own happiness and his own memory to delete junk files, but also happy.

woman

eight, Life is not perfect, but it can be done without regret. Woman

as naive, as naive, flowers inserted in their own their own cow dung. Because the woman

woman Therefore, women can be

Three-dimensional painting

You will see three-dimensional art? Each picture has a name. Try a few of your eye can see ? Is really too beautiful to see a few Guestbook ah This map is two hearts
rings < br> Spring garden hat


Daniel calf welfare of eggshell characters

backwards antique telephone table



spent underwater world ring ring

cattle
gold ingot

volume coffee maker and coffee cup children

spiral garland
Mermaid

mushroom < br>
How are you?
beautiful car
tunnel
hammer
tulip
a three-dimensional box
a badminton
a stone diamond ring of dolphins
mandrel
a ring and a disc

map of China Moon Night



cave deep
a kangaroo snake
unlimited
World Cup Happy Birthday emblem

Dalmatians
three mushrooms



dinosaur

Flat tube tide turn in the 2006 Mid-Autumn Festival Review (2)

 There was a time, different smell recorded But he knows the appropriate arrangements for the story is very interesting to complement the relative regret. Unfortunately, the demons did not start this book a good blueprint for planning, thanks to the gradual progress of the narrative techniques pistol remedies, but do not understand time off, this is the biggest flaw of a pistol.
few days ago, had Replies yhntgb, talking about have a big trap, is clearly seen many of, but could not help but fall into it. do not know the next time by station vehicles, is the biggest trap of writing. yhntgb ask, NA me of how to get off early?
This is a good question, excess and deficiency are relative regret.
of off prematurely , brings a boundless sense of the shortcomings, but some can take the time to add enough, it also easy to remedy in the future. And on to silver, multi-code word's nothing to criticize. But for the sake of many of the irrigation, but dilution the original hard-won tension plot cohesion, so that later deteriorated, the quality of a roll than a roll, until the readers to give birth to resentment.
have had a site too far away, still reluctant to get off, inevitably bound for ice and snow all the way Siberia.
long is not wrong, but experience tells us that long to write the main story relies on the complete structure. Many of the order to write some words, in the main story in the Hengshengzhijie, interspersed with a lot for no reason does not matter cumbersome description. the patience of many readers is relatively limited, while the expectations of readers wistfully looking forward, not of redemption has been finally led to mental fatigue, anxiety, and then give birth to a sense of disappointment. to long-term interests point of view, which in terms of reputation, not Shiyao a good thing.
study of people writing . speaking, reading of the lost continent in writing the first few chapters, is not completely into the situation. conspire to wait until a major role, the plot will start up before the characters are vivid throughout.
look lost continent , is hard not to think of Dragonlance, Raistlin is also hard not to think about, but learning to read in its own way, writing is the characters he described the helpless and lost.
or should're so said lost several main characters in the mainland, have been written out of the great features of inner struggle. So when the people will gather to read the focus of the light hit his face in the figures, they seem to see the characters that make vivid expression, it is difficult not to be brought into the story being created by the tension.
excellent background if the description can be interesting if immersive, NA me create the success of an outstanding figure, it is the work , the most impressive of the three-dimensional elements.
days of the crime of different smell is reminiscent of registered Rhode Island Wars. the original days of the crime reviewer, the light of a writer's dragon.
Jia Xu's works,
denied that the growth period from the experience comic books and video games, creative writing is often unintentional capture of nutrients.
such as Baldur, Diablo, Town guardian heroes invincible, until the World of Warcraft and so on, the settings have tended to balance stable, relatively easy to use. The main pan-regional Strategy RPG mode map, the description of both the author, or the reader process, conditions are relatively easy to enter.
also part of the same authors, the experience is drawn from the film tends to be the inspiration for the film. This one, perhaps not with the background of the growth is not related to life. limited by age and living environment, Many of the authors and do not have much life experience, so books, comics, movies, games, life has become the subject of the most accessible source.
pistols have a little spread of the Internet, 2, is a very good online essay.
the emergence of online class work, but just two or three years, a night like mushrooms in one after another, in a very short time the rise and is rapidly becoming a shares important forces can not be ignored. It feels like sudden such as spring night, the Trees of pear blossoms.
fine though many of them, but unfortunately, many authors failed to stick with it, but at the time river gradually sank, and even forgotten.
once again and a few friends over to discuss why the creation of online classes rapid fire of reason, perhaps just the timing coincides with ONLINE gaming in power, perhaps because of online games Rules of freedom, of love set to ruffle ruffle set, of course, may be other reasons, the development of online games story would be so up!
early online boutique, and angels of twelve-tone writing Games Rhapsody imperial hegemony very popular. woodlands Kikunami finished two long masterpiece, period of time, frequency Bangding in that a few works with the configuration is too high, people are not prone to long impressive works of writing online games to their attention.
X's out of the new perspective, people are very surprised. Dream Devil King of the novel can be said that the earliest pioneer of online games, text Road divide our forces, both the virtual and the real story in the interspersed.
rely on, have become a amoeba that there are promising you?
uh! for later wrote Escape quickly go.
two fronts at the same time, there goes the hundred word passage: white light, between black Mountain roar, it seems, China has been peaceful for too long, long time to forget this in addition to killing or kill the death star. and then, then no, you will continue contempt cloud!
continue to divide our forces Road, there I am a cat is written, In the real impact of the environment, can make it test? must say that the writing language light and dark song, with some large Tangshuang Long Shadow.
uh, thinking and dreaming. Pull back! continue to talk about ho war record. 're so write this? But the book is not only the actor with the body, but also the biggest suspense book. He really is a one-eyed? or San Yu Lin Kun? or just a wandering soul is not a trace of Shiyao?
From the eyes of a corpse and see the world, very creepy, but also quite makes a great time. As far as I know, the Internet has this strange hobby of a few, but there was this level of attainment and skill the author, but seems to be a hand over the number of hh hh Who does this? uh, this is definitely a misleading idea, just saying it.
good book gives people food for thought. the essence of life Why? between soul and body, there Shiyao kind of association? between justice and evil, do only simple right and wrong? When the dead hero, becoming a zombie activity, how should the people face? When all people are found, you have a brilliant presence, they suddenly discovered that it was just a beautiful misunderstanding, NA me there is still Shiyao value?
I read the one-eyed ghost volume bears a just broken volume , then the flag of the volume read from the nether one eye cut off the volume, this book makes the ideas of their own frustration. Qiu ghost book, on the last page, there exists beyond the reality of the dream screen, a matter of unlimited periods of accidents.
drunk bat's reflection of the place. As a member of the souls of song and dance continued to expand, gradually towards the climax of the story, the works of drunk bat that I am looking forward to this.
Peach Jiro wrote cruel fairy tale card . Jie Li Wu Yi blend of magic, Taoism, martial arts, citing a number of lessons from the myth of the system, creating a style of rigorous background setting.
world surging, turbidity combined sewage, Wu Yi dressed, aloof from the world.
black clothing in the cultural heritage has a profound knowledge, it is difficult to match the advantages of others, Wu Yi also praised the commentary text.
black clothing if Ukraine is a Maundy's aloof from the world Canglang, NA me Tu Qingfeng hair white overnight, the situation is not broken off the road very situation. silent rain, the big burst to start the sixth Ji Wenming, an attempt can only say that integration of multi Mo rain set in a furnace.
say rain on the silent way, the power sub-scattered power flocculating coke, which is the trade-off way.
Weiyue officials far away in the quiet before the bandits to create a very heterogeneous classical bandits, a Water Margin Yangsan Fei Qi can not think of, but also set off some storms today, it really is the rivers to the east, the stars participate in the Big Dipper. Speaking of Water Margin bandits, black belly these days write But my favorite is Master Lu Boxer rogue, there was a small B Prodigal Boxer Yan is also good.
ichthyosaur has not changed earlier, it seems that the frequency is to begin only after a serious look, only to see to set the front seven, and then began a long Jiaoxin wait, impermanence Old Wei's character seems much better than good on somebody!
cold drill write turning point from the overall conduct of the plot to look critically at the time, people feel there is not smooth. But the pen force cold description of drilling can be considered powerful. rely on the technique of writing romance, fine plot, arouses sympathy and affection of the few female characters, writing a wealth of interesting, Diaozhu a bookworm's appetite to help College. Although the structure is not complete, but rather rely on considerable interest, is still the red half of the sky.
the other half of the sky is the Laozhu wrote funny people insipid. But behind the development of Sichuan purple classic but very unexpected, prodigal son, Jesus really Sweet Basil?
purple Sichuan description may be a good war, but it is truly wonderful place, but look him finally from the Laozhu characters described by start. When the story to gather up the tension, role conflict of interest because of each other, and natural emotions, and Laozhu characters so alive.
people live, purple River transformed into a truly difficult people Sichuan purple homes.
addition, Dark River except incisive comments, but also wrote a number of colleagues papers, including a very funny ending.
said people lived, thought of the Ming Mei's even the thought of a go, see Ming Mei's writing in many years tirelessly, melting the Zoran excellent calligraphy. When Ming Mei Tse particular description to the Philippines died that moment, I can not help but eyes were moist.
Ya Later is music in Italy write is a round of applause and the achievement is not directly proportional to the book. In short, I very much appreciate the reflection of the book Star.
Tigers go back to talk about writing to his charm, but escaped from the arena after the Tigers down the book as if it began to flaunt an intense vigorous momentum bite people. Whether fort conflicts have blitzkrieg cavalry, combat arms grams each, the river channel war, etc., all are stunning to see, dazzlingly, and political struggle under the table, multi-line interlaced ruthless battle of wits, it makes for an imminent plot, give birth to a confusing feeling.
History of Continental hegemony, Chen tears after the robbery alone, the war in the intertwined with blood and tears, to see who is dead than the more tragic death, tragic death.
『life and soul of honor, cemented in blood Narcissus The emblem! 』This is my new moonthe emblem, the achievements of a legendary Jagged family.
gossip sentence, in fact, I have always wanted to see the new moon Titan to write killer exposed, and the unknown killer, Oscar was a mentor to remain in prison.
Corrigan's , the compact is too inadequate, the more the longer the result of writing that is beyond the reach of some of the story. relative to the moon, this is the place to note Swiss roots.
soldiers read the book front to tail echo Changshan side of the snake can run through together, and this truth must understand the root Sweden, between willing and reluctant, I also changed is difficult to make a decision. Jiangshan ending of this book has come to the situation, we see Swiss roots in the .
continental hegemony has never lacked for good works, color coat of arms of the escape evaluation of anticlimactic, but the Dragon King of comedy from the Institute of National Cheng Kung Road hegemony change, to become sub-Ranger style, is quite silent, can be considered big mistake.
mercenary Amy King and his partners story is the sudden emergence of the continent is dominated.
that no master in the temperament are the main features of each. driven by the character story, and then from the story to develop their characters. to control freely the strokes, that really is a fine not master storyteller. a lizard He bought the sacred dragon the beck and call rights, do not lose this sale.
Italy's who do not mind not intended to, but those who understand the meaning that is not good in areas away from their part to create a good story.
Network Knight wrote, YY modes of play to the extreme, so that caused a lot of negative comments. And to a large number of Master Wu is strongly Fans were escorting, kind words hanging by a thread. everyone fighting in the air, forming a not a small storm and Later, a black Ttrce even leads to the , X, foxflame, Barry, Wei Yue and others to speak, I still have some impressions still vaguely.
fact, many negative comments, usually not for the beginning of, but by some irresponsible commentators dismissed. The original of cool to write their own, something that is beyond reproach, but an open reading works on the network, have similarities and differences due to reader experience, naturally there were many discordant voices.
It was originally is not the person, but some of the critics have when it comes to personal statements, and some of the Fans who are unable to tolerate others scorn his idol, the statement would tend to counter the sharp mean, it would make people under fire battle not without regret.
misfortune. spread the words I do not know how long, I still incisive and prophetic.
Review article written in earlier years, most of the people to exchange views, so the point view of solely on the works put forward their views on some of the relative, learn from each other in seeking further tempering across the Internet.
written comments later, back to the post comments, you people are often hot face to cold ass. so for a long time, not write comments.
is not a matter of fact do not understand some of the authors also explore the lack of creative assertive way, for others to hear a lot of the comments, do not know where to go, instead of an understanding of the confusion myself . and some of the most stereotyped, they used to just listen to the book fans say good words, the nerve on the numbness, it was hard to listen to different voices carefully.
look at the small turtle and rich Guinness views as much as possible pick out the strengths of the talk, so slowly, some only occasionally and write a lot of book reviews also relatively modest. That's why when that band who helped organize search of gold, only a few rooms in the essay.
who see gold find . Yudong Lou's the cardinal of the Swordsman chef.
duck knife from the hand of the prototype, it seems from the film
, occasionally I can vaguely see some context Zi Yan Yun Zhongyue and traces of Sima.
handsome romantic aquamarine lot of people think that perhaps the wrong impression from the and blood of three coral pseudonym, he wrote one of the few pure wind of medieval Europe, whether it is written, representative crystal system.
from ordinary to extraordinary, we saw the legendary figure, in fact, will be just an ordinary person, in irresistible fate, he also plagued with, bored with, secretly pleased with. And what is Shiyao kind of factors make a relatively ordinary like you and I like people, become a person beyond the earthly existence, it is worth pondering.
aquamarine of the best features, is depicted in his works social background, culture, people can eleven research source, a brief but not entirely groundless space, after a skilful blend of aquamarine in the following styles constructed with a deep sense of magical realism community. aquamarine at the same time know how to properly excite the highly philosophical dialogue, which enabled him to elevate the level of work a lot of height. However, the distribution of aquamarine in the plot, and sometimes uneven weight status occurs.
Mofaxuetu appeared Simon Enlai Ke generation, and that Simon would think of sorcerer.
magician era of rampant, from the wandering frog write the refreshing of the demon king of the world's birds rampant king of kings, Yue Peng, and his seven brothers and holy.
demon, my favorite is the demon of the.
beard had made the Soviet Union, no Bamboo makes custom, no demon is the beast? uh, I remember correctly you?
forget that, 话不投机半句多, we disband the.
heard that the demon has been called Half Human , NA me who has the demon of what should be Shiyao? Then I saw the The Heavy wind and rain can not help mentioning the just think of bombs, gospel, and other five-star masterpiece.
parties to the later by the Mech flow Xinghai legend. Night of the marks of the Star of the times, across from the fairy magic to the Star, you can understand a toad faint attempt to multi-dimensional ecological systems. But a little toad is not good, every time he opened a new pit, the old pit will vaguely have hastily ending trend. This is a very bad habit, although wood has the palace, but there are nasty greatly.
Xiao Qian wrote pioneer. Xiao Qian and created a wave of comprehension for the series, the good temper, can not offend the author, perhaps in the future have to rely on the local as well Shiyao him. ethereal journey is a kind of simple fun of narrative rhythm, turning interesting but not boring to attract the reader into one, but also to many of the nightmare into the realm of comprehension.
rain like a ghost live in marginal, fall into the unwieldy problem. In the present situation, write to pop out the idea of ​​a creative might.
old crab write , most of which is almost a big hurdle. But the crab is very hard on writing the new book , between the beginning, some abrupt transition, showing that control a large territory is really not easy. bamboo Crow write, Jing Ke Shou same problems.
Jing Ke Shou's Need.
wind of free papers a unique concept, using my words to describe it: 『What is immortal? is inhumane too! cicadas drink dew, I wonder if there is winter. The golden moments, the night she explains Tan. Life BES, time moment. 』Unfortunately, the wind was free articles into a predicament, but no idea came, it is really silent.
for an author, with the most popular words to create a popular story, to the face of the overwhelming majority of the general market. but some of the creators, selfish most want to create, but it is the text of a vast lofty dream. popular and ideas, this is not impossible to reconcile the two, but most require a relatively carefree life or ignore the reader-response self-confidence, this easy to achieve.
pressure in the real environment, many of the swing is inevitable that many artists face the challenge, they can only go by the authors to make their own choice , make a decision as early as possible is good.
Replies few days ago when the written words: drift, interpretation is a wonderful tale, not a bad idea Allure; aloof from the world, the pursuit of meaning is meaningful, and perhaps it can become a classic . choice early as possible, otherwise the more Cuotuo, the more difficult to escape.
is thirteen write were appreciative. just a flawed sense of rhythm, slightly missing the point of soul-stirring description. to look at the reading habits of readers today, this story need to be patient to start the book, is a big challenge, but not afraid of writing a good test Because word of mouth will accumulate.
from the description of the evil Dark Master Wang Xia Ermeng the mentality of the beginning, Xiao Ding launched the Sisters in front of struggling to survive. Although both deep enough, but it is also extremely depressed people can not think of is his over, Xiao Ding still hanging in the air so that everyone flattening, indeed when the vocal! Xiao Ding burned a few days ago, but the book, hair struggling to write, hope to continue to see exciting follow-up!
do not use pick up a pen to write not a life story. but do not use after all, is not enough to calm, although a little more gas channel, but a bit less thick solid condensate.
then again, for a fascinating story you want to run, some interest is still necessary is indispensable. this fair, do not use the temporary soldiers, can be said to have been dominated and shaped the easy trying to balance the road!
I have always love to read books written by Sima Zhongyuan Uncle countryside adventures, artificially low voice from the elderly, began to touch countless generations of ancestors that the odd word of mouth about the strange charm, the children looked attentive listening, one curious eyes, raised several more immature from time to time exclaimed, and Chang Xiao elderly enlightening.
the grassroots culture, perhaps, that is, generation after generation so that has survived.
about culture, they think flat tube tide of the Sin Road dust lightly Tianshi book style, I like this theme, but the beginning of the serial, was not optimistic about it, but the flat tube tide still stuck with it, the success of everyone's glasses off the ground. Xian Road style, great charm of the Ming and Qing novels, although the main line of thin, but the slow second phase in which the paragraph, with the rhyme connected. the book several major male and female interaction, it makes us look forward, but your role is not the average allocation, it is somewhat inadequate. or the old pipe has already made a choice.
read this story as if in a small Shushe tea, lit a pot of charcoal, while cooking the tea, while listening to Dr. Tea, Warren anecdotal gossip. Snow days of sunny, Yun Qing Mei Xiang with some leisurely.
Berserk.C's between half awake, reading a tour of the charm is very Nanke also like to see some of Dali's paintings.
cultural temper reason and strength of character, with this relative, is the blood, the natural flow of passion and indignation. < br> Some of the dramatic rise of blood-red, but not surprising. bloody good writing can be said. Linke he began to write, write rogue, because of the reasons for the choice of theme, but also once been a relatively negative evaluation, but blood-red and this is not depression, but persistent efforts to write the elegant, cunning, sinister underworld godfather, has successfully created a wretched way of Qi Kefu adhere to adults, of course, there are many other roles. Unfortunately, the latter part of the development of Thang Long Road, some pale, this two-day AT sky review fine, even put this point of view, all the three countries with a writer can still compete against them, but then the story may be punk busy writing Go A troubled times.
essence this book, however, there are two major flaw, and one is part of the modern words appear, the other is part of the people close to the demon; the second volume of people after they start feeling some bad to worse Some pity.
e_mc2 the Good article, the reason for the e_mc2 clues hidden in some thinking behind the words. or e_mc2 is by a fictional character, from the time he and the interaction in an attempt to depict the history of the hidden face of another.
write Mengzi The inadvertently opened a corner. leopards Li Hongyi Yue set foot out of the stage of history, as the current situation of the vagaries of the situation Han children, age makes a hero, heroes carry the day, the blood that kill a killing field stroke, and the secret of the political struggles seek painting turns into a huge storm, and promote the fate of everyone!
fictional and the real subject matter, the infinite possibilities that alternative history, and often is worth pondering over. tomorrow's Sun Moon Song Ji begins with a rather impressive, but the story development process, but gradually transcended the expectations of some readers, can only show that has a mind of your day.
the composition of the early Ming era, and both are from the iron and blood , to the resurgence of the figure in a troubled world, and both are generation of outstanding personality. the emperor to kill enemies to kill both the benefactor, and boarded the Throne sword around his waist in the blood of the hero still Lek. In a year of turmoil after the man in the street have not seen ...

2011 college entrance essay college entrance essay material applied water Rao Concert Ten Tips

 2011 college entrance application essay material for a Top Ten Tips
, college entrance essay material application techniques of the so-called reasonable case management patients with
combination, that is, examples and references will be in the composition or the famous principle of combining the specific examples and scientific principle, favorite sayings complement each other to play better effect. particularly in the argumentative writing, the only pay attention to theoretical arguments, but also pay attention to the fact that argument, the fact that you can visually reproduce the scenario, the reference can be enhanced by the celebrity talk the language of the intensity of the second The combination of those commonly used in argumentative writing.
Here we look at two examples:
Edison, right? his eggs in one hand, a hand-held form, ready to put the egg under the pot for five minutes, but he thought is an invention, goes table to vote in the pot, his eyes staring at the egg.
was Newton right? concentrate on an experiment, forget to eat a meal on the table. was deliberately teasing him , to which plate dishes for leftovers as a bone. He was very hungry, come eat, see a plate of bone sighed: > In fact, these two things can not be forgetful, distraction because of their heart, absent-minded ... ...
forget it is not necessarily a bad thing. to take the initiative to completely forget, you need a superior effort was done. person scourge is thinking you can forget the body that is to the realm of ecstasy. And a person only to reach the realm of ecstasy can be a big as.
the text in the paragraph above, around the selection, through the strong reference to the right, the typical accuracy is very convincing. Just imagine, if only cases, or only a reference, there is such a good effect of expression you?
Second, college entrance essay material application techniques of material processing material processing is
universal lingua franca of writing skills in writing, copying material is very small, usually have to write content according to the needs or the needs expressed, the author has mastered the material for processing, so that the material from the original processed to become the subject of the article. And in the drafting process, usually the processing of materials to achieve two purposes: One is to center around the topic and, second, to properly express the feelings of. In other words, the elections given the phenomenon of material life, and reading to get the written material, to remove the part with the title has nothing to do, and tend to inject their own feelings.
Here we look at a process before the material:
remember one time, in the relatives to eat, I feel very good to eat sweet and sour fish burned to casually said one, I said: bought two fish from the markets, busy burning sweet and sour fish, even enjoying themselves too tired sweating.
Here is the scene after processing:
last Spring, I grandma house eat. sweet and sour fish to put in front of me, that feeling tempted me, knew it, I had sweet and sour fish perish! wait aware of this point, I blushed like Guan same. mother broke the awkward silence: you do. The sweet and sour fish definitely spoiled.
at home, Gang Daojia door to door in the rains of that familiar, seductive fragrance. I really do not want to go, I'm afraid my tears do not live up to expectations ! I really do not want to go, because my guilt and selfishness! I really do not want to go, because the mother's sweet and sour fish with a body temperature above the material ... ...
processing manifested in two aspects: First, the real bottom in the arts Kung Fu, to buy fish, broiled fish, set the scene. The second is described in detail the work up and down, not only meet the real dialogue of life, but also people's mental activity. In this way, maternal love for the true performance of a more specific and more intense .
expression in the reference material in order to better support the argument, we need to elaborate on the material from the language processing, the material looks dull, shiny. Please compare the following segments.
( 1) Li Bai paths of made me impressed. missing fair to say though, I still feel the hardships of Li Bai's life on the road is bumpy though, but he believes his vision will be achieved, as he said I'm Born with a With dance Nong Ying Hui month, ;, his chant with great boldness of vision, so the addition of Datang's landscape a bit heavy on the history, the Smart air! is enough to say that no career as Li Bai did not reflect their value? not.
the above cases (2) ratio (1) to vivid image of being more. which is mainly of (2) when dealing with multi-material description and imagination to the same material to a new level.
three , college entrance essay material application techniques applied the combination of parallelism
material in the . Here the word that seems endless, material enrichment, justifiably, to achieve good rhetorical effect. In combination, concise language to note neatly arranged in the order of the rational (such as chronological, from far to near, from primary to second-class ).
such as the following example:
south, is the resting places of your heart
How many people here looking for ages to the end of life. legendary woman San Mao, a few years of wandering, the hair on the dip of the What wind there, she will be a cry to the south, like to see a kind old grandmother, she finally found a life where you can stop the heart. Jiangnan businessmen Shen mountains, after shopping the ups and downs, the last remains settled in Zhouzhuang water, not fight for fame. Literati still unnamed hermit, perhaps they also want to pass the examination, career proud. and then day after day, intrigues, Gouxindoujiao, and finally make them tired So they packed up their bags. to the south and died in Sri Lanka. (excerpt from 2006 paper out of college entrance essay, Zhejiang are typical examples, one is wandering in the San Mao, one is regarded as the southern end of life, even showing the South's beautiful. This is of course a single example can not be achieved.
combination of the alignment will be of similar material, both in point of view has increased efforts to enrich content, but also in language shows a momentum, showing a certain amount of literary talent. This method of timber, is the result of subjective selection, processing, and the kind of disregard for the needs of the content or practices of the pile material is completely different.
four, college entrance essay material application techniques of survival
entrance to avoid the familiar outline of Writing the era of view, may not belong to the new material, but because people know little or not much used, and thus has considerable freshness. But in fact, college entrance essay material aging is a serious problem, always, is sometimes combined with the article, as do the song for the Poems. traditional materials can of course, but the material will give readers fresh surprises.
students write one to People's material, but the characters will be moved to China that year - Baoshan City, Yunnan Province Public Security Bureau deputy director of the Ming Bin examples are included in the article:
Baoshan City, Yunnan Province, is Bin Ming, deputy director of the Public Security Bureau, the sword, tip the dancers, in the forefront of anti-drug front has experienced death in the face numerous times, has experienced numerous symphony of iron and blood. In front of drug traffickers, he threatened not afraid to buy fixed, beat; drug traffickers in his men, go through, can not hide, no escape. because he and his comrades, in the test before the Tingde Zhu, stand straight and carry the move out, so we can enjoy the fresh air, bright sun.
Such cases, close to reality, strong sense of the times, very happy.
five, college entrance essay against the background of the contrast material application techniques demonstrated positive and negative
argumentative writing argument is demonstrated in two ways. When you are sure After the argument, we must use the arguments to prove your argument is correct. Comparative study method is both a demonstration, but also a method of application materials. It is a commonly used method of convincing arguments. contrary to nature The two things to control, compared to derive the differences between them, enabling the conclusion against the background out of the can to persuade the reader to make the points clear of the highlights. because of the character and nature of things most easily revealed in the comparison out, in particular, positive and negative things against each other compared to the distinct nature of great, can leave a deep impression. by contrast, the right of the stronger arguments. ancients said: ;, a comparison between positive and negative, people will discover the truth more clearly, and understand the essence of things.
such as this to say: Beethoven pulling away from the hustle and bustle of earth, enjoy the music of the country where the jump; Curies abandoned the fame of the troubles in the world of science has taken a more far-reaching steps; Tao forget the darkness of the secular, in a free leisurely taken in the Chrysanthemum Nanshan their lives easier ... ... wander, sniffing the fragrance world. but not in Cove is bound sets of secular yard, Grandet was towed to the death of money around, they do not easily run the full, final turbidity was involved in the secular ... ... (from the entrance out of the text
we are faced with the same topic, can always find positive and negative aspects of the character material, the use of Contrast these two figures together to make a thorough comparison, superiority and inferiority, good and bad, beauty and ugliness will naturally be more distinctive prominent. This method can be widely used in the writing of various articles.
six, college entrance essay material application techniques New Stories
topic composition of stories allowed, the use of classic, etc. Stories need to select the theme of characters, plots for some reform, the formation of new stories, characters are changed little, largely maintain the original style. Such stories not only to avoid making things up nonsense, but also in the context of the new era of the story increase the number of interesting, it is like to read.
Consider the following example:
yu Union really touching, can not I Dream of plotted out, I also pursue their own love it! When gem beaten, I do not have true feelings it? but Lin's eyes red and swollen that her sister won the sympathy of everyone, people I naturally ignore it. Changeling account provoke condemning me, who knows when I can hear the gem bang Baochai Idealists name of the relevant materials used for writing the examination room the center of their service is invaluable.
seven, college entrance essay material application techniques of extended material
the memory of our material lives, mostly in broad, simple lack of full details of the rough, often in the use of the time be extended. nothing more than specific methods to expand the plot and add details to make stories of flesh and blood, and more conducive to the performance of the theme and the author's thoughts and feelings. our modern occasional famous writer Zhao I heard militias in the liberated areas, a small village in the village with a girl captain and free love, the results were both beaten to death by stoning villagers love tragedy, flying imagination, embellished the story, for a reasonable expansion and transformation, so there will be a famous novella state of mind of care, such as a presentiment of joy, according to topic, subject, follow the inherent laws of life, triggering associations, or additional extension, or embellished, enrich and develop, so commonplace events are brilliant.
2003 college entrance examination excellent composition, Hebei Province, small, relatively thin characters. In the essay, the grandson of candidates confused as to shape the main characters, as he added a lot of psychological description: the wife of the United States, one side is nagging at the ear doctor day, my heart began a long weighing balance. snake woman; Why should I exile my 'Sanlv', the loyal patriotism of the Magi exile! I will never forget Chodo figure, he walked away, I will never forget his tears hanging at the corner of affection ... ... Wang contradictions mind, heart, repentance, the point to understand the In some cases renovation
old classics, some well-known characters and stories, there are a large number of ancient fable. These materials are often frequently described by the candidates out of the entrance, a college entrance essay material in the ;. These are the people learning to use the material, due to too many scoring opportunities for teachers to meet, it will produce fatigue. If the use of these contents neatly in his article, and give new ideas, can the impossible. This kind of New Biography, and modern time-honored characters and stories, but also those that often appear in articles and college entrance essay into the general has long been widely used material. or because of well-known, too ; vulgar read the classic works and popular books, but also exposed to film and television characters, or examples (moved Chinese characters, etc.). In general, these materials are Well, it will be difficult to achieve a unique and fresh expression of results. college entrance essay if the frequent use of these old cases, it may cause expression of the ills. Basically, candidates should select fresh ingredients, including from the time point is the recent events, from the space point of view what is happening around us, these are new for readers of material. But when we find than fresh material, and transform the old material, it would have a justified the Wu dip solution, the more the country to death who is? ; the model. the use of the old cases refurbished method has its unique advantages. at least two advantages: First, the old cases of many, for us to calmly choose; two old cases of people familiar, easy to accept, at the same time, after the transformation of the old cases and melt into the unique personality and creative spirit, to give fresh, can flash of wisdom.
nine, one of college entrance essay material application techniques of writing materials and more argumentative with
, most of the students suffer no material available. In fact, we We have saved a lot of head material, but why would worry about it for the lack of material? Here is a very important issue, is that some students do not make efficient use of their possession of the material, not good for a multi-purpose timber. As things their colorful, a good material is always three-dimensional, with diverse properties, together with different people with different understanding of the material and shows a different point of view, therefore, the same then the material can often dig out a few different point of view. such as buried for decades and shame. to old age, national crisis, was the committee in the important task of the state of Qin mission to save the country's crisis.
② Maxima need to discover and foster horses. Maxima is Zhu Zhiwu, Bole Lost is the solitary. Without the lone pair Zhu Zhiwu Lost the full understanding and strongly recommend, Zhu Zhiwu vertical display how much talent there is no chance.
③ the overall situation, national interests above everything else. Zhu Zhiwu young is not reuse, hard to avoid grievances and discontent, but the national crisis, he does not count personal grudges, decided ambassador Qin.
④ responsibilities are afraid of people, tolerance towards others. the face of the complaint Zhu Zhiwu, Bor not showed no resentment, but deep remorse, and even said Strategists with the Warring States Period, the alarmist not the same, Zhu Zhiwu the diplomatic euphemism twists and turns, there are just soft, string, a sound. in today's market economy, the significant increase interpersonal communication, rhetoric of poor people will not find own place.
a multi-purpose timber can be, but first have to have analytical mind, it may be found from the same material bears a different meaning. At the same time, the use of copied material is not intact, but according to the different points of view need for certain trade-offs, in the narrative to highlight and strengthen and opinions related to the place, and other related content can be in passing. If we can do a build multi-purpose, then a material can be demonstrated in several different views to illustrate a few different problem, then the minds of the students will be doubled inventory of materials, no need to worry Piper bounce the opposite point of view to establish the new point of view, to the elucidation of new ideas. For a material, if we consciously use this way of thinking will allow us to create a new realm of composition, received a surprise move effect.
not red, near Mexico are not black may not be as interested in Pipa, thinking, courage from the traditional ideas of liberation. Su Shi's poem: too much influence by the environment, people will form a habit of thinking of the fixed pattern, which makes the multiple properties of things and its true colors do not know. This mode also often governed by a certain mode of people to solve the problem , despite the sometimes puzzling questions, or solve problems that effect is not significant, but because he thought it was well placed to exploit, so I do not think change. However, at this time if the use of reverse thinking, ;, things will be disseminated in the long jump out, resulting in scientific justification, contrary to common people and hurt the feelings of the people the traditional concept, it will be difficult to endorse.
When you write the conventional idea of a full of personality!
2011 College Entrance Language Reference (145) Guangdong Guangya Middle School entrance exams such as the three schools in February, Shijiazhuang City, the first semester of the 2010-2011 school year, first year final exam high Important: guard against false information in 2011 winning College Entrance Examination Reference (145) Guangdong Guangya Middle School entrance exams such as the three schools in February, Shijiazhuang City, the first semester of the 2010-2011 school year, first year final exam high Sina BLOG feedback message board About Sina SINA English

Olympic coach voted via SMS

 Olympic coach
voted by SMS text / grapes are sour
Ah you know the Chinese Football Association will launch the , nonsense reporter rushed to attack, related to the Chinese Football Association charge for an exclusive interview.
Reporter: China Football Association after a miscarriage in the Xuanshuai plan, not the beginning of the pregnancy you Xuanshuai program again?
Football Association: Yes , the former England coach Glenn Hoddle calls wings fan here, just from Porto, Chinese Football Association of discernment.
Q: Why do not Jiangzai pregnant were in the end?
Football Association: The reason is simple, abortion is no immunity, in other words, we fear another miscarriage, abortion, you should be clear that China can not afford Football the.
Reporter: China Football Association fear Xuanshuai plan What is the reason abortion again?
Football: Quite simply, we and the last, like always not clear who in the end the love.
Reporter: Is it possible This understanding, for the first time the root cause of abortion is the Chinese Football Association not sure who they like.
Football: You can say, from our promises to let the new coach of the Olympic site observation Toulon Tournament, to the flag of the World Cup are Yan interest rates, but also, and Wilkinson house on fire? of course, the old lover Horton, confidante Crow Chen, and why? is not clear who in the end the love.
Reporter: start great audition coach is what the original intention?
Football: China comes just a Xuanshuai plan is no longer abortion in order to prevent future tragedies, to Chinese football tomorrow, we decided the way to a new selection of Olympic coach.
Reporter: You can pick a simple activity introduction to you?
Football: Central Television will assume the task of selecting and coach, this will launch a fusion of . audition draft model will be successful from home and abroad, which lasted 12 months, is expected to draft around the end of next September, is divided into preliminary, Zhou race, Season three. The show will start in September on a global scale select the right players, is expected to questionnaires and interviews by 100 participants will be selected in mid-.9, trials will be broadcast in prime time slots, there will be 20 finalists the last game of the week to accept the judges and the audience judge. more bad than anyone else.
Reporter: What are the characteristics of
audition Football Association: participants regardless of their occupation, men and women, all aspiring to become the Olympic coach who are placed in the same starting line. by Heat players will be professional packaging, to participate in the interactive program According to the Internet and text messaging support for click-through rate and assessed with reference to the views of professional coaches decided to coach the ownership position.
Reporter: What do you think audition positive significance? can achieve the desired objectives?
Football: Despite the trials a strong business atmosphere, but the activities of the Chinese Football Association coach draft a universal fundamental purpose is to create an atmosphere of participation in sports, which launched in the country before 2008 that the sports boom worldwide. Let the world know football, soccer to China to The world is the purpose of this event.
We believe that the majority of the audience through SMS, Internet voting broad participation in the TV show, we can help us to elect a talented coach requirements.
Reporter: audition in several Division, the differences with the civilian draft?
Football: audition will be divided into Asia, Europe, Africa, America, Oceania and the five Division, continental level by the central television station in a joint television co-production, you need to emphasized that, this is not similar to the special significance is related to the future of Chinese football.
Reporter: countless eager to : After a miscarriage Xuanshuai plan after bitter experience, we believe that Olympic coach's role is very special, do not need excellent coaching ability, expect a coaching experience in Asia or have experience in teaching people to teach the World Cup is extremely non- reality, this selection of less demanding, candidates can not ask for much as long as the annual salary.
reporters: > FA: Yes, as of now, Coca-Cola and other companies have expressed their letter the desire to become sponsors, is expected to exclusive sponsorship rights for this program will be worth over 2,000 million dollars. The name can be like What it means?
Football:
1. direct support to the Football Association to register registration information (contact: X Miss, Tel :010-250250); 
3. by letter sent to the Chinese Football Association, (marked interview with this newspaper, in one word as your interview, please
Football Conclusion: you want to be the Olympic coach? Chinese Football Association gives you such an opportunity to select from the vast sea of the world, a representative of China's Olympic coach. Opportunity knocks but once, the heart as action, you Ah so what.
Disclaimer: non-authenticity, pure entertainment

Digging treasure the experience of small talk

 We would first like to say hi! My interest since gone after the upgrade! Obsessed with digging treasure! Now every night every day, dig dig ~ ~! Dig eyes sometimes have spent ~ ~ it just to wait for six characters ( create a copy of the success)
There are many posts that are digging treasure! I could not watch it! In my experience I can talk about it! and share with you! I am now 85 from 80 dug Mingjiao ~ Now! area in the figure rose from the 2J 3.50J ~ now closed graph, then if you are like me, 3J ~ treasure those guys every day, digging victims prices! good! long story short! Here I talk about my experience it !
first closing figure! not figure how to dig ah! because I dug every day! famous for! hit map that people who make money often contact you! you add them all to establish supply relationships friends! you an on-line they ~ I pull on to supply general warehouse full of all income received ~ warehouse is also full to prevent digging to sad about not figure out! figure a lot of fight to get it! now!
then the material is also full of boxes! I get 10 Resolution ~ Souls to play well to get the key! then the figure compiled from near to far ~ ~ a line all lined up!
personal experience with three of the important points!
first! eg ~ a 4 Zhang map in the South! you dig into it the first time a copy! attention next time you're out of time not to go somewhere else! and go directly to the South China Sea dig! this again into a high chance! One time I even enter 4 times! not bragging! to enable people to pull cool! I mean to say into the copy in the same area! Next time, keep on digging it!
second! hit the keys on! I think there is a skill! One day I dug! into the copy is a 5! I gas ah! to having a bit of skill! lest go on like this die ah! I also dug a secret treasure master asked him what experience? he say you ran into a copy of the stairs there ~! first mobs killed the first! you ran stealth dismount! got left out the first mobs! that two go! I think this is feasible and me ~ own set of experiences that when hit master ~ 4 / 1 blood when I ~ wild skills base and BB groups put the final! out of the 2 key is also very high ~ 80%
third! to open the box! their 2nd floor of the box says more than a book! I also like to open 2nd floor! to the top of it! but also on the 2nd floor when the total not to book you! I am now looking to open display! 2, more than if I put the box open! by the stairs that! well as the most over there 2 ~ the best book out! 1st floor by the stairs where I think it is as if there is a corner stone portrait to open that box was also high probability!
good write so much! We looked tired ~ on to here! meet the bridge south of Telecom ~ ~ leaf by Xuan