Let me show you these first.
Memos that are easy to make mistakes, confuse and forget in high school mathematics.
1. When the condition A∪B = Ba∪B = AAB is applied, it is easy to ignore that A is an empty set φ.
2. It is easy to ignore the principle of domain priority when solving problems related to functions.
3. When judging the parity of a function, it is easy to ignore whether the domain of the function is symmetrical about the origin.
4 When finding the inverse function, it is easy to ignore the domain of finding the inverse function.
A useful conclusion between 5 function and its inverse function;
6 If the original function monotonically increases in the interval [-a, a], there must be an inverse function, and the inverse function also monotonically increases; But functions have inverse functions and are not necessarily monotonous. For example:
7 What is the standard format for proving monotonicity of a function according to the definition? (value, difference, positive or negative)
When using the mean value theorem to find the maximum value (or range), it is easy to ignore the condition of verifying "one positive, two definite and three equal"
Do you know the monotone interval of a function? (This function is monotonically increasing in number; This is a widely used function! (Its image in the first quadrant "√", specially named as tick function) is odd function, and the image is symmetrical about the origin.
Monotone interval of function: increasing monotonously in the world; Odd number function, the image is symmetrical about the origin.
10 When solving the logarithmic function problem, did you notice the restrictions on real numbers and bases?
(The true number is greater than zero, and the cardinal number is greater than zero and not equal to 1) The letter cardinal number needs to be discussed.
1 1 When judging the number of solutions (or the number of intersections) of an equation by discriminant, it is easy to ignore whether the coefficient of the quadratic term is 0, especially when a straight line intersects a conic curve.
Important properties in 12 arithmetic progression: if m+n=p+q, then; (otherwise)
Important properties in geometric series: if m+n=p+q, then (the opposite is not true).
When summing 13 with the summation formula of equal ratio series, it is easy to ignore the common ratio Q = 1.
When 14 is known, it is easy to ignore the case of n = 1.
A property of 15 arithmetic progression: Let it be the sum of the first n terms of the sequence {0}, and the necessary and sufficient conditions for {0} to be arithmetic progression are: (a, b are constants) Its tolerance is 2a.
16 do you know the method of "dislocation subtraction" in the summation of series? (If {} is arithmetic progression and {} is geometric progression, find the sum of the first n items of {}).
17 Remember the split term summation? (for example)
18 When solving trigonometric problems, did you notice the domain of tangent function and cotangent function? Notice the boundedness of sine and cosine functions?
19 do you remember the general method of triangle simplification? (Chord cutting, power reduction formula, transformation by trigonometric formula, special angle, abnormity, homonym, high order and low order)
Remember the formula of arc length and sector area under arc system? )
2 1 in the triangle. Do you know how much 1 equals? These are collectively referred to as 1 substitution) constants.
The substitution of "1" is widely used.
22 is different from the real number 0, and its modulus is 0. It is not that there is no direction, but that the direction is uncertain. It can be considered to be parallel to any vector, but not perpendicular to any vector.
23, then, but can't get the task force.
At 24: 00, if there is inversion, it cannot be launched.
Generally 25.
26 in the middle,
When sine theorem is used, the forgetting rate is equal to 2R.
When multiplying two inequalities, we must pay attention to the same direction and the same time to multiply, that is, we can multiply in the same direction; At the same time, we should pay attention to "the same number can be reversed"
That is, a > b > o, a < b < o.
What is the general idea of solving fractional inequality? (General division of shift term, zero segmentation)
30 solution refers to what problems should be paid attention to in inequality? Monotonicity of exponential function and logarithmic function, the real number of logarithm is greater than zero)
3 1 How to discuss when solving inequalities with parameters? After the discussion (especially the bottom sum of exponent and logarithm), write: In summary, the solution of the original inequality is …
32 common zoom techniques:
The main idea of analytic geometry is to study the properties of graphics by algebraic method. The main method is coordinate method.
It is easy to ignore the fact that the slope does not exist when establishing an equation of a straight line with inclined points and inclined sections.
35 The values of inclination angle, arrival angle and included angle of straight line are as follows
The formulas of image translation, equation translation and point translation of function 36 are chaotic;
⑦ Translation formula of points: point P(x, y) translates to point P/ (x/, y/) according to vector =(h, k), then x/= x/=x+ h, y/= y/ =y+
k
37 What is the coordinate formula of the fixed point? (You can specify the starting point, midpoint, equinox and value)
38 pairs of non-overlapping two straight lines,, have
; (When solving problems, use slope and intercept after discussion)
The intercept of a straight line on the coordinate axis can be positive, negative or 0.
There are two ways to deal with the positional relationship between a straight line and a circle: (1) the distance from a point to a straight line; (2) The equation of a straight line is simultaneous with the equation of a circle, and the discriminant is generally simple.
4 1 deals with the positional relationship between circles, and the relationship between the center distance and radius of two circles can be used.
In a circle, pay attention to the right triangle composed of radius, half chord length and chord center distance.
Remember the two definitions of conic section? Will solving related problems be related to these two definitions?
Do you remember the meaning of a, b, c, p,, in the conic equation?
What is the relationship between eccentricity and curve shape? What is the eccentricity of equilateral hyperbola?
When solving with conic curve and straight line at the same time, we should pay attention to the equation obtained after elimination: Is the coefficient of quadratic term zero? Limitations of discriminant (finding intersection, chord length, midpoint, slope, symmetry and existence are all carried out below)
In the ellipse, pay attention to the right triangle (A, B, C) consisting of the focus, the center of the circle and the endpoint of the short axis.
Path 48 is the shortest chord of all focus chord of parabola (think about the conclusion in hyperbola? And a representation of the length)
Do you know the difference between a, b and c in elliptic and hyperbolic standard equations?
If a straight line is parallel to the asymptote of hyperbola, then this straight line intersects with hyperbola at only one intersection point; If the straight line is parallel to the axis of the parabola, and the straight line intersects the parabola with only one intersection point, then the two equations are simultaneous, and after elimination, they are linear equations.
The definition of latitude and longitude of 5 1 is confusing.
When finding the angle formed by two straight lines on different planes, the angle formed by a straight line and a plane, and the dihedral angle, if the angle is 90, don't forget that there is another way to find the angle, which is to prove that they are vertical.
The judgment theorem and property theorem of line-plane parallelism are three conditions in application, but these three conditions are easy to be confused; The judgment theorem of plane-to-plane parallelism is easy to record the condition as "two intersecting straight lines in one plane are parallel to two intersecting straight lines in another plane", which leads to too big steps in the proof process.
What is the main method to make the plane angle of dihedral angle? (Definition method, three perpendicular lines method, vertical plane method) Three perpendicular lines method: a plane, two perpendicular lines and three diagonal lines, and the projection is visible.
What is the conventional method to find the distance from a point to a surface? (direct method, equal volume method, change point method, vector method)
What is the conventional method to find the volume of polyhedron? (Cut and Complement Method, Equal Product Transformation Method)
57 Angle range formed by two straight lines in different planes: 0
The range of the angle formed by the straight line and the plane: 0o≤α≤90.
The plane angle range of dihedral angle is 0 ≤α≤ 180.
The order of a and b in binomial expansion formula remains unchanged.
The binomial coefficient is easily confused with the expansion coefficient. The binomial coefficient of R+ 1
The maximum binomial coefficient is easily confused with the maximum binomial coefficient in expansion, and the maximum binomial coefficient is one or two in the middle; The solution of the maximum coefficient term in the expansion is to determine R by solving the inequality group.
6 1 solve the permutation and combination problem on the basis of classified addition, step-by-step multiplication, orderly arrangement and disorderly combination.
The laws to solve the permutation and combination problem are: adjacent problem binding method; Interpolation methods for non-adjacent problems: single-line method for multi-line problems; Positioning problem priority method; Double reduction method of scheduling problem: classification of multivariate problems; Ordered distribution problem method; Select a question first, and then return; At most, at least the indirect method of the problem may be regarded as some justice.
The general formula of binomial expansion, the probability of event A occurring k times in n independent repeated tests, and the distribution table of binomial distribution are all easy to remember.
General formula: (r+ 1 term instead of r term)
Probability of event a happening k times:
Where k = k=0, 1, 2, 3, …, n …, n and 0.
Derivative formulas of 64 commonly used functions:
; ; ;