High School Mathematics Elective 4 5 Inequality Elective Learning Summary Report

To give you a lesson plan, it's better for you to refer to it, this thing is almost the same when you write it around.

The basic properties of inequalities.

Theorem 1, symmetry).

2) (Theorem 2, Transitivity).

Theorem 3, additive monotonicity).

Theorem 3 corollary, the sum of homotropic inequalities).

Heterotropic inequality subtracted).

Theorem 4, multiplication monotonicity).

Theorem 4 Corollary 1, multiplication of inequalities in the same direction).

Heterotropic inequality division) (10) * reciprocal relation).

Theorem 4, Corollary 2, Flat Method).

Method) Inequality Summary and Review (1).

Teaching Objectives: 1. Master the common basic inequalities, and be able to use them to prove inequalities and find the maximum value;

2. Understand the nature of inequalities with absolute values;

3. Solve simple higher order inequalities, fractional inequalities, inequalities with absolute values, simple irrational inequalities, exponential inequalities, and logarithmic inequalities. Learn to use the ideas and methods of number and form combination, classification discussion, and equivalent transformation to analyze and solve problems.

Teaching process: 1. Review and introduction: the knowledge points of this chapter.

2. Explanation examples: several types of common problems.

a) Solutions to inequalities with parameters.

Example 1: Solve the inequality about x

Example 2: Solve the inequality about x

Example 3: Solve the inequality about x

Example 4 solves the inequality with respect to x.

Example 5 The set of x satisfying is a; Meet x

The set of b 1 if a b finds the range of a 2 if a b finds the range of a 3 if a b is a set of only one element, finds the value of a.

2) The maximum value and range of the function.

Example 6 To find the maximum value of the function, is the following solution correct? Why?

Solution 1: , Solution 2: When is , Example 7 If , find the maximum value of .

Example 8 Knowing that x and y are positive real numbers, and are in a series of equal differences, and in a series of proportional numbers, find the range of values for .

Example 9 Let and , find the maximum value of .

Example 10 The maximum value of the function is 9 and the minimum value is 1, find the values of a and b. 3. Assignments:

2. If , find the range of values of a.

5 When a is in what range of the equation: There are two different negative roots6 If both roots of the equation are for 2, find the range of the real number m7 Find the maximum value of the following function:

8 1 when finding the minimum value of , the minimum value of .

2 Let , find the maximum value of .

3 If , find the maximum value of .

4 If and , find the minimum value of .

9 If , verify that the minimum value of : is 3

10 Make a cylindrical container with a volume of (with a bottom and a cover), ask the radius of the bottom of the cylinder and the radius.

How much is the height of each high, the most economical material? (Excluding the loss during processing and the materials used for the joints).

This can be done by categorical discussion, or it can be done with a number line. 1. Classification discussion, take the first problem as an example, divided into three types of situations, x<-3, -3<=x<=2, x>2, so that they are solved separately, there is x belongs to r2, the number axis, the meaning of the first question is the distance from point x to point 2 and the distance from point x to point -3, and the graph is solved.

(1) First, set the zero point of the absolute value to x=2 and x=-3, so the zero point is discussed in segments.

When x<-3: -(x-2)-(x+3)=-2x-1 4, get x, so x<-3

When x=-3: 5+0 4 holds.

When -32: x-2+x+3=2x+1 4, we get: x, so x>2 In summary: x is an arbitrary real number.

2）。Ditto.

Firstly, the linear relation (multivariate one-time) is used, and the known (x+y, x-y) is used to represent the desired (x+5y).

Secondly, the property of the absolute value inequality is used to obtain the required conclusions.

For reference, please smile.

The formula that uses the symbol ">" to indicate the relationship between size and size is called an inequality. The formula that uses "≠" to represent an inequality relationship is also an inequality.

Usually the numbers in inequalities are real numbers, and letters also represent real numbers, and the general form of inequality is f(x,y,......z)≤g(x，y，……z) where the inequality sign can also be one of , the common domain of the analytic formula on both sides is called the definition domain of the inequality, and the inequality can express both a proposition and a problem.

Generally speaking, the formula that expresses the size relationship with the pure greater than sign ">" and less than the sign "<" is called an inequality. The formula that uses "≠" to represent an inequality relationship is also an inequality.

The common domain of the analytic formula on both sides is called the domain of the inequality.

Integer inequality:

Integer inequalities are integers on both sides (i.e., unknowns are not on the denominator).

Unary Inequalities: Inequalities that contain one unknown number (i.e., unary number) and the number of unknowns is one (i.e., one). Such as 3-x>0

In the same way, a binary inequality is an inequality that contains two unknowns (i.e., binary) and the number of unknowns is one (i.e., one).

In addition, there are three special properties of inequalities:

Inequality property 1: the same number (or formula) is added (or subtracted) on both sides of the inequality at the same time, and the direction of the inequality sign does not change;

Inequality property 2: both sides of the inequality are multiplied (or divided) by the same positive number at the same time, and the direction of the inequality sign is unchanged;

Inequality property 3: Both sides of the inequality are multiplied (or divided) by the same negative number at the same time, and the direction of the inequality sign changes.

I hope I can help you with your doubts.

When x>=1, the original formula is 20

The solution set is x>=1

When -1-4 solves the set is -4-4