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Reprinted from 794415719 at 22:55 on September 14 2010 read (loading. ..) Comments (0) Category: Game of Life
three Jinnian Xin (xīn) c a water study Miao (miǎo) read the three fire Yan (yàn) read the three soils (yáo)
read three cattle (bēn) three hands read (pá) read the three projects (mò) three field study (lěi )
three horses read (biāo) read the three sheep (shān) read the three dogs (biāo) three deer study (cū)
three fish study (xiān) read the three beta (bì) read the three forces (lie) read three vellus hair (cuì)
; Three ear read (niè) three cars read (hōng) read three straight chu (chù) read the three dragons (tà, dá)
Three of the original concept (yuán) three mine-read (bìng) three fly read (fēi) read three knives (lí)
; three and read (ruò) three persons read (zhuàng) three small read (mó) three sub-concepts (zhuǎn)
; three only read (sè) three wind read (xiū) ; three Falcon read (zá) three Kyrgyzstan read (zhé)
Three words read (tà) read the three tongue (qì) Three Hong Nian (xīn) Sangequan read (xún)
Three mind (suǒ) read the three white (xiǎo)
primary to junior high school mathematics all formulas
1, each number × total number of shares = ; total ÷ number = number of copies of each
÷ total number of shares each
= number of
2, 1 × multiple times = number of times the number of ÷ 1 times multiple = multiple
times the number of times = 1 ÷ multiple
3, speed × time = distance speed = distance ÷ time
time = distance ÷ speed
4, unit price × quantity = total ; unit price = total ÷ number
÷ total number = unit price
5, the efficiency of the total work × hours = volume
÷ efficiency = total work hours
÷ total hours of work efficiency
= ; 6, addend + addend = and, and - another one addend = addend
; 7, minuend - subtrahend = difference minuend - subtrahend = difference ;
subtrahend = difference +
minuend
8, factor × ÷ Factor = Product product = Another factor
a factor 9, dividend ÷ divisor = business = Business dividend ÷ divisor
provider × divisor = dividend
Primary School mathematical formula graphics
1, square: C perimeter area of a side perimeter S = side × 4C = 4a
area = side × side length S = a × a
2, cube: V: Volume a: surface area = edge long edge long edge long × × 6
S table = a × a × 6
Volume = length × edge × edge long edge long V = a × a × a
3, rectangular:
C perimeter area of a side length S ; perimeter = (length + width) × 2 C = 2 (a + b)
area = length × width S = ab
4, rectangular
V: Volume s: size a: Long b: W h: high
; (1) surface area (length × width × height + length + width × height) × 2 S = 2 (ab + ah + bh)
(2) Volume = length × width × height V = abh
5, an area of a triangle
s high end of h area = base × height ÷ 2 s = ah ÷ 2
triangle = area × 2 ÷ high end
; triangle = area × 2 ÷ the end of high
6, parallelogram: s area of a high-end h ; area = base × height s = ah
7, Ladder: s area of a base b on the h following the end of the high
area = (base + down on the bottom) × high ÷ 2 s = (a + b) × h ÷ 2
; 8 round: S surface perimeter Π d = diameter of C r = radius
(1) circumference = diameter × Π = 2 × Π × radius ; C = Πd = 2Πr
(2) area = radius × radius × Π
; 9, cylinders: v volume h: high-s: basal area
r: radius of the bottom c: bottom perimeter
; (1) side of the area = circumference × height bottom
(2) area = side area + base area × 2
(3) Volume = base area × height
(4) volume = side area ÷ 2 × radius
10, a cone: v s bottom area of the high volume of h
r the radius of the bottom volume = base area × height ÷ 3
÷ total number of shares =
average
and differential equation problems
(and + poor) ÷ 2 = large Number
(and - worse) ÷ 2 = decimal
and times of problems and ÷ (factor -1) = decimal
; decimal × multiplier = large numbers
(or with - decimal = large numbers)
difference times the difference between the issue
÷ (multiples -1) = decimal
; decimal × multiplier = large numbers
(or decimal + SD = large numbers)
planting questions
1, non-closure of the main line of the tree planting issue can be divided into the following three cases:
⑴ closed if the non-tree planting both ends of the line, then:
; number of trees = number of segments + 1 = length ÷ spacing -1
; length = spacing × (number of plant -1)
spacing = length ÷ (number of plant -1)
; ⑵ If the non-closed end of the line to plant trees, not planted the other end, then:
number of trees = number of segments = length ÷ spacing = spacing × number of trees
full
spacing = length ÷ number of trees
⑶ If both ends of the non-closed circuit Do not plant trees, then:
number of trees = number of segments -1 = length ÷ spacing -1
length = spacing × (NUMBER +1)
spacing = length ÷ (NUMBER +1)
2, tree planting on the closed circuit between the number of issues are
number of trees = number of segments = length ÷ spacing = spacing × number of trees
full
spacing = length ÷ number of trees
profit and loss issues
(profit + loss) ÷ volume of distribution of the difference between the two = participate in the distribution of shares
(large surplus - a small profit) ÷ = twice the difference between the amount allocated to participate in the distribution of copies
(burned - a small loss) ÷ = twice the difference between the amount allocated to participate in the distribution of shares
encounter problems
meet the speed and distance = time × met
encounter time = distance ÷ speed and
meet the speed and distance ÷ = meet meet Time
catch problems
distance = speed chase and chase and the time difference ×
; recovery and time = distance ÷ speed chase and the velocity difference = difference
chase and chase and the distance ÷ time
downstream water problems
hydrostatic speed + speed = flow velocity
hydrostatic upstream speed = speed - the speed
hydrostatic flow velocity = (speed + upstream downstream speed) ÷ 2
flow rate = (downstream speed - upstream speed) ÷ 2
the weight of the solute concentration problems
+ solvent = solution of the weight of the weight
÷ solution of the weight of the solute weight concentration × 100% = weight × concentration solution
= weight of solute ÷
concentration of solute = solution of the weight of the weight of
profit and discounts
profit = selling price - cost
margin = Profit ÷ Cost × 100% = (selling price ÷ cost -1) × 100%
; Change Change amount = principal × the percentage of the actual selling price = ÷
discount the original price × 100% (off <1)
Interest = principal × rate × time
after-tax interest = principal × rate × time × (1-20%)
length unit conversion
1 km = 1000 meters 1 meter = 10 decimeters
1 decimeter = 10 cm 1 meter = 100 centimeters
; 1 cm = 10 mm
area unit conversion
1 square kilometer = 100 hectares
; 1 hectare = 10,000 square meters
1 square meter = 100 square decimetres
; 1 square decimeter = 100 square centimeters
1 平方 cm = 100 mm
body (content) product unit conversion
1 cubic meter = 1000
1 cubic decimetre cubic decimeter = 1000 cubic centimeters
1 cubic decimeter = 1 liter
1 立方厘米 = 1 ml
1 cubic meter = 1000 liters
Weight unit conversion
1 ton = 1000 kg
; 1 kg = 1000 grams = 1 kg
1 千克
RMB unit conversion
1 dollar = 10 angle
; an angle = 10
1 dollar = 100 cents
time unit conversion
1 century = 100 years 1 year = December
big month (31 days): 1 3 5 7 8 10 December
Satsuki (30 days) were: 4 6 9 November
; average year on February 28 days, a leap year on February 29 天
-average 365 days a year ; leap year 366 days
1 day = 24 hours 1 hour = 60 points
1 min = 60 sec 1 hour = 3600 seconds
Primary Mathematics geometry perimeter area volume formula
1, the rectangular perimeter = (length + width) × 2 C = (a + b) × 2
; 2, the perimeter of the square side length × 4 = ; C = 4a
3, the rectangle area = length × width ; S = ab
4,
la gear originals, area = side of square length × side length S = aa = a
5, the triangle area = base × height ÷ 2 S = ah ÷ 2
6, the area of parallelogram = base × height ; S = ah
7,
la gear sale, trapezoid area = (base + down on the bottom) × high ÷ 2 ; S = (a + b) h ÷ 2
8,
la gear womens shoes, diameter = radius × 2 d = 2r ; Radius = diameter ÷ 2 r = d ÷ 2
9, circumference of a circle = pi × pi × diameter = radius × 2 c = πd = 2πr
10, circle area = pi × radius × radius
common mathematical formula
1 junior high school had two points and only a straight line
; 2, the shortest line between two points with the angle or isometric
3 of the supplementary angle equal
4, the complementary angle with the same angle or isometric
5 had a little one and only one line and known straight line perpendicular to
6 point outside the points connected with straight line segments in all, the shortest vertical segment
7 point outside a straight line through the parallel axiom,
and only a straight line parallel with this line if two lines are
8 and a third line parallel to the two lines are parallel to each other
9 Tong Weijiao equal, the two straight lines parallel to the
; 10 to the alternate angles equal, two lines parallel to the
11 complementary with the adjacent angles, two straight lines parallel to the
; 12, two parallel lines, 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 theorem of complementary
15 and greater than the third side
16 inference on both sides of the triangle is less than the third side
17 angles of a triangle and the three angles of a triangle theorems and is equal to 180 °
; 18, Corollary 1, each triangle of the two acute angles of more than
19 Corollary 2 an exterior angle of a triangle is equal to and It is not two adjacent interior angles
20 Corollary 3 the triangle exterior angle is greater than any one and it is not adjacent interior angle
21, the corresponding sides congruent triangles, corresponding angles are equal
22 corner edge axiom (SAS)
both sides and their angles are equal to the corresponding two triangles congruent angle corner axiom
23 (ASA)
folder with two horns and their corresponding equal sides
two triangles congruent 24 Corollary (AAS)
had two horns and one corner of the same on the opposite side of the two triangles congruent corresponding
25 Collage justice side (SSS) with the corresponding three sides of equal triangles congruent
26 hypotenuse of two right-angled edge of axioms (HL)
beveled edge and a right-angle equal to the corresponding two triangles congruent
27 Theorem 1 In the angle bisector of a point to distance both sides of this angle is equal
28 Theorem 2-1 the same distance on both sides of corner points, in this corner bisector
29 angle to the angle bisector is equidistant from all points on both sides of the set of
the nature of the isosceles triangle isosceles triangle theorem of 30 two bottom corners are equal
(the other side of the equiangular)
31 Corollary 1 angle of the bisector of an isosceles triangle split the bottom and perpendicular to the bottom of the
32 isosceles triangle the angle bisector,
la lights, the bottom edge of the middle and the bottom edge of the high overlap with each other
33 Corollary 3 corners of an equilateral triangle are equal, and each angle is equal to 60 °
; 34 decision theorem of isosceles triangle has two angles of a triangle if equal,
then the two angles on the sides of the equal (equiangular, equilateral)
35 inference 1 three angles are equal is equilateral triangle
36 Corollary 2 has an angle equal to 60 ° of the isosceles triangle is equilateral
37 In a right triangle, if one acute angle is equal to 30 °
then it is equal to the hypotenuse of a right-angle side of half
38 middle on the hypotenuse of a right triangle 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 can be regarded as equidistant from two end points of the set of all points of Theorem 1
42 symmetrical about a straight line shape
two graphs are congruent 43 Theorem 2 If two graphics on a straight-line symmetry,
then the corresponding point of the axis of symmetry perpendicular bisector of the connection
44 Theorem 3 on the two graphics symmetry of a straight line,
if their corresponding intersection line or extension cord, then the intersection of the inverse of the axis of symmetry
45 ; if the two corresponding points in the connection graph is a straight line with the vertical,
then the two graphics on this line symmetry
46 Pythagorean Theorem the two right-angle triangle edge a, b of the square and,
equal to the square of the hypotenuse c, ie a ^ 2 + b ^ 2 = c ^ 2
47 The converse of the Pythagorean Theorem
If the triangle triangular
long a, b, c has a relationship a ^ 2 + b ^ 2 = c ^ 2,
then the triangle is right triangle
48 Theorem quadrilateral is equal to 360 °
angles quadrilateral exterior angle is equal to 49 and 360 °
50 side polygon-shaped angles and theorems of angles n and is equal to (n-2) × 180 °
51 deduction equal to any multilateral exterior angle and 360 °
52 nature of Theorem 1 parallelogram the diagonal of the parallelogram is equal
53 parallelogram parallelogram nature of Theorem 2 on the opposite side equal
54 inference caught in between two parallel lines parallel to line the nature of equal
55 parallelogram parallelogram's diagonal theorem 3 to each other equally
decision theorem parallelogram 56 1
two groups were equal to the diagonal of the quadrilateral is a parallelogram parallelogram
57 decision theorem 2
two groups were equal on the side of a quadrilateral is a parallelogram parallelogram decision theorem
58 3
diagonal split each quadrilateral is a parallelogram parallelogram decision theorem
59 4
a set of edges parallel to the quadrilateral is a parallelogram equal rectangular nature of Theorem 1
60 the four corners of the rectangle are right angles
61 rectangular nature of Theorem 2 ; the diagonal of the rectangle is equal
62 has three rectangular determine angle of Theorem 1 right angles to the rectangular quadrilateral is a rectangle
63 Theorem 2 to determine the diagonal of the parallelogram is a rectangle equal to
64 diamond-shaped nature of Theorem 1, the four sides are equal diamond
65 diamond-shaped diamond of diagonal nature of Theorem 2, perpendicular to each other,
and split each set of diagonal diagonal diagonal
66 diamond-shaped area = product of half, or S = (a × b) ÷ 2
67 diamond-shaped sides are equal Theorem 1 determine a quadrilateral is a rhombus
; 68 Diamond Theorem 2 to determine the diagonal of the parallelogram are perpendicular to each other diamond
69 square nature of Theorem 1 the four corners of a square are right angles, four sides are equal
70 square nature of Theorem 2, equal to the square of the two diagonals ,
and perpendicular to each other equally, and each diagonal split a set of Theorem 1 on the corner
71 centrosymmetric two graphics are congruent
72 Theorem 2 on the center of symmetry of the two graphics,
symmetry point connections have been the center of symmetry and is split
73 inverse symmetry ; if the corresponding point of connection of two graphics have been some point,
and is it equally, then the two graphics on this isosceles symmetry
74 Theorem isosceles trapezoid trapezoidal nature of the end of the two at the same angle isosceles trapezoid are equal
75
the two diagonals are equal 76 isosceles trapezoid decision theorem
in the same two corners on the bottom of the ladder are equal isosceles trapezoid
77 is equal to the diagonal The trapezoid is isosceles trapezoid
78 segments of parallel lines decile Theorem
If a group of parallel lines cut in a straight line segment was the same,
then the other straight line intercepted the line are equal
79 Corollary 1, the midpoint of the waist through the ladder and at the end 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 Theorem triangle triangle median line parallel to the median line the third side,
and equal to half of it
82 trapezoid trapezoid theorem of the median line median line parallel to the two at the end,
and equal to the bottom and two
half
; L = (a + b) ÷ 2 S = L × h
83 (1) the proportion of the basic properties
If a: b = c: d, then ad = bc if ad = bc,
then a: b = c: d
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,
la gear police,
from the corresponding proportion
87 segment inference straight line parallel to the cut-off the other side of the triangle on both sides
(or both sides of the extension cord), which is proportional to
88 should line if a straight line cut Theorem both sides of a 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, and straight line intersecting the other side,
the intercepted three sides and the original triangle is proportional to the corresponding sides of a triangle theorems
90 a straight line parallel to the other side of the triangle sides
(or both sides of the extension line) intersects the triangle composed of triangles similar to the original decision theorem of similar triangles
91 corners correspond to equal 1, the two triangles similar to the (ASA)
92 high on the hypotenuse of a right triangle is divided into two right triangles and the original Similar
93 triangles on both sides of Theorem 2 to determine the corresponding angles are equal and proportional,
two triangles similar to the (SAS)
94 to determine the corresponding Theorem 3 into a triangular the ratio of two similar triangles (SSS)
95 Theorem If the hypotenuse of a right triangle and a right angle with another side of the hypotenuse and a right-angle side of the corresponding proportion, then the two triangles similar to the properties of Theorem 1
96 higher than the corresponding similar triangles, corresponding to the center line than the corresponding angle bisectors are equal to the ratio of similar nature than
97 Theorem 2 is equal to the ratio of the circumference of similar triangles similar ratio
98 Theorem 3 similar nature than the area of a triangle is equal to the square of
99 similar than the sine of any acute angle is equal to the cosine of its complementary angle, arbitrary the cosine of an acute angle equal to its complementary angle of the sine
100 tangent of any acute angle equal to its complementary angle of the cotangent value, the value of any acute angle is equal to the cotangent the value of its complementary angle of the tangent circle is fixed
101 a distance equal to the set of points fixed length
102 inside the circle can be seen as the distance is less than the radius of the center set of points outside the circle
103 can be seen as the distance is greater than the radius of the center point of the set
104 circle with the radius of a circle or other equivalent
105 a distance equal to the fixed point of the trajectory length , is designated as the center of the circle of radius length and known
106 segments of equal distance from both end points of the track, is the perpendicular bisector of line segments
107 to a known angular distance equal points on both sides of the track, is the angle bisector
108-2 equidistant parallel lines locus of points,
la gear mens shoes, and it is parallel to the two parallel lines and a straight line from the Phase Theorem
109 not in the same three-point line has been set a circle.
110 vertical diameter of Theorem
diameter perpendicular to the string split this string by string and split the two arcs of Corollary 1
111
① split the string (not diameter) of the diameter perpendicular to the string,
and split the two strings of the arc of the strings
② vertical bisector through the center of the circle, and the strings are split on the two arcs
③ split string by an arc of diameter, vertical split the string,
and split the right chord to another circular arc
112 Corollary 2, the two parallel strings of the folder circular arc is equal to
113 center as the center of symmetry theorem of symmetry
114 or so round the same circle , the equivalent of the arc of the central angle equal to,
The equivalent of the string
, the heart strings of the chord from the same reasoning in
115 circle with a round or so, if the two central angle, two arcs, two string or two strings of the chord in the heart of a group from the same amount so they correspond to the amount of the other groups are equal
Theorem 116 of the circumference of an arc 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 right The circumferential angle a right angle; 90 ° angle of the circle is the diameter of the strings
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 one of the exterior angle is equal to its diagonal
; 121 ① ⊙ O intersecting lines L and d r
; 122 decision theorem of tangent through the outer end of the radius 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 the radius of the
124 Corollary 1 through the center and perpendicular to the tangent line through the tangent point will
After a cut point of 125 Corollary 2 and will be perpendicular to the tangent line through the center of the circle theorems
126 long tangent point outside from the circular argument rounded two tangent, tangent of their appearance so that the connection center and the tangent of the angle between two equally
127 circumscribed circle of the two groups on the edge of Quadrilateral and equal
128 Xian Qiejiao Theorem Xianqie Jiao is equal to its arc on the circumference of clip angle
; 129, folder inference that if two Xianqie Jiao arc equal,
Xian Qiejiao
then the two strings are equal
130 intersection of two circle theorems intersection string,
into the intersection of two line segments are the product of length equal to
131 deduction if the chord and the diameter of the vertical intersection, p>
then string it points to the diameter of the half as the ratio of two line segments cutting
132 items Line Theorem quoted from the point outside the circle circle tangent and secant,
long is this tangent to the secant and the circle intersection of two line segments in the proportion of long-term
133 deduction from the circle round the two point outside cited secant, which is to each of the intersection of the secant and the circle the product of two equal length segments
134 If the two circles tangent, then the cutoff point must be in line with the heart outside the two circles
135 ① from the d> R + r
② two circles circumscribed d = R + r
③ two circles intersect Rr r)
④ two circles inscribed d = Rr (R> r) ;
⑤ two circles containing d r)
136 Theorem ; intersection of two circles with center line of the axis of two circles of the 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
138 Theorem Any regular polygon has a circumscribed circle 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 regular n-gon theorem of the radius and the edge of the heart from the regular n-gon into two congruent right triangle
2n n-gon 141 is the area of Sn = pnrn / 2 p n-gon that is the perimeter of an equilateral triangle area
142 √ 3a / 4 a side said
143 if a vertex k-regular around the corner n-gon, as these angles and
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 = n Wu R Sector ^ 2 / 360 = LR / 2
146 within the common tangent length = d-(Rr) grandfather tangent length = d-(R + r)
utility: common mathematical formulas
classification formula formula expression
multiplication and factoring a2-b2 = (a + b) (ab) ;
a3 + b3 = (a + b) (a2-ab + b2)
; a3-b3 = (ab (a2 + ab + b2)
triangle inequality | a + b | ≤ | a | + | b | | ab | ≤ | a | + | b |
| a | ≤ b -b ≤ a ≤ b | ab | ≥ | a | - | b | - | a | ≤ a ≤ | a |
the solution of a quadratic equation-b + √ (b2-4ac ) / 2a-b-√ (b2-4ac) / 2a
relationship between roots and coefficients X1 + X2 =- b / a X1 * X2 = c / a
Note: Whyte Theorem
discriminant
; b2-4ac = 0 Note: The equation has two equal real roots
b2-4ac> 0 ; Note: The equation has two unequal real roots
b2-4ac 0
the standard equation of a parabola y2 = 2px
y2 =- 2px x2 = 2py x2 =- 2py
straight prism lateral area S = c * h oblique prism lateral area S = c '* h
are pyramid lateral area S = 1/2c * h '
are bevel side of the area S = 1 / 2 (c + c ') h'
round table side of the area S = 1 / 2 (c + c ') l = pi (R + r) l
ball surface area S = 4pi * r2
cylindrical side of the area S = c * h = 2pi * h
cone lateral area S = 1 / 2 * c * l = pi * r * l
; arc length formula l = a * r a central angle of the arc is the number of r> 0
fan formula s = 1 / 2 * l * r
; cone volume formula V = 1 / 3 * S * H
cone volume formula V = 1 / 3 * pi * r2h
oblique prism volume V = S'L
Note: where, S 'is a straight cross-sectional area, L is the side of the edge length
cylinder volume formula V = s * h
cylinder V = pi * r2h
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