"Solid geometry" will generally appear in the form of "two small and one big" or "one small and one big" in the college entrance examination. This "two small" or "one small" mainly investigates the relationship between the surface area of three views and the position of volume, space point, line and surface (especially parallel and vertical).
When examining a small question, this small question usually appears in the position of 6 ~ 7 questions, and the difficulty is average; When examining two small questions, one of them is generally more difficult, and the other is slightly more difficult, which usually appears in the position of 9 ~ 1 1. Although this small question is slightly more difficult, it is mainly reflected in the amount of calculation, and the essence is the examination of basic knowledge and basic formulas.
The answer questions mostly appear in the position of 18 or 19, and its basic mode is "one certificate and two calculations", that is, in the following figure, the question T3 (1) examines the proof of the spatial parallel or vertical relationship, and the question (2) examines the angle, line plane angle or dihedral angle formed by using the space vector to find the straight line of the different plane, which is moderately difficult.
Let's compare the real questions of the college entrance examination, trace back to the source of the teaching materials, and feel the connection and difference.
T 1 test questions are from textbooks, both of which are combinations, and the test questions only require further calculation of the surface area of the combination.
T2 problem is a topic in the textbook reform. The topic in the textbook is that the triangular prism cuts the cylinder, but the topic has been changed, that is, the triangular prism is cut outside the sphere to find the maximum volume of the sphere.
T3 exam questions and textbook questions are cleverly constructed with two special triangles as the main framework.
The (1) test question replaces the line-plane angle and line-included angle in the textbook (1)(2), but the thinking method is the same.
(2) On the basis of the original question, using the volume relation to set the midpoint E is based on the cosine value of dihedral angle, and the textbook questions and examination questions are actually twin brothers.
(3) The examination questions are transplanted into the textbook questions, seeking common ground while reserving differences, exchanging conditions and conclusions, so that the three questions become two questions (in essence, the three topics after finding the volume), and through the solid geometry questions, the knowledge points of vertical, dihedral and volume are integrated, which can be described as flowing water from the source. The test questions originated from textbooks, which embodies the perfect combination of textbook questions and test questions.