Summary of compulsory knowledge points from one to five in senior high school mathematics 1
1, the definition of a circle:
The set of points whose distance from a point on a plane is equal to a fixed length is called a circle, with the fixed point as the center and the fixed length as the radius of the circle.
2. Equation of circle
(1) standard equation, center and radius r;
(2) General equation
At that time, the equation represented a circle. At this point, the center is and the radius is.
At that time, I said a point; At that time, the equation did not represent any graph.
(3) Method of solving cyclic equation:
Generally, the undetermined coefficient method is adopted: first set, then seek. Determining a circle requires three independent conditions. If the standard equation of a circle is used,
Demand a, b, r; If you use general equations, you need to find d, e, F e, f;
In addition, we should pay more attention to the geometric properties of the circle: for example, the vertical line of a chord must pass through the origin, so as to determine the position of the center of the circle.
3, the position relationship between straight line and circle:
The positional relationship between a straight line and a circle includes three situations: separation, tangency and intersection:
(1) Set a straight line and a circle, and the distance from the center of the circle to L is, then there is
(2) Tangent of a point outside the circle:
①k does not exist, verify ②k exists, establish an oblique equation, and solve k with the distance from the center of the circle to the straight line = radius to get the equation.
(3) The tangent equation of a point passing through a circle: circle (x-a)2+(y-b)2=r2, and a point on the circle is (x0, y0), then the tangent equation passing through that point is (x0-a) (x-a)+(y0-b) (y-b) =
4, the position relationship between the circle and the circle:
It is determined by comparing the sum (difference) of the radii of two circles with the distance (d) between the center of the circle.
Set a circle,
The positional relationship between two circles is usually determined by comparing the sum (difference) of the radii of the two circles with the distance (d) between the center of the circle.
At that time, the two circles were separated, and there were four common tangents at this time;
At that time, the two circles were circumscribed, and the connection line crossed the tangent point, with two outer tangents and one inner common tangent;
At that time, the two circles intersect, and the connecting line bisects the common chord vertically, and there are two external tangents;
At that time, two circles were inscribed, and the connecting line passed through the tangent point, and there was only one common tangent;
At that time, two circles included; It was concentric circles.
Note: when two points on the circle are known, the center of the circle must be on the vertical line in the middle; It is known that two circles are tangent and two centers are tangent to the tangent point.
The auxiliary line of a circle generally connects the center of the circle with the tangent or the midpoint of the chord of the center of the circle.
Summary of compulsory knowledge points from one to five in senior high school mathematics
Sequence definition:
If a series starts from the second term, the difference between each term and its previous term is equal to the same constant. This series is called arithmetic progression, and this constant is called arithmetic progression's tolerance, which is usually represented by the letter D.
The general formula of arithmetic progression is an = a1+(n-1) d (1).
The first n terms and formulas are: Sn=na 1+n(n- 1)d/2 or Sn=n(a 1+an)/2(2).
All the above n are positive integers.
Explanation:
As can be seen from the formula (1), an is a linear function (d≠0) or a constant function (d=0) of n, and (n, an) is arranged in a straight line. As can be seen from the formula (2), Sn is a quadratic function (d≠0) or a linear function (d=
Arithmetic average in arithmetic progression: generally set as Ar, Am+an=2Ar, so Ar is the arithmetic average of Am and An, which is the average of series.
The relationship between any two items am and an is: an = am+(n-m) d.
It can be regarded as arithmetic progression's generalized general term formula.
Reasoning formula:
From arithmetic progression's definition and general formula, we can also deduce the first n terms and formulas: A1+an = A2+an-1= A3+an-2 = … = AK+an-k+1,k ∈ {1.
If m, n, p, q∈N_, m+n=p+q, then am+an=ap+aq, Sm- 1=(2n- 1)an, s2n+1= (2n+.
Basic formula:
Sum = (first item+last item) × number of items ÷2
Number of items = (last item-first item) ÷ tolerance+1
First Item =2, Number of Items-Last Item
Last item =2, number of items-first item
The last term = the first term+(number of terms-1)× tolerance.
Summary of compulsory knowledge points from one to five in senior two mathematics 3
1. Division is a method to find the common divisor. This algorithm was first proposed by Euclid around 500 BC, so it is also called Euclid algorithm.
2. The so-called phase shift method is to divide the larger number by the smaller number for a given two numbers. If the remainder is not zero, the smaller number and the remainder form a new pair of numbers, and continue the above division until the larger number is divided by the decimal, then the divisor is the common divisor of the original two numbers.
3. Multiphase subtraction is a method to find the common divisor of two numbers. Its basic process is: for a given two numbers, subtract the smaller number from the larger number, then compare the difference with the smaller number, subtract the number from the larger number, and continue this operation until the obtained numbers are equal, then this number is the common divisor.
4. Qin algorithm is a method to calculate the value of univariate quadratic polynomial.
5. The commonly used sorting methods are direct insertion sorting and bubble sorting.
6. The carry system is an agreed counting system for the convenience of counting and operation. "All in one" is a K-base system, and the base of the base system is K.
7. The method of converting decimal number into decimal number is: first, write decimal number as the sum of the product of the number on each bit and the power of k, and then calculate the result according to the operation rules of decimal number.
8. The method of converting decimal numbers into decimal numbers is: divide by k and take the remainder. That is, k is used to continuously remove the decimal or the quotient until the quotient is zero, and then the remainder obtained each time is arranged backwards into a number, which is the corresponding decimal.
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