Summary of knowledge points in the next semester of senior two mathematics 1. 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: What is the inclination of the known straight line? There are still 90? , slope k=tan? .
The slope of the straight line passing through two points (X 1, Y 1) and (X2, Y2) is k=( y2-y 1)/(x2-x 1), and the slope of the tangent line is obtained.
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=2px Note that there are three more, which can distinguish the opening direction; ② definition: |PF|=d focus f (0), directrix x =-; ③ focal radius; Focus chord = x1+x2+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 product of quantities: Two non-zero vectors A and B are known, and what is their included angle? , the amount of |a||b|cos? It's called the product of a and b, called a? B, that's
3. Calculation of modulus: |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 Ox and Oy in the known graph. When drawing a vertical view, draw the corresponding axes o'x' and o'y' and make them? x'o'y'=45？ (or 135? ); (2) The length of the line segment parallel to the X 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, derivative: the meaning of derivative-derivative formula-derivative application (extreme value problem, curve tangent problem)
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/(x0) represents the tangent slope of P(x0, f(x0)) on the curve y=f(x). V=s/(t) represents the instantaneous speed. A=v/(t) stands for acceleration.
3. Derivative formulas of commonly used functions: ①; ② ; ③ ;
⑤ ; ⑥ ; ⑦ ; ⑧ 。
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 I; Two. Compare the function values of roots and interval endpoints, and the maximum value is the maximum value and the minimum value is the minimum value.
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. Proposition? Or? What is the negative? And then what? ; ? And then what? What is the negative? 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
? Or a proposition? What are the characteristics of authenticity and falsehood? Is it really true, or is it all fake? ;
? There are propositions? What are the characteristics of authenticity and falsehood? Fake is fake, is it true? ;
? Non-proposition? What are the characteristics of authenticity and falsehood? One true and one false?
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? Representing the whole in a sentence is usually called a full-name quantifier in logic and is represented by symbols. A proposition containing all quantifiers is called a full name proposition.
There is one phrase? Or? Some? Or? At least one? An individual or part that represents something in a sentence is usually called an existential quantifier in logic and is represented by a symbol. The proposition containing existential quantifiers is called existential proposition.
Full name proposition p: the negation of full name proposition p:.