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;

The distance between two parallel lines and is

2. The standard equation of a circle: (2) General equation of circle:

Note that the standard equation can be transformed into a general equation.

3. 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.

4. 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 (X 1, Y 1) and (X2, Y2) is k=( y2-y 1)/(x2-x 1), and the slope of the tangent line is obtained.

5. Distance formula from point to straight line;

6. 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.

7. 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

8、 , ,① ∥ , ; ② .

The relationship between straight lines:

(1) Parallel A 1/A2=B 1/B2 Attention test (2) Vertical A 1A2+B 1B2=0.

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. 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;

3. Hyperbola: ① Equation (a, b >；; 0) Note that there is another one; ② definition: || pf 1 |-| pf2 || = 2a

4. The chord length formula of conic section line:

5. Pay attention to the combination of analytic geometry and vector:

1, the definition of the product of quantities: two non-zero vectors A and B are known, and their included angle is θ, then the quantity |a||b|cosθ is called the product of the quantities of A and B, which is denoted as A B, that is.

2. The complete square formula is also suitable for vector operations, such as

3. Calculation of modulus: |a|=. To calculate the modulus, you can first calculate the square of the vector.

Three, straight line, plane, simple geometry:

1, learning three views analysis:

2. Find the corner: (Step 1. Find or make the corner; 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.

3, 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 it as the corresponding axes o'x' and o'y' so that ∠ x' o' y' = 45 (or135); (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.

4. Proof of position relationship (main method): Pay attention to the writing of solid geometry proof.

(1) The line is parallel to the plane: ① The line is parallel, and the line is parallel to the plane; (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, 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=

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. Derivative formulas of commonly used functions: ①; ② ; ③ ;

⑤ ; ⑥ ; ⑦ ; ⑧ 。

3. Four algorithms of derivative:

4. Geometric and physical meaning of derivative: the slope of the tangent of the curve at this point.

① k = 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.

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. Note whether the proposition is negative. The difference between propositions: the form of proposition negation is; No proposition is. The negation of proposition or is "harmony"; The negative form of "and" is "or".

2. 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.

3. 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.

4. 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"

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;