1. Three math knowledge points required in the first volume of Senior Two.
1. Commutation 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 exchange method is to divide a larger number by a 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 the above division is continued until the larger number is divided by a decimal. At this time,
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 number into decimal number is: divide by k, and the remainder. That is to say, k is used to continuously divide the decimal number or quotient until the quotient is zero, and then the remainder obtained each time is arranged as an inverse number, which is the corresponding decimal number.
2. Three knowledge points must be tested in the first volume of high school mathematics.
1. What are the properties of hyperbola?
1, hyperbolic focal radius formula:
The distance from any point on the conic to the focus. The radius of the right focus is r = | ex-a |；; Radius of left focus r=|ex+a|
2. Right-angled hyperbola
The real axis and imaginary axis of hyperbola are equal in length, 2a=2be=√2.
3. * * * Yoke hyperbola
(x 2/a 2)-(y 2/b 2) = 1 and (y 2/b 2)-(x 2/a 2) = 1 called * * yoke hyperbola.
(1)*** asymptote
(2)e 1+E2 & gt； =2√2
4. Alignment:
X = a 2/c or y = a 2/c.
Second, the definition of hyperbola
1: On the plane, the locus of a point whose absolute value of the difference between the distances to two fixed points is a constant 2a (less than the distance between two fixed points) is called a hyperbola. The fixed point is called the focal point of hyperbola, and the distance between the two focal points is called the focal length, which is represented by 2c.
2. On the plane, the ratio of the distance to a given point and a straight line is a constant e (e >; 1 is the eccentricity of hyperbola; The locus of a point whose fixed point is not on a straight line is called hyperbola. The fixed point is called the focus of hyperbola, and the fixed line is called the directrix of hyperbola.
3. Plane cutting conical surface. When the cross section is not parallel to the generatrix of the conical surface and does not pass through the vertex of the conical surface, and the two conical surfaces of the conical surface intersect, the intersection line is called hyperbola.
4. In the plane rectangular coordinate system, when the binary quadratic equation F (x, y) = AX2+2bxy+CY2+2dx+2ey+f = 0 meets the following conditions, the image is hyperbolic.
3. Three knowledge points are needed in the first volume of senior two mathematics.
Examples of 1 and divisor are in the range of natural numbers (0 and positive integers).
Any positive integer is a divisor of 0.
The positive divisor of 4 is: 1, 2,4.
The positive divisor of 6 is 1, 2, 3, 6.
The positive divisor of 10 is: 1, 2,5, 10.
The positive divisors of 12 are: 1, 2,3,4,6, 12.
The positive divisor of 15 is: 1, 3,5, 15.
The positive divisor of 18 is: 1, 2,3,6,9, 18.
The positive divisors of 20 are: 1, 2, 4, 5, 10, 20.
Note: The divisor of a number must include 1 and itself.
2. How to find the divisor?
Using divisor theorem
For a number A, the prime factor can be decomposed into: a=a 1 times the power of r65438 +0 times the power of r2 of a2 times the power of a3 ... Then the divisor of A is (r1+1) (R2+1) (R3+/kloc).
It should be pointed out that all prime factors of a 1, a2, a3…… .................................................................................................................................................. ...
For example, 360 = 2 3 * 3 2 * 5 (for power)
So the number is (3+1) * (2+1) * (1+1) = 24.
4. Three knowledge points are needed in the first volume of senior two mathematics.
1, what are the conditions for derivation?
1, the function is defined in the centripetal neighborhood of this point.
2. The left and right derivatives of the function exist at this point.
3. Left derivative = right derivative
Note: This is similar to the limit existence of a function at a certain point.
2. The concept of derivative
Derivative is also called derivative function value. Also known as WeChat quotient, it is an important basic concept in calculus. When the independent variable x of the function y=f(x) generates an increment δ x at the point x0, if there is a limit a in the ratio of the increment δ y of the function output value to the increment δ x of the independent variable when δ x tends to 0, then A is the derivative at x0, which is denoted as f'(x0) or df(x0)/dx.
Derivative is the local property of function. The derivative of a function at a certain point describes the rate of change of the function near that point. If the independent variables and values of the function are real numbers, then the derivative of the function at a certain point is the tangent slope of the curve represented by the function at that point. The essence of derivative is the local linear approximation of function through the concept of limit. For example, in kinematics, the derivative of the displacement of an object with respect to time is the instantaneous velocity of the object.
Not all functions have derivatives, and a function does not necessarily have derivatives at all points. If the derivative of a function exists at a certain point, it is said to be derivative at this point, otherwise it is called non-derivative. However, the differentiable function must be continuous; Discontinuous functions must be non-differentiable.
For differentiable function f(x), x? F'(x) is also a function called the derivative function of f(x). The process of finding the derivative of a known function at a certain point or its derivative function is called derivative. Derivative is essentially a process of finding the limit, and the four algorithms of derivative also come from the four algorithms of limit. Conversely, the known derivative function can also be used to find the original function, that is, indefinite integral.
5. The first volume of senior two mathematics requires three knowledge points.
1, how to calculate the slope?
The tangent value of the angle formed by a straight line and the positive and semi-axis directions of the horizontal coordinate axis of the plane rectangular coordinate system is the slope of the straight line relative to the coordinate system. If the straight line is perpendicular to the X axis, then the tangent of the right angle is infinite, so the straight line has no slope. For any point on any function, its slope is equal to the tangent value of the angle formed by its tangent and the positive direction of X axis, that is, k=tanα. The product of slopes of two vertically intersecting lines is-1:k1+k2 =-1. The general calculation method is as follows:
general formula
For straight lines, the general formula Ax+By+C=0, and the slope formula is: k =-a/b.
slope intercept form
When the slope of the straight line L exists, the oblique formula y=kx+b, and when x=0, Y = B. ..
Point-oblique type
When the slope of the straight line L exists, the point inclination y2-y 1=k(x2-x 1).
2. Slope correlation formula
When the slope of the straight line L exists, the inclined section y = KX+B. When x=0, y = B.
When the slope of the straight line L exists, the point inclination y2-y 1=k(x2-x 1).
For any point on any function, its slope is equal to the tangent value of the angle formed by its tangent and the positive direction of X axis, that is, k=tanα.
Slope calculation: straight line ax+by+c=0, and slope k =-a/b.
Let the straight line y=kx+b(k≠0), then there is
① The product of the slopes of two vertically intersecting straight lines is-1:k1* k2 =-1;
② The slopes of two parallel straight lines are equal: k 1=k2, b 1≠b2.