Test site requirements: 1. The unfolding of geometry and three views are still hot spots in the college entrance examination.

2. The proposition of combining three views with other knowledge points is the trend of new textbooks to examine students' three views and geometric quantity calculation.

3. Focus on the topic of spatial geometric structure characteristics with three views as the proposition background.

4. Be familiar with some typical geometric models, such as three views of triangular prism, long (regular) cube and triangular pyramid.

Knowledge structure:

Structural characteristics of 1. polyhedron

Two faces of a (1) prism are parallel to each other, the other faces are parallelograms, and the common edges of every two adjacent quadrangles are parallel.

Regular prism: a prism whose side is perpendicular to the bottom is called a regular prism, and a regular prism whose bottom is a regular polygon is called a regular prism. On the contrary, a regular prism has a regular bottom surface and rectangular side surfaces, and the side edges of the bottom surface are perpendicular to the bottom surface.

(2) The base of the pyramid is an arbitrary polygon, and the sides are triangles with common vertices.

Regular pyramid: A pyramid whose bottom is a regular polygon and whose vertices are projected on the bottom is called a regular pyramid. In particular, an equilateral regular triangular pyramid is called a regular tetrahedron. On the contrary, the base of a regular pyramid is a regular polygon, and the projection of its vertex on the base is the center of the regular polygon.

(3) A frustum can be obtained from a plane truncated pyramid parallel to the bottom surface, and its upper and lower bottom surfaces are similar polygons.

2. Structural characteristics of the rotating body

(1) A cylinder can be obtained by rotating a rectangle around a straight line with one side.

(2) Turn the right triangle around a straight line with right angles to get a cone.

(3) The frustum can be a right-angled trapezoid rotating once around the straight line where the right-angled waist is located, or an isosceles trapezoid rotating half a circle around the straight line where the centers of the upper and lower bottom surfaces are located, or a plane truncated cone parallel to the bottom surface.

(4) The ball can be a semicircle that rotates once around the diameter, or it can be a semicircle that rotates once around the diameter.

3. Three views of space geometry

Three views of space geometry are obtained by parallel projection. Under this projection, the shadow left by the plane figure parallel to the projection plane is congruent with the plane figure, and its shape and size are equal. Three views include front view, side view and top view.

The length characteristics of the three views are "long alignment, equal width and high level", that is, the front view is as high as the side view, the front view is as long as the top view and the side view is as wide as the top view. If the surfaces of two adjacent objects intersect, the intersection line of the surfaces is their dividing line. Attention should be paid to the drawing of virtual and real lines in three views.

4. Intuition of space geometry

Orthographic drawings of space geometry are often drawn by oblique survey, and the basic steps are as follows:

(1) Draw the bottom surface of the geometry.

Take the X axis and Y axis which are perpendicular to each other in the known figure, and they intersect at the O point. When drawing the vertical figure, draw them into the corresponding X ′ axis and Y ′ axis, and they intersect at the O ′ point, so that ∠ X ′ O ′ Y ′ = 45 or 135, and the known figure is parallel to the X axis and Y axis.

(2) the height of the drawing geometry

In the known graph, the Z axis passing through the O point is perpendicular to the xoy plane, and the corresponding Z' axis in the orthogonal graph is also perpendicular to the X'O'Y' plane. In the known figure, the line segment parallel to the Z axis is still parallel to the Z' axis in the orthographic drawing, and its length remains unchanged.

2. Two knowledge points are required in senior three mathematics.

Test site 1: Interpretation of the concept and basic theorem of vector Understand the actual background of vector, master the concepts of vector, zero vector, parallel vector, * * line vector, unit vector and equal vector, understand the geometric representation of vector, and master the basic theorem of plane vector.

Pay attention to the understanding of the concept of vector, the vector can move freely, and the translated vector is the same as the original vector; The sizes of two vectors are not comparable, but their moduli are comparable.

Test site 2: vector operation

The operation of content interpretation vector requires mastering the addition and subtraction of vectors, and using parallelogram rule and triangle rule to add and subtract vectors; Master the product operation of real numbers and vectors, understand the meaning of straight lines of two vectors, and judge the parallel relationship of two vectors; Master the operation of vector's scalar product, understand the relationship between plane vector's scalar product and vector projection, and understand its geometric meaning. Master the coordinate representation of scalar product, and can perform the operation of plane cross product, express the included angle of two vectors with scalar product, and judge the vertical relationship between two plane vectors with cross product.

The propositional form of propositional law mainly appears in the form of multiple-choice questions and fill-in-the-blank questions, which is not difficult. The focus of the examination is the definition of the angle between module and vector, the formula of the angle, the coordinate operation of vector, and sometimes other contents.

Test center 3: Set score points

In content interpretation, you can master the coordinate formulas of fixed points and midpoint of line segments and skillfully use them. When calculating the ratio of point-to-point directed line segments, graphics can be used to help understand.

Propositional laws focus on definitions and formulas, which mainly appear in the form of multiple-choice questions or fill-in-the-blank questions, with average difficulty. Because of the wide application of vectors, they are often examined together with trigonometric functions and analytic geometry. If it appears in solving problems, the difficulty is mainly intermediate and occasionally slightly higher.

Test site 4: synthesis of vectors and trigonometric functions

The synthesis of content interpretation vector and trigonometric function is a common problem in college entrance examination. Examining the knowledge of vectors and trigonometric functions meets the requirements of the coverage of college entrance examination questions.

Proposition law proposition takes trigonometric function as coordinate, coordinate operation of vector or combination of vector and trigonometric solution, and image translation problem of vector and trigonometric function, which is an intermediate easy problem.

Test site 5: the intersection of plane vector and function problem

The intersection of plane vector and function in content interpretation is mainly the combination of vector and quadratic function, so we should pay attention to the range of independent variables.

Propositional law propositions are mostly based on solving problems, which are intermediate questions.

Test Site 6: Application of Plane Vector in Plane Geometry

The coordinate representation of the content interpretation vector is actually an algebraic representation of the vector. After introducing the coordinate representation of vectors, the operations between vectors are algebraic, so that "shape" and "number" can be closely combined. So many difficult problems in plane geometry problems can be transformed into familiar demonstrations of algebraic operations. That is, the plane geometry is put in a suitable coordinate system, and the relevant points of the geometry and the plane vector are given specific coordinates, so that the plane geometry can be related.

The law of proposition mainly focuses on solving problems, which is a moderately difficult problem.