High school mathematics exam knowledge point daquan
A, straight lines and circles:
1, the inclination range of the straight line is
In the plane rectangular coordinate system, for a straight line intersecting the axis, if the axis rotates counterclockwise around the intersection point to the minimum positive angle when it coincides with the straight line, it is called the inclination angle of the straight line. When the straight line coincides or is parallel to the axis, the specified inclination angle is 0;
2. Slope: If the inclination of the straight line is known as α, α ≠ 90, then the slope k=tanα.
The slope of the straight line passing through two points (_ 1, Y 1) and (_ 2, Y2) is k=( y2-y 1)/(_2-_ 1), and the slope of the tangent is found.
3. Straight line equation: (1) point oblique type: if the slope of the intersection of straight lines is 0, then the straight line equation is 0.
⑵ Oblique intercept type: If the intercept of a straight line on the axis is sum slope, the straight line equation is
4、 , ,① ‖ , ; ② .
The relationship between straight lines:
(1) Parallel A 1/A2=B 1/B2 Attention test (2) Vertical A 1A2+B 1B2=0.
5. Distance formula from point to straight line;
The distance between two parallel lines and is
6. Standard equation of circle: .2 General equation of circle:
Note that the standard equation can be transformed into a general equation.
7. A circle must have two tangents outside the circle. If only one tangent is found, the other tangent is a straight line perpendicular to the axis.
8. The positional relationship between a straight line and a circle is usually transformed into the relationship between the center distance and the radius, or a right triangle is constructed by using the vertical diameter theorem to solve the chord length problem. ① Separation ② Tangency ③ Intersection.
9. When solving the relationship between a straight line and a circle, we should give full play to the plane geometric properties of the circle (such as radius, half chord length and chord center distance to form a right triangle), and the chord length obtained by the intersection of a straight line and a circle.
Second, the conic curve equation:
1, ellipse: ① equation (A >；; B>0) Note that there is another one; ② definition: pf1+pf2 = 2a > 2c； ③ e= ④ Long axis length 2a, short axis length 2b and focal length 2c; a2 = B2+C2；
2. Hyperbola: ① Equation (a, b >；; 0) Note that there is another one; ② definition: pf 1-pf2 = 2a.
3. Parabola: ① Equation y2=2p_ Note that there are three more, which can distinguish the opening direction; ② Definition: PF=d focus f (0), directrix _ =-; ③ focal radius; Focus chord = _1+_ 2+p;
4. The chord length formula of conic section line:
5. Pay attention to the combination of analytic geometry and vector: 1, (1); (2) .
2. Definition of scalar product: given two non-zero vectors A and B, their included angle is θ, and the quantity abcosθ is called scalar product of A and B, and denoted as A B, namely
3. Calculation of the module: a=. To calculate the modulus, you can first calculate the square of the vector.
4, in the process of vector operation, the complete square formula is still applicable:
Three, straight line, plane, simple geometry:
1, learning three views analysis:
2, oblique mapping method should pay attention to the place:
(1) Take the mutually perpendicular axes O_ and Oy in the known graph. When drawing a vertical view, draw it as the corresponding axes o'_' and o'y', so that ∠ _' o' y' = 45 (or135); (2) The length of the line segment parallel to the _ axis is unchanged, and the length of the line segment parallel to the Y axis is halved. (3) The original 45-degree map is 90 degrees under direct vision, and the original 90-degree map under direct vision shall not be 90 degrees.
3, table (edge) area and volume formula:
(1) column: (1) surface area: S=S side +2S bottom; ② Lateral area: S side =; ③ volume: V=S bottom h
⑵ Cone: ① Surface area: S=S side +S bottom; ② Lateral area: S side =; ③ volume: V= S bottom h:
(3) Platform surface area ①: S=S side +S upper bottom S lower bottom ② side area: S side =
⑷ Sphere: ① Surface area: S =；; ② Volume: V=
4. Proof of position relationship (main method): Pay attention to the writing of solid geometry proof.
(1) Straight lines are parallel to the plane: ① Straight lines are parallel to each other; (2) Face-to-face parallel lines are parallel to each other.
(2) Plane is parallel to plane: ① Line is parallel to plane, and surface is parallel to surface.
(3) Vertical problem: the line is vertical, the line surface is vertical, and the surface is vertical. The core is line-plane verticality: two intersecting straight lines in a vertical plane.
5. turning: (step-I. find or make an angle; Two. Cornering)
(1) Solution of included angle formed by straight lines on different planes: translation method: translating straight lines to construct triangles;
⑵ Angle between straight line and plane: Angle between straight line and projection.
Fourth, the derivative:
1, the definition of derivative: the derivative of a point is written as.
2. Geometric and physical meaning of derivative: the slope of the tangent of the curve at this point.
①k=f/(_0) represents the tangent slope of P(_0, f(_0)) on the curve y=f(_). V=s/(t) represents the instantaneous speed. A=v/(t) stands for acceleration.
3. Derivative formulas of commonly used functions: ①; ② ; ③ ;
4. Four algorithms of derivative:
5. The application of derivative:
(1) Using derivative to judge monotonicity of function: Let the function be derivable in a certain interval, and if it is, it is increasing function; If it is, then it is a decreasing function;
Note: If the letter range of the subtraction function is known, then the inequality holds.
(2) The step of finding the extreme value:
① Derivation;
② Find the root of the equation;
(3) List: Check the symbols at the left and right of the root of the equation. If the Zuo Zheng is negative to the right, then the function gets the maximum value at this root; If the left side is negative and the right side is positive, then the function takes the minimum value at this root;
(3) finding the maximum and minimum values of differentiable functions:
? The root of seeking; ? Comparing the root and interval endpoint function values, the largest is the maximum, and the smallest is the minimum.
Five, common logical terms:
1, four propositions:
(1) Original proposition: If p is q; ⑵ Inverse proposition: If q is p; (3) no proposition: if p is q; (4) negative proposition: if q is p
note:
1, the original proposition is equivalent to the negative proposition; Whether the inverse proposition is equivalent or not. To judge whether a proposition is true or not, we should pay attention to transformation.
2. Pay attention to the difference between whether the proposition is negative or not: the negative form of the proposition is; No proposition is. The negation of proposition or is "harmony"; The negative form of "and" is "or".
3. Logical connector:
(1) and: propositional form p q；; p q p q p q p
⑵ or (or): propositional form p q；; True, true, true, false.
(3) not: propositional form P. True false false true false.
Fake, real, fake, real.
False false false true
The true and false characteristics of "or proposition" are "one truth, all false";
The true and false characteristics of the "and proposition" are "if one is false, it must be true";
The true and false feature of "non-proposition" is "one truth and one falsehood"
4. Necessary and sufficient conditions
The conclusion can be deduced from the condition, which is a sufficient condition for the conclusion to be established; If the condition can be deduced from the conclusion, then the condition is the necessary condition for the conclusion to be established.
5. Full name proposition and proper name proposition:
The phrase "all" refers to all in a sentence, which is usually called a full-name quantifier in logic and represented by symbols. A proposition containing all quantifiers is called a full name proposition.
The phrase "you yi" or "some" or "at least one" indicates an individual or part of something in a statement, which is usually called an existential quantifier in logic and is represented by symbols. Propositions containing existential quantifiers are called existential propositions.
Full name proposition p: the negation of full name proposition p:.
Special proposition p: the negation of special proposition p;
Summary of five knowledge points of compulsory mathematics in senior two
permutation and combination
Schedule p- related to the order.
Combination C- does not involve the order problem.
Arrange in order, regardless of combination.
For example, there are several ways to distribute five different books to three people.
There are several ways for three people to divide five books.
1. Arrangement and calculation formula
From n different elements, any m(m≤n) elements are arranged in a column in a certain order, which is called the arrangement of m elements in n different elements; All permutation numbers of m(m≤n) elements from n different elements are called permutation numbers of m elements from n different elements, which are represented by the symbol p(n, m).
p(n，m)= n(n- 1)(n-2)……(n-m+ 1)= n！ /(n-m)！ (regulation 0! = 1).
2. Combination and calculation formula
Taking out any m(m≤n) elements from N different elements and grouping them is called taking out the combination of M elements from N different elements; The number of all combinations of m(m≤n) elements from n different elements is called the number of combinations of m elements from n different elements. Use symbols.
C(n, m) represents.
c(n，m)=p(n，m)/m！ =n！ /((n-m)！ _! ); c(n，m)=c(n，n-m)；
3. Other permutation and combination formulas
Cyclic permutation number of r elements in n elements =p(n, r)/r=n! /r(n-r)！ .
N elements are divided into K classes, and the number of each class is n 1, n2, ... nk. The total arrangement number of these n elements is
n！ /(n 1！ _2! _.._k！ ).
K-type elements, the number of each class is infinite, and the combined number of M elements is c(m+k- 1, m).
Arrangement (Pnm(n is subscript, m is superscript))
Pnm=n×(n- 1)....(n-m+ 1)； Pnm=n！ /(n-m)！ (Note:! Is a factorial symbol); Pnn (two N's are superscript and subscript respectively) =n! ; 0! = 1; Pn 1(n is subscript 1 is superscript) =n
Combination (Cnm(n is subscript, m is superscript))
CNM = Pnm/Pmm； Cnm=n！ /m！ (n-m)！ ; Cnn (two n's are superscript and subscript respectively) =1; Cn 1(n is subscript 1 is superscript) = n；; Cnn = Cnn-m
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Formula P refers to arrangement, and R elements are selected from N elements for arrangement. Formula c refers to the combination, in which r elements are taken from n elements without arrangement. N- the total number of elements, r, the number of elements participating in the selection! -factorial, like 9! =9________
R starts from n, and the expression should be n _ n-1) _ n-2) .. (n-r+1);
Because the number from n to (n-r+ 1) is n-(n-r+1) = R.
Summary of key knowledge of mathematics in senior two.
Set concept
Characteristics of elements in (1) set: certainty, mutual difference and disorder.
(2) The relationship between sets and elements is represented by the symbol =.
(3) Symbolic representation of common number sets: natural number set; Positive integer set; Integer set; Rational number set, real number set.
(4) Representation of sets: enumeration method, description method and Wayne diagram.
(5) An empty set refers to a set without any elements.
An empty set is a subset of any set and a proper subset of any non-empty set.
Encyclopedia of knowledge points in senior two mathematics exams;
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★ Summary of knowledge points in the final exam of the second volume of senior high school mathematics.
★ What does the second year exam mean?
★ 20 17 Senior Two Mathematics Test Questions and Answers
★ 20 17 knowledge points that must be memorized in the midterm exam of senior two mathematics.
★ Summary of knowledge points in chemistry examination of senior two.