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Reprinted from 504443985 at 17:42 on February 19, 2011 Reading (loading. ..) Comments (0) Category: the other side
【High School Mathematics, all, the formula】 .. high school math theorems large concentration of f (x2), called f (x) in D is a decreasing function
(3 ) parity
the function f (x) within the definition of any one of x, if f (-x) = f (x),
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if f (-x) =- f (x),
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(4) periodic
the function f (x) within the definition of any x,
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男人的深度 - Qzone日志, so f (x + T) = f (x), called f (x) is a periodic function (1) Score Index Score Index of power is power of
negative score meaning is the meaning of power indices is
(2) of the nature and number of algorithms
loga (MN) = logaM + logaN
logaMn = nlogaM (n ∈ R)
exponential function logarithmic function
(1) y = ax (a> 0, a ≠ 1) is called exponential function
(2) x ∈ R,
“女朋友”到底是什么？ - Qzone日志, y> 0
image through the (0,1 )
a> 1 时, x> 0, y> 1; x 0,0 1
a> 1 时, y = ax is an increasing function of
0 0, a ≠ 1) is called the logarithmic function
(2) x> 0, y ∈ R
image through the (1,0) ;
a> 1 时, x> 1, y> 0; 0 1, y 0
a> 1 时, y = logax is an increasing function of
0 0, a ≠ 1)
with 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) general formula of the series an = f (n)
(2) series of the recurrence formula
(3) series with a general formula of n items and the relationship
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 a geometric G2 = ab
m + n = k + l aman = akal
inequality inequality basic properties of important inequalities
a> bb 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 b> 0, c> d> 0 ac 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 0 (or a-b 0, to permit a> b, only need to prove that,
to permit a 0, b2 = c2-a2)
eccentricity
alignment equation
focus radius | MF1 | = ex0 + a, | MF2 | = ex0-a parabola y2 = 2px (p> 0)
focus F ;
equation
alignment axis translation
where (h, k) is the origin of the new coordinate system in the original coordinate system coordinates.
1. a collection of elements each with the opposite ###### 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 mathematics Summary
a concept, function
1, if set A has n elements, then set A subset of all the different number to all non-empty proper subset of the number is.
secondary function of the image axis of symmetry equation is, vertex coordinates are. Method of Undetermined Coefficients of the analytic quadratic function, the analytic expression of trying to have three forms, namely, and (vertex type).
2, the power function, when n is a positive odd number, m is a positive even number, m 0, = 0, 0);
sector area formula:;
cone side expansion plan (sector) of the central angle formula:;
round table side expansion plan (fan ring) of the central angle formula:. through the cone vertex
area of the largest cross-section (cone of bus length, shaft cross-section angle is θ):
XI, the proportion of several properties
1, proportion of basic properties:
2, inverse theorems:
3, more than Theorem:
5, combined ratio theorems;
6, percentage Theorem:
7, combined percentage theorem:
8, division and more than Theorem:
9, geometric theorem: if, then.
second, composite second radical simplification of
When is a perfect square, the radicals of the shape-ju's more convenient to use the simple formulation.
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 and false non-p
false true
II. Function
1. Quadratic function of the pole coordinates:
function vertex coordinates
2. Monotonic function:
in the Department of the extreme value
3. Parity function:
within the definition, if, for the dual function; if 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 angle or isometric angle equal to the same
4 or isometric of the complementary angle equal
5 and only a little over a straight line and known outside the lines a little vertical
6 straight points connected with straight line segments in all, the shortest vertical segment parallel axiom
7 After a point outside a straight line, and only a straight line and this line parallel to the
8 If two lines are parallel and the third line, these two lines are parallel to each other
9 Tong Weijiao equal, the two straight lines parallel to the
10 are equal in the wrong angle, the two straight lines parallel to the
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
14 straight line parallel with the adjacent interior angles on both sides of the triangle complementary
15 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 is equal to 180 °
18 Corollary 1 right triangle the two acute angles of more than
19 Corollary 2 each triangle and it is not an exterior angle is equal to two adjacent interior angles
20 an inferences triangle exterior angle is greater than 3 and it is not adjacent to any one of the 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 of Justice (ASA) had two horns and their corresponding folders sides equal two triangles congruent
24 Corollary (AAS) with corners and one corner of the same on the opposite side of the two triangles corresponding to the whole Collage side of justice and other
25 (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 equal the whole Theorem 1 and other
27 split line in the corner to this corner point equidistant from both sides of Theorem 2-1
28 angle from both sides of the same points in the angle bisector
29 angle to the angle bisector is equidistant from all points on both sides of the set of
30 isosceles triangle isosceles triangle theorem of the nature of the two bottom corners are equal (that is, on the other side isometric)
31 Corollary 1 isosceles triangle the bisector of angle and split the bottom edge of the bottom edge of
32 perpendicular to the angle bisector of an isosceles triangle, the center line of the bottom edge and bottom edge of the coincidence of high mutual Corollary 3 equilateral
33 The angle of the triangle are equal, and each corner of the isosceles triangle is equal to 60 °
34 Judgement Theorem If a triangle has two angles equal, then the two angles on the sides of the equal (equiangular, etc. side)
35 Corollary 1 the three angles 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 a acute angle is 30 ° so that it is equal to the hypotenuse of a right-angle side of half
38 right triangle hypotenuse hypotenuse is equal to the middle half of
39 Theorem on the axis line segment and this segment of two points endpoints are equidistant
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