Mathematics examination paper for college entrance examination
Analysis of the answers to the real questions in the college entrance examination mathematics paper
Arrangement of Mathematics Knowledge Points in College Entrance Examination
First, linear equations.
1. Inclination angle of a straight line: the minimum positive angle formed by the upward direction of a straight line and the positive direction of the shaft is called the inclination angle of this straight line, where the inclination angle when the straight line is parallel or coincident with the shaft is 0, so the range of inclination angle of the straight line is.
Note: ① When or, the straight line is perpendicular to the axis, and its slope does not exist.
(2) Every straight line has a unique inclination, except the straight line perpendicular to the axis has a unique slope. When the slope of the straight line is constant, its inclination will be determined accordingly.
2. Several forms of linear equation: point skew, intercept, two points, skew.
In particular, when a straight line passes through two points, that is, the intercept and axis of the straight line on the axis are respectively, the straight line equation is:
Note: If it is the equation of a straight line, the equation of this straight line is, but if it is not this straight line.
Attachment: linear system: for the oblique equations of straight lines, when they are all fixed values, they represent a certain straight line. If they change, the corresponding straight line will also change. (1) when they change, they represent a straight beam passing through a fixed point (0,). (2) when they are fixed values, they represent a set of parallel straight lines when changing.
3.( 1) Two straight lines are parallel:
‖ The conditions for two lines to be parallel are: ① sum is two non-overlapping lines; ② It is obtained on the premise that the slopes of sum exist. Therefore, we should pay special attention to the fact that removing or ignoring any "premise" will lead to wrong conclusions.
(The general conclusion is that for two straight lines, their longitudinal intercept on the axis is, then ‖, and the slope of or does not exist, which is a necessary and sufficient condition for parallelism, and)
Inference: If the inclination of two straight lines is ‖.
(2) Two straight lines are vertical:
Conditions for two straight lines to be perpendicular: ① If the slopes of the sum of two straight lines are sum, then the premise here is that both slopes exist; ②, and the slopes of the two lines do not exist or, and the slopes of the two lines do not exist. (that is, the necessary and sufficient condition of verticality).
4. Angle of intersection of straight lines:
(1) Angle of straight line (direction angle); The angle of a straight line refers to the angle at which the straight line rotates counterclockwise around the intersection point and coincides with it, and its range is, at that time.
⑵ Angle between two intersecting straight lines and: The angle between two intersecting straight lines and refers to the smallest positive angle among the four angles formed by intersecting with, also called the angle formed by and, and its value range is, if, then.
5. The equation of straight line system passing through the intersection of two straight lines is a parameter, excluding)
6. Distance from point to straight line:
⑴ Distance formula from point to straight line: Set a point, and if the distance to straight line is 0, there will be.
note:
1. The distance formula between two points P 1(x 1, y 1) and P2(x2, y2) is:
Special case: distance from point P(x, y) to origin o:
2. Coordinate scores of fixed score points. If the point P(x, y) is divided into directed line segments, where p 1 (x 1, y 1) and p2 (x2, y2), then
Special case, midpoint coordinate formula; Important conclusion, triangle barycenter coordinate formula.
3. The inclination angle of the straight line (0 ≤
4. After two o'clock.
When (that is, the straight line is perpendicular to the X axis), the inclination of the straight line is =, and there is no slope.
⑵ Distance formula between two parallel lines: Let the distance between two parallel lines be.
Attention; Linear system equation
1. The linear system parallel to a straight line: Ax+By+C= 0 has the equation: Ax+By+m=0. (m？ r，C≠m)。
2. The equation of the straight line system perpendicular to the straight line: Ax+By+C= 0 is Bx-Ay+m=0. (m？ r)
3. The linear system equation passing through the fixed point (x 1, y 1) is: a (x-x1)+b (y-y1) = 0 (a and b are not all 0).
4. The equation of line system passing through the intersection of line l 1 and l2: (a1x+b1y+c1)+λ (A2x+B2y+C2) = 0 (λ? R) Note: This linear system does not contain l2.
7. About point symmetry and about straight line symmetry:
(1) Two straight lines symmetrical about a point must be parallel lines, and the distance from the point to the two straight lines is equal.
⑵ The properties of two straight lines that are symmetrical about a straight line: If the two straight lines are parallel, the symmetrical straight lines are also parallel, and the distances from the two straight lines to the symmetrical straight lines are equal.
If two straight lines are not parallel, the symmetrical straight line must cross the intersection of the two straight lines, and the symmetrical straight line is the bisector of the included angle between the two straight lines.
⑶ A point is symmetrical about a straight line, and the midpoint represents two symmetrical points, then the midpoint is on the symmetrical straight line (Equation ①). The required symmetrical point can be found by the linear equation of the two symmetrical points being perpendicular to the symmetrical straight line equation (Equation ②) ① ②.
Note: ① Solution of curve and straight line symmetry about a straight line (): y is x, and x is y Example: curve f(x, y)=0 about straight line y = x–2 Symmetrical curve equation is f (Y = X-2, x–2) = 0.
② Curve C: f(x, y)=0 The symmetric curve equation about point (a, b) is f (a–x, 2b–y) = 0.
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