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Master: Xu Keyong Profile: Teaching in Zhenhai Middle School,1990 was awarded as a provincial-level special-grade teacher in August. 1996 won the Jiangsu Mathematics Education (Individual) Award, 1997 was recognized as a professor-level senior middle school teacher by the Ningbo Municipal Government, 1999 was awarded a special government allowance by the State Council, and was named a famous teacher in Ningbo in 2000.
The thinking method of middle school mathematics is the essence of solving mathematical problems, which mainly includes mathematical thoughts: the thought of function and equation (transforming the problem of non-functional equation into the form of functional equation and solving the problem by using the relevant meaning and properties of functional equation).
The idea of combining numbers with shapes (according to the structural characteristics of numbers, construct geometric figures compatible with the three, and solve the problem of numbers by using the characteristics and laws of shapes or vice versa).
The idea of classified discussion (according to the essential attributes of mathematical objects, the objects are divided into different categories and then operated one by one, thus solving the whole problem).
Transformation and regression thinking (directly transforming difficult problems into new related problems or familiar problems to solve when solving mathematical problems).
Mathematical methods: analysis, synthesis, induction, method of substitution, definition, construction, symmetry, overall grasp, etc.
There are various specific thinking methods in every specific mathematical content, such as direct method, transfer method (or substitution method), parameter method, definition method and so on.
Reading before the exam:
1 emphasizes the mutual anisotropy of set elements, such as a = {0, 1, x2, -x}, which real numbers can't X take? (A: x≦)
0，x≠ 1，x≠( 1 √5)/2
{y=x2
y=x+2 }
12, when solving the equations of straight lines and circles, we should choose the equation form reasonably according to the characteristics, pay attention to the limitations of various equation forms, and prevent missing solutions.
13, straight lines and circles are the main objects of leveling research, and we should be good at using leveling knowledge to solve problems about straight lines and circles. For example, the determination of the positional relationship between a straight line and a circle, and the chord length obtained by cutting a circle with a straight line can be converted into the distance from the center of the circle to the straight line.
14. Flexible application of the definition of conic curve. (Choice related to focus, often used to fill in the blanks) Pay attention to the unified definition of conic to solve the problem that indefinite conic is ellipse, hyperbola or parabola.
15. Determine the standard agenda of conic section. Don't forget the diversity of standard equations. The important method used is the undetermined coefficient method.
16. What is an equilateral hyperbola? And what is the hyperbolic equation of hyperbola?
17, the positional relationship between straight line and conic curve.
① Number of common * * * points: eliminate simultaneous equation (eliminate X or y)→ unary equation ② Chord length: linear parameter equation method, projection method (flexibly use Vieta theorem).
18, find trajectory, trajectory equation, and don't forget to find constraints.
19, pay attention to make full use of plane vector method to analyze geometric problems.
For example, in 2003, the college entrance examination in Jiangsu Province asked the 20th question (stress).
20. The formula for finding the distance by volume method: (D is the distance from A to surface BCD, V is the volume of triangular pyramid A-BCD, and S is the area of △BCD.
Vertex transfer method or dig-and-fill method is often used to find the volume v.
2 1, understanding: polyhedral Euler formula: F+V=E+2, which can be tested by triangular pyramid.
Solution set, not {- 1, 1, 2,4}, another example: A={x│x=t2, t∈R}B={y│y=lgx2, x≠0}, then a ∩.
2. A function monotonically increases at (-∞,-1)], [1,+∞), so it cannot be recorded that this function monotonically increases at shuxue07.jpgrshuxue07.jpgshuxue07.jpgr, nor is it a decreasing function at r, nor is it a increasing function.
3. The parity of a function is related to the whole domain, so to judge the parity of a function, we must first determine whether its domain is symmetrical about the center of the origin, and then use f(-x)=f(x) (or f(-x)-f(x)=0), f(-x)=-f(x) (or
4. Master three transformations of function image: (1) translation, (2) expansion and contraction, and (3) symmetry, paying special attention to the influence of absolute value sign on function image.
For example, if the image of shuxue 1 2.jpgrshuxue12.jpgshuxue12.jpgr is (1), then y = | f (x) |, y = f (| x |), y = |.
5. The function f(x) is defined on R. (1) If the image of f(a-x)=f(a+x) and y=f(x) is symmetrical about the straight line x=a,
(2) If f(x)+f(2a-x)=2b, the image of y=f(x) is symmetrical about the center of point (a, b).
6. Understand and use the formula: {an} Arithmetic: (1) If m+n=p+q(m, n, p, q∈N*), then am+an=ap+aq.
(especially when m= 1, AP+An+ 1-P = A 1+An, that is, the sum of the term "equidistant" from beginning to end is equal to the sum of the first term and the second term. )
(2)S2n- 1=(2n- 1)an .
{an} is proportional: if m+n=p+q(m, n, p, q∈N*), then am an = AP AQ.
7. When calculating the sum of series, discuss the common ratio q= 1 or q≠ 1:x+x2+x3+…xn, that is, 8. When shuxue15.jpgrshuxue65438+performs trigonometric function operation. Shuxue16.jpgrshuxue16.jpgshuxue16.jpgr Pay attention to the deformation and application of the formula. shuxue 17 . jpgrshuxue 17 . jpgrshuxue 17 . jpgrshuxue 17 . jpgrshuxue 17 . jpgrshuxue 1 7. The change form of jpgr's attention angle: shuxue18. jpgrshuxue18. jpgshuxue18.
9. The image of is obtained by shifting the image of y=sin2x to the left through shuxue21.jpgrshuxue21.jpgr.
10, generally, we should use inductive formula to make the x coefficient positive, and then find the monotonous interval.
1 1. Understand the geometric meaning of derivatives. F(x0) is the slope of the tangent of curve y=f(x) at point (xo, f(xo), while s, (t0) is the instantaneous motion speed at t0, and v, (t0) is the acceleration at t0. In the new high examination questions in 2002, derivative is also widely used in finding monotonicity of function, maximum value of function and proving inequality. See the new college entrance examination questions 19 in 2003, 2 1 in 2006, 2 1 in 2000 and 2 1 in 2003. Let's write down the following questions: Known.
1 √52
{y=x2
y=x+2} .
12, when solving the equations of straight lines and circles, we should choose the equation form reasonably according to the characteristics, pay attention to the limitations of various equation forms, and prevent missing solutions.
13, straight lines and circles are the main objects of leveling research, and we should be good at using leveling knowledge to solve problems about straight lines and circles. For example, the determination of the positional relationship between a straight line and a circle, and the chord length obtained by cutting a circle with a straight line can be converted into the distance from the center of the circle to the straight line.
14. Flexible application of the definition of conic curve. (Choice related to focus, often used to fill in the blanks) Pay attention to the unified definition of conic to solve the problem that indefinite conic is ellipse, hyperbola or parabola.
15. Determine the standard agenda of conic section. Don't forget the diversity of standard equations. The important method used is the undetermined coefficient method.
16. What is an equilateral hyperbola? And what is the hyperbolic equation of hyperbola?
17, the positional relationship between straight line and conic curve.
① Number of common * * * points: eliminate simultaneous equation (eliminate X or y)→ unary equation ② Chord length: linear parameter equation method, projection method (flexibly use Vieta theorem).
18, find trajectory, trajectory equation, and don't forget to find constraints.
19, pay attention to make full use of plane vector method to analyze geometric problems.
For example, in 2003, the college entrance examination in Jiangsu Province asked the 20th question (stress).
20. The formula for finding the distance by volume method: (D is the distance from A to surface BCD, V is the volume of triangular pyramid A-BCD, and S is the area of △BCD.
Vertex transfer method or dig-and-fill method is often used to find the volume v.
2 1, understanding: polyhedral Euler formula: F+V=E+2, which can be tested by triangular pyramid.