Three knowledge points are required in the first volume of mathematics in senior three.

# Senior 3 # Introduction The learning method of Senior 3 is actually very simple, but this method must be maintained all the time to see the results in the final exam. If you are interested in a certain subject or have talent, your academic performance will be significantly improved. If you have enough motivation to study or are influenced or stimulated by some positive factors, your score will also rise sharply. No senior three channel has prepared the compulsory three knowledge points of mathematics in the first volume of senior three for you, hoping to help you!

1. Mathematics in the first volume of Senior Three requires three knowledge points.

Transition section 1. Transition division is a method to find 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 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. The first volume of mathematics in senior three needs three knowledge points.

The domain of (1) exponential function is the set of all real numbers, where a is greater than 0. If a is not greater than 0, there will be no continuous interval in the definition domain of the function, so we will not consider it.

(2) The range of exponential function is a set of real numbers greater than 0.

(3) The function graph is concave.

(4) If a is greater than 1, the exponential function increases monotonically; If a is less than 1 and greater than 0, it is monotonically decreasing.

(5) We can see an obvious law, that is, when a tends to infinity from 0 (of course, it can't be equal to 0), the curves of the functions tend to approach the positions of monotonic decreasing functions of the positive semi-axis of Y axis and the negative semi-axis of X axis respectively. The horizontal straight line y= 1 is the transition position from decreasing to increasing.

(6) Functions always infinitely tend to a certain direction on the X axis and never intersect.

(7) The function always passes (0, 1).

(8) Obviously, the exponential function has no XX.

3. Three knowledge points are needed in the first volume of senior three mathematics.

First, find the probability of complex events:

1. It is impossible to find the probability of some random events by tree diagram and list method, only by experiment and statistics.

2. Any random event has a fixed probability.

3. When doing a lot of experiments on random events, according to the characteristics of repeated experiments, we should pay attention to the following points when determining the probability:

(1) Try to experience the process of repeated experiments, and don't make judgments for granted;

(2) The experiment should be carried out under the same conditions;

(3) The number of experiments should be enough, but not too little;

(4) Record the results of each experiment accurately and in real time;

(5) Calculate the frequency of events in stages from the first time, and express these frequencies intuitively with a broken line statistical chart;

(6) Observe and analyze the statistical chart, find out the gradual stable value of frequency change, and use this stable value to estimate the probability of the event. The advantage of this method of estimating probability is intuitive, but the disadvantage is that the estimated value must be obtained after the experiment, and it is impossible to predict the event.

Second, judge the fairness of the game:

The fairness of the game means that both sides have the same possibility of winning.

Third, the comprehensive application of probability:

Probability can be combined with a lot of knowledge, mainly involving plan, statistical diagram, average, median, mode, function and so on.

4. The first volume of senior three mathematics needs three knowledge points.

Trajectory contains two problems: all points on the trajectory meet the given conditions, which is called the purity of trajectory (also called inevitability); None of the points that are not on the trajectory meet the given conditions, that is, the points that meet the given conditions must be on the trajectory, which is called the completeness (also called sufficiency) of the trajectory.

First, the basic steps of finding the moving point trajectory equation.

1. Establish an appropriate coordinate system and set the coordinates of the dispatching point m;

2. Write a set of points m;

3. List the equation = 0;

4. Simplify the equation to the simplest form;

5. check.

Second, the common methods to find the moving point trajectory equation:

There are many methods to solve the trajectory equation, such as literal translation, definition, correlation point method, parameter method, intersection method and so on.

1, literal translation method: directly translate conditions into equations, and simplify them to get the trajectory equations of moving points. This method of solving trajectory equation is usually called literal translation.

2. Definition method: If it can be determined that the trajectory of the moving point meets the definition of the known curve, the equation can be written by using the definition of the curve. This method of solving trajectory equation is called definition method.

3. Correlation point method: use the coordinates x and y of moving point Q to represent the coordinates x0 and y0 of related point P, and then substitute them into the curve equation satisfied by the coordinates (x0, y0) of point P to simply get the trajectory equation of moving point Q.. This method of solving trajectory equation is called correlation point method.

4. Parametric method: When it is difficult to find the direct relationship between the coordinates of the moving point X and Y, the relationship between X and Y and a variable T is often found first, and then the parameter variable T is eliminated to get the equation, which is the trajectory equation of the moving point. This method of solving trajectory equation is called parameter method.

5. Trajectory method: eliminate the parameters in the two dynamic curve equations, and get the equation without parameters, that is, the trajectory equation of the intersection of the two dynamic curves. This method of solving trajectory equation is called trajectory method.

The general steps of finding the moving point trajectory equation;

(1) Establish a system-establish a suitable coordinate system;

② set point-set any point on the trajectory P(x, y);

(3) Formula —— List the relationship that the moving point P satisfies;

④ Substitution-according to the characteristics of conditions, the distance formula and slope formula are selected, converted into equations about X and Y, and simplified;

⑤ Proof —— Prove that the equation is a moving point trajectory equation that meets the requirements.

5. Three knowledge points are required in the first volume of senior three mathematics.

1, cylinder: surface area: 2πRr+2πRh volume: πR2h(R is the radius of the upper and lower bottom circles of the cylinder, and h is the height of the cylinder).

2. Cone:

Surface area: π R2+π R [square root of (H2+R2)] Volume: πR2h/3(r is the radius of the cone's low circle and H is its height.

3. Cubic

Length of side A, S=6a2, V=a3.

4. Cuboid

A- length, b- width, c- height S=2(ab+ac+bc)V=abc.

5. Prism

S- bottom area h- height V=Sh

6. pyramids

S- bottom area h- height V=Sh/3

7. Prism

S 1 and S2- upper and lower floor area h- height v = h [s1+S2+(s1S2)1/2]/3.