Summary of compulsory math formula 2 in senior one.
There are four axioms in solid geometry:
Axiom 1 If two points on a straight line are on a plane, then the straight line is on this plane.
Axiom 2 passes through three points that are not on a straight line, and there is only one plane.
Axiom 3 If two non-coincident planes have a common point, then they have one and only one common straight line passing through the point.
Axiom 4 Two lines parallel to the same line are parallel.
Cubic figure
Solid geometry formula
Name symbol area s volume v
The side length of cube a is s = 6a 2 v = a 3.
The length of cuboid a is S=2(ab+ac+bc) V=abc.
B width
C Gao
The bottom area of the prism V=Sh.
H height
The bottom area of the pyramid is s V=Sh/3.
H height
Upper and lower bottom areas of prism S 1 and S2 v = h [s 1+S2+? (S 1^2)/2〕/3
H height
Prismatoid S 1 upper and lower area V=h(S 1+S2+4S0)/6.
S2 bottom area
S0 cross-sectional area
H height
The bottom radius of cylinder R is C=2? R V=S bottom h= rh
H height
Bottom circumference
S bottom area s bottom =? R^2
Transverse area of s side s side =Ch
Surface area s table =Ch+2S bottom
S bottom =？ r^2
Radius r of external circle of hollow cylinder
R inner circle radius
H high V=? h(R^2-r^2)
R base radius of straight cone
H high V=? r^2h/3
Radius of top and bottom of frustum R.
R bottom radius
H high V=? h(R^2+Rr+r^2)/3
R radius of sphere
D diameter V=4/3? r^3=？ d^2/6
Leakage height
R sphere radius
The toe radius of a ball a 2 = h (2r-h) v =? h(3a^2+h^2)/6 =？ h2(3r-h)/3
The mesa radius r 1 and the top and bottom surfaces of r2 mesa.
H high V=? h[3(r 12+r22)+h2]/6
Radius r of the ring.
D-ring diameter
R-ring section radius
D-ring section diameter V=2? ^2Rr^2 =？ ^2Dd^2/4
Barrel d belly diameter
D barrel bottom diameter
H barrel height V=? H (2D 2+D2)/ 12 (the bus is circular, and the center of the circle is the center of the barrel)
V=？ H (2D 2+DD+3D 2/4)/ 15 (the bus is parabolic)
Plane analytic geometry includes the following parts:
cartesian coordinates
1. 1 directed line segment
1.2 Cartesian coordinates of points on a straight line
Several Basic Formulas of 1.3
Rectangular coordinates of points on 1.4 plane
Basic principle of 1.5 projection
Several Basic Formulas of 1.6
Two curves and agenda
2. The definition of1curve directly solves the coordinate equation.
2.2 Find each curve and find its equation.
2.3 Known curve equation, describe the curve.
2.4 Intersection of curves
Three straight lines
3. 1 Angle and slope of straight line
3.2 linear equation
Y=kx+b
3.3 Directed distance from straight line to point
3.4 Plane Region Represented by Binary Linear Inequality
3.5 the relative position of two straight lines
3.6 Conditions for Binary Equation to Express Two Straight Lines
3.7 Relative position of three straight lines
3.8 Linear system
Siyuan
4. Definition of1circle
4.2 Equation of Circle
4.3 Relative position of point and circle
4.4 Tangent of a circle
4.5 Chords and Polar Lines of a Point on a Circle
4.6 *** axis circulation system
4.7 Inverse evolution on the plane
Five ellipses
5. Definition of1ellipse
5.2 An ellipse can be obtained by cutting a conical surface with a plane.
5.3 Standard Equation of Ellipse
5.4 Basic properties and related concepts of ellipse
5.5 Relative position of point and ellipse
5.6 Tangents and normals of ellipses
5.7 Points on the tangent and polar lines of an ellipse
5.8 area of ellipse
Six hyperbola
6. Definition of1hyperbola
6.2 A hyperbola can be obtained by cutting a conical surface with a plane.
6.3 standard equation of hyperbola
6.4 Basic properties and related concepts of hyperbola
6.5 equilateral hyperbola
6.6 *** Yoke Hyperbola
6.7 Relative position of point and hyperbola
6.8 Tangents and normals of hyperbola
6.9 the tangent of hyperbola and the point on the polar line
Seven parabolas
7. Definition of1parabola
7.2 A parabola can be obtained by cutting a conical surface with a plane.
7.3 standard equation of parabola
7.4 Basic properties and related concepts of parabola
7.5 Relative position of point and parabola
7.6 Tangents and normals of parabolas
7.7 Points on the tangent line and polar line of parabola
7.8 Area of Parabolic Arch
Eight coordinate transformation? General theory of quadratic curve
8. The concept of1coordinate transformation
8.2 Translation of Axis
8.3 Simplify the curve equation by translation
8.4 Standard Equation of More General Conic Curve
8.5 Rotation of coordinate axis
8.6 General formula of coordinate transformation
8.7 Classification of curves
8.8 Invariants of Quadratic Curve under Cartesian Coordinate Transformation
8.9 curve of binary quadratic equation
8. Simplification of10 quadratic equation
8. 1 1 Conditions for Determining Quadratic Curve
8. 12 conic system
Nine-parameter equation
Ten polar coordinates