Knowledge points of the first volume of eighth grade mathematics in Shanghai Science Edition (1)
Coordinate characteristics of points on the plane
1, the coordinate characteristics of point P(a, b) in each quadrant:
The first quadrant: a>0, b>0; The second quadrant: a
(Note: Quadrants 1 and 3 have the same horizontal and vertical symbols, namely ab>0; Two or four quadrants, with opposite signs, namely AB.
2. Coordinate characteristics of point P(a, b) on the coordinate axis:
On the x axis: a is an arbitrary real number, and b = 0；; On the y axis: b is an arbitrary real number, and a = 0；; Origin of coordinates: a=0, b=0.
(Note: If P(a, b) is on the coordinate axis, then ab = 0；; Conversely, if ab=0, then P(a, b) is on the coordinate axis. )
3. Coordinate characteristics of point P(a, b) on the bisector of two axes:
Mathematics knowledge points of eighth grade in Shanghai science edition (2)
Angular attribute of triangle
1, trilateral relation of triangle:
The sum of any two sides in a triangle is greater than the third side; The difference between any two sides is less than the third side.
2, triangle triangle relationship:
Theorem of sum of interior angles of triangle: the sum of three interior angles of triangle is equal to 180? .
Theorem of sum of external angles of triangle: The sum of three external angles of triangle equals 360? .
3. Exterior Angle Properties of Triangle
(1) An outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it;
(2) The outer angle of a triangle is larger than any inner angle that is not adjacent to it.
Mathematics knowledge points of eighth grade in Shanghai science edition (3)
linear function
1, general form: y=k x+b(k and b are constants, k? 0), when b=0, y=k x(k? 0), where y is a proportional function of x.
2. Images and properties of linear functions
3. Determine the intersection of the linear function image and the coordinate axis.
(1) and the intersection of the x axis:
(2) Intersection with Y axis: (0, b), solution: let x=0 and find Y. ..
4. Determine the resolution function once? method of undetermined coefficients
Determine the resolution function once, just x and y.
(1) Let the functional relationship be: y = k x+b;
(2) Substituting two pairs of corresponding X and Y values to obtain the equations about K and B;
(3) Solve the equation and find out K and B. ..
5. The meaning of k and b (1)∣k∣ determines a straight line? Flat and steep? . ∣k∣ The bigger the straight line, the steeper it is (or the closer it is to the Y axis); The smaller ∣k∣, the flatter the straight line (or the farther away from the y axis);
(2)b represents the intercept on the y axis. (Intercept and Positive and Negative)
6. Determine the sign of k and b (1) to rise linearly from the linear function image, where k >；; 0; Go straight, K.
(2) The straight line intersects the positive semi-axis of the Y axis, b >；; 0; The straight line intersects the negative semi-axis B of the Y axis.
7. The positional relationship between two straight lines
Straight line l 1: y? k 1x？ B 1 and L2 line: y? k2x？ b2