The third year last semester mathematics book catalogue the third year second volume mathematics book catalogue the third year mathematics important knowledge points (1) A quadratic equation
1. An integral equation that contains only one unknown (unary) and the highest degree of the unknown is 2 (quadratic) is called unary quadratic equation.
2. Solution of quadratic equation in one variable
(1) Kaiping method (2) Matching method
(3) Factorization method (4) Root formula method
3. Discriminating formula
Using the discriminant of the roots of quadratic equation (△=b? -4ac), we can judge the root of the equation.
(1) when △ >; 0, the equation has two unequal real roots;
(2) When △=0, the equation has two equal real roots;
(3) When△
(2) circle
1. In a plane, a closed curve formed by a moving point rotating around a certain point is called a circle. A circle has countless axes of symmetry.
2. Diameter
The line segment connecting the center of the circle and any point on the circle is called radius, and the letter is expressed as R.
The line segment passing through the center of the circle with both ends on the circle is called the diameter, and the letter is expressed as D.
A straight line with a diameter is the symmetry axis of a circle. In the same circle, the diameter of the circle is d=2r.
3. Chord: A line segment connecting any two points on a circle is called a chord.
The longest chord in the same circle is the diameter. The straight line with the diameter is the symmetry axis of the circle, so there are countless symmetry axes of the circle.
4. Arc: The part between any two points on the circle is called arc.
5. The vertical diameter theorem of a circle
(1) bisects the chord perpendicular to its diameter and bisects the two arcs it faces.
(2) The perpendicular line of the chord passes through the center of the circle and bisects the two arcs opposite to the chord.
(3) bisect the diameter of an arc opposite to the chord, bisect the chord vertically, and bisect another arc opposite to the chord.
6. Tangent Theorem of Circle
(1) The radius perpendicular to the tangent point; The straight line passing through the outer end of the radius and perpendicular to the radius is the tangent of the circle.
(2) Determination method of tangent: The straight line passing through the outer end of the radius and perpendicular to this radius is the tangent of the circle.
7. Round corner theorem of a circle
(1) The degree of the circumferential angle is equal to half the degree of the arc it faces.
(2) The angle of the arc is equal to half of its central angle.
(3) "Equal arc and equal angle" and "Equal angle and equal arc".
(4) "Diameter to right angle" and "Right angle to diameter".
8. The circumference is equal, and the area of a circle is larger than that of a square, rectangle or triangle.