Senior one mathematics compulsory 2 catalogue
Chapter I Space Geometry
1. 1 spatial geometry
1.2 Three Views and Straight Views of Space Geometry
Descriptive Geometry and gaspard monge's Reading and Thinking
1.3 surface area and volume of space geometry
Explore and discover the principle of ancestral pestle and the volume of cylinder, vertebral body and sphere
Practice homework
summary
Review reference questions
Chapter II Positional Relations of Points, Lines and Surfaces
2. 1 The positional relationship among points, lines and surfaces in space
2.2 Determination of parallelism between straight line and plane and its properties
2.3 Determination and characteristics of vertical lines and planes
Reading and Thinking of Euclid's Elements of Geometry and Axiomatic Methods
summary
Review reference questions
Chapter III Linear Sum Equation
3. 1 Angle and slope of straight line
Explore and discover the magician's carpet.
3.2 linear equation
3.3 Formula for coordinates and distance of intersection points of straight lines
Reading and Thinking of Descartes and Analytic Geometry
summary
Review reference questions
The fourth chapter circle sum equation
4. Equation of1circle
Reading thinking coordinate method and machine proof
4.2 The positional relationship between straight line and circle
4.3 Spatial Cartesian Coordinate System
Using information technology to explore the trajectory of points: draw circles with geometric sketchpad.
summary
Review reference questions
High school mathematics compulsory 2 knowledge points
Structural characteristics of 1, column, cone, platform and ball
(1) prism:
Definition: Geometry surrounded by two parallel faces, the other faces are quadrangles, and the common edges of every two adjacent quadrangles are parallel to each other.
Classification: According to the number of sides of the bottom polygon, it can be divided into three prisms, four prisms and five prisms.
Representation: Use the letter of each vertex, such as a five-pointed star, or use the letter at the opposite end, such as a five-pointed star.
Geometric features: the two bottom surfaces are congruent polygons with parallel corresponding sides; The lateral surface and diagonal surface are parallelograms; The sides are parallel and equal; The section parallel to the bottom surface is a polygon that is congruent with the bottom surface.
② Pyramid
Definition: One face is a polygon, and the other faces are triangles with a common vertex. These faces enclose a geometric figure.
Classification: According to the number of sides of the bottom polygon, it can be divided into three pyramids, four pyramids and five pyramids.
Representation: Use the letters of each vertex, such as a pentagonal pyramid.
Geometric features: the side and diagonal faces are triangles; The section parallel to the bottom surface is similar to the bottom surface, and its similarity ratio is equal to the square of the ratio of the distance from the vertex to the section to the height.
(3) Prism:
Definition: Cut off the part between the pyramid, the section and the bottom with a plane parallel to the bottom of the pyramid.
Classification: According to the number of sides of the bottom polygon, it can be divided into triangular, quadrangular and pentagonal shapes.
Representation: Use the letters of each vertex, such as a pentagonal pyramid.
Geometric features: ① The upper and lower bottom surfaces are similar parallel polygons; ② The side is trapezoidal; ③ The sides intersect with the vertices of the original pyramid.
(4) Cylinder:
Definition: Geometry surrounded by a surface with one side of a rectangle and the other three sides rotating around a straight line.
Geometric features: ① The bottom is an congruent circle; ② The bus is parallel to the shaft; ③ The axis is perpendicular to the radius of the bottom circle; ④ The side development diagram is a rectangle.
(5) Cone:
Definition: Rotate the geometry surrounded by the surface of Zhou Suocheng with the right-angled side of the right-angled triangle as the rotation axis.
Geometric features: ① the bottom is round; (2) The generatrix intersects with the apex of the cone; ③ The side spread diagram is a fan.
(6) frustum of a cone:
Definition: Cut the part between the cone, the section and the bottom with a plane parallel to the bottom of the cone.
Geometric features: ① The upper and lower bottom surfaces are two circles; (2) The side generatrix intersects with the vertex of the original cone; (3) The side development diagram is an arch.
(7) Sphere:
Definition: Geometry formed by taking the straight line where the diameter of the semicircle is located as the rotation axis and the semicircle surface rotates once.
Geometric features: ① the cross section of the ball is round; ② The distance from any point on the sphere to the center of the sphere is equal to the radius.
2. Three views of space geometry
Define three views: front view (light is projected from the front of the geometry to the back); Side view (from left to right) and top view (from top to bottom)
Note: the front view reflects the position relationship of the object, that is, it reflects the height and length of the object;
The top view reflects the position relationship between the left and right of the object, that is, the length and width of the object;
The side view reflects the up-and-down and front-and-back positional relationship of the object, that is, it reflects the height and width of the object.
3. Oblique dichotomy with intuitive space geometry.
The characteristics of oblique bisection method are as follows: ① The line segment originally parallel to the X axis is still parallel to X, and its length remains unchanged; ② The line segment originally parallel to the Y axis is still parallel to Y, and its length is half of the original.
Mathematics knowledge point formula in senior one.
I. Settings and functions
Content intersection and complement set, and power exponential pair function. Parity and increase and decrease are the most obvious observation images.
When the compound function appears, the law of property multiplication is distinguished. To prove it in detail, we must grasp the definition.
Exponential function and logarithmic function are reciprocal functions. Cardinality is not a positive number of 1, and 1 increases or decreases on both sides.
The domain of the function is easy to find. Denominator cannot be equal to 0, even roots must be non-negative, and zero and negative numbers have no logarithm;
The tangent function angle is not straight, and the cotangent function angle is uneven; The real number sets of other functions have intersection in many cases.
Two mutually inverse function have that same monotone property; The images are symmetrical with Y=X as the symmetry axis;
Solve the very regular inverse solution of substitution domain; The domain of inverse function, the domain of original function.
The nature of power function is easy to remember, and the index reduces the score; Keywords exponential function, odd mother and odd son odd function,
Even function with odd mother and even son, even mother non-parity function; In the first quadrant of the image, the function is increased or decreased to see the positive and negative.
Second, trigonometric functions
Trigonometric functions are functions, and quadrant symbols are labeled. Function image unit circle, periodic parity increase and decrease.
The same angle relation is very important, and both simplification and proof are needed. At the vertex of the regular hexagon, cut the chord from top to bottom;
The numb 1 records that triangle connecte the vertices in the center; The sum of the squares of the downward triangle, the reciprocal relationship is diagonal,
Any function of a vertex is equal to the division of the last two. The inductive formula is good, negative is positive and then big and small,
It is easy to look up the table when it becomes a tax corner, and it is essential to simplify the proof. Half of the integer multiple of two, odd complementary pairs remain unchanged,
The latter is regarded as an acute angle, and the sign is judged as the original function. The cosine of the sum of two angles is converted into a single angle, which is convenient for evaluation.
Cosine product minus sine product, angular deformation formula. Sum and difference products must have the same name, and the complementary angle must be renamed.
The calculation proves that the angle is the first, pay attention to the name of the structural function, the basic quantity remains unchanged, and it changes from complexity to simplicity.
Guided by the principle of reverse order, the product of rising power and falling power and difference. The proof of conditional equality, the idea of equation points out the direction.
Universal formula is unusual, rational formula is ahead. The formula is used in the right and wrong direction, and the deformation is used skillfully;
1 add cosine to think of cosine, 1 subtract cosine to think of sine, power-on angle is halved, and power-on and power-off is a norm;
The inverse function of trigonometric function is essentially to find the angle, first to find the value of trigonometric function, and then to determine the range of angle value;