Mathematics in senior high school is compulsory. Chapter 1 Preliminary prism surface area A=L*H+2*S, volume V = S * H.
(L- bottom perimeter, H- column height, S- bottom area)
Cylinder surface area A=L*H+2*S=2? *R*H+2？ * r 2, volume V=S*H=? *R^2*H
(l- bottom circumference, h- column height, s- bottom area, r- bottom circle radius)
Sphere surface area A=4? * r 2, volume V=4/3? *R^3
(R- radius of sphere)
Cone surface area A= 1/2*s*L+? * r 2, volume V= 1/3*S*H= 1/3? *R^2*H
(S- length of conical generatrix, L- perimeter of bottom surface, R- radius of bottom surface circle, H- height of cone)
The surface area of the pyramid is A= 1/2*s*L+S, and the volume is v =1/3 * s * h.
(height of S- side triangle, circumference of L- bottom, area of S- bottom, height of H- pyramid)
The circumference of a rectangle = (length+width)? 2 square a? Side length C=4a
S=a2 The sides of rectangle A and B are C=2(a+b).
S=ab triangle A, B, c- the length of three sides h- the height of one side.
S- semi-perimeter a, b, C- internal angle, where s=(a+b+c)/2 S=ah/2 =ab/2? sinC
[s (s-a) (s-b) (s-c)]1/2a2sinbsinc/(2sina) quadrilateral d, D- diagonal length? -Diagonal angle S=dD/2? Sin? Parallelogram a, b side length h side height? -included angle S=ah =absin? =
A side length of diamond? -included angle d- long diagonal length D- short diagonal length S=Dd/2
=a2sin？ Trapezoids a and b- upper and lower bottom length h- height.
M- centerline length S=(a+b)h/2 =mh d- diameter C=? d=2？ r
S=？ r2 =？ D2/4 zone R? Sector radius, perimeter of square = side length? 4 Rectangular area = length? extensive
Area of a square = side length? Side length = triangle area of the bottom? Tall? 2 area of parallelogram = bottom? high
Area of trapezoid = (upper bottom+lower bottom)? Tall? 2 diameter = radius? 2 Radius = diameter? 2 circumference = pi? Diameter = pi? Radius? 2 The area of a circle = π? Radius? radius
Surface area of cuboid = (length? Width+length? Height+width? High)? 2 cuboid volume = length? Wide? Surface area of high cube = side length? Side length? 6 volume of cube = side length? Side length? Lateral area of prism = perimeter of base circle? high
Cylinder surface area = upper and lower bottom areas+side area = cylinder volume = bottom area? high
Volume of cone = bottom area? Tall? 3 Cuboid (cube, cylinder)
Volume = bottom area? What are the perimeter c and area S a of the name symbol of the high plane figure respectively? Center angle
C=2r+2？ r？ (a/360) S=？ r2？ (a/360)
Bow l- arc length b- chord length h- rising height r- radius? -The degree of the central angle S=r2/2? (/ 180-sin？ )= r2arccos[(r-h)/r]-(r-h)(2rh-H2) 1/2
=r2/360 - b/2？ [r2-(b/2)2] 1/2
=r(l-b)/2 + bh/2
? 2bh/3 ring r- outer diameter R- inner diameter d- outer diameter D- inner diameter S=? (R2-r2)
=? (D2-d2)/4 Ellipse d- major axis D- minor axis S=? Dd/4
Cubic graphic name symbol area S and volume V Cube a- side length S=6a2 V=a3
Cuboid a- length b- width c- height S=2(ab+ac+bc)
V=abc prism S- bottom area h- height V=Sh pyramid S- bottom area.
H- height V=Sh/3 prism S 1 and S2- upper and lower bottom areas h- height v = h [s1+S2+(s1)1/2]/3.
Prismatoid S 1- Upper bottom area S2- Lower bottom area
S0- cross-sectional area h- height V=h(S 1+S2+4S0)/6.
Cylinder r- bottom radius h- height c? Bottom circumference
S bottom? Bottom area s side? Side area s table Surface area C=2? R S bottom =？ r2
S plane =Ch S table =Ch+2S bottom V=S bottom h =? r2h
Hollow cylinder r- outer circle radius R- inner circle radius
H- high V=？ H(R2-r2) straight cone r- base circle radius h- height V=? r2h/3
Cone r- upper bottom radius R- lower bottom radius
H- high V=？ H(R2+Rr+r2)/3 r- the radius of the sphere
D- diameter V=4/3? r3=？ D2/6 ball missing h ball missing height r ball radius
A ball is missing the bottom radius V=? h(3a2+h2)/6 =？ H2(3r-h)/3 a2=h(2r-h) Table r 1 and r2- Radius h- Height V= Above Table? H[3(r 12+r22)+h2]/6 ring R- ring radius
D-ring diameter R-ring section radius D-ring section diameter V=2? 2Rr2 =？ 2Dd2/4
Bucket d- drum belly diameter D- drum bottom diameter h- drum height V= H(2D2+d2)/ 12 (the bus is circular with the center of the barrel) V=? h(2D2+Dd+3d2/4)/ 15
(The bus is a parabola)
The projection rule of three views is:
Length alignment between front view and top view
Superior vision and left vision are high.
The width of the left view and the top view are equal.
Point-line plane position relation
Axiom 1: If two points of a straight line are on a plane, then the straight line is on a plane.
Axiom 2: If two planes have a common point, they have a common straight line, and all the common points are on this straight line.
Axiom 3: It is not three points of a line that determine a plane.
Inference 1: A straight line and a point outside the straight line determine a plane.
Inference 2: Two intersecting lines define a plane.
Inference 3: Two parallel straight lines define a plane.
Axiom 4: Lines parallel to the same line are parallel.
Definition of non-planar straight lines: two straight lines that are not parallel or intersect.
Decision theorem: A straight line passing through a point out of plane and a point in plane is a non-plane straight line.
Equiangular Theorem: If two sides of one angle are parallel and in the same direction as two sides of another angle, then the two angles are equal.
Parallel lines? Line-plane parallelism If a straight line out of plane is parallel to a straight line in this plane, then this straight line is parallel to this plane. Parallel lines and planes? Parallel lines If a straight line is parallel to a plane and the plane passing through the straight line intersects the plane, the straight line is parallel to the intersection line.
Parallel lines and planes? Face-to-face parallelism If two intersecting lines on one plane are parallel to the other plane, then the two planes are parallel. Face to face parallel? Parallel lines If two parallel planes intersect the third plane at the same time, their intersection lines are parallel.
Is the line vertical? If a straight line is perpendicular to two intersecting straight lines in a plane, then the straight line is perpendicular to the plane. Is the line vertical? Parallel lines If two straight lines are perpendicular to a plane at the same time, then the two straight lines are parallel.
Is the line vertical? If one plane passes through the perpendicular of the other plane, then the two planes are perpendicular to each other.
Is the line vertical? Vertical definition of straight line and vertical line: if a straight line A and a plane? Any straight line is vertical, so we say that straight line A is vertical to the plane? .
Face to face, vertical? If two planes are perpendicular to each other, a straight line perpendicular to their intersection on one plane is perpendicular to the other plane.
Three perpendicular theorems If a straight line in a plane is perpendicular to the projection of blood in the plane, it is perpendicular to the diagonal.
The first chapter of compulsory mathematics in senior high school is a preliminary example of solid geometry of tetrahedron ABCD. (1) If AB = AC and BD = CD, how to prove that BC is perpendicular to AD? (2) If AB is perpendicular to CD and BD is perpendicular to AC, how can we prove that BC is perpendicular to AD?
Prove:
(1). Take the midpoint f of BC, connect AF and DF, and then
AB = AC，BD=CD，
? △ABC and△ △DBC are isosceles triangles,
AF？ BC，DF？ BC. And AF? DF=F，
? BC? Aircraft AFD AD is on the plane AFD,
? B.C.
(2) let the projection of a on the surface BCD be O. COnnect BO, co and DO.
∵CD？ AB，CD？ AO，AB？ AO=A，？ CD？ Facing ABO
BO is on ABO's plane. Bo? CD.
Similarly, DO? BC. So o is the center of △BCD, so there is
CO？ BD。
∵BD？ CO，BD？ AO，CO？ AO=O，？ BD？ Facing AOC