"Properties of Equality and Properties of Inequality" Quadratic Functions, Equations and Inequalities PPT (Lesson 1: Inequality Relations and Inequalities)

Description

"Properties of Equality and Properties of Inequality" Quadratic Functions, Equations and Inequalities PPT (Lesson 1: Inequality Relations and Inequalities)

Part One: Learning Objectives

1. Be able to use inequalities (groups) to express inequality relationships in practical problems. (difficulty)

2. Be able to use the comparison method to compare the size of two real numbers. (emphasis)

core competencies

1. Use practical problems to express inequalities and improve mathematical modeling literacy.

2. Cultivate logical reasoning skills through size comparison.

PPT on the properties of equations and inequalities, part 2: independent preview to explore new knowledge

A preliminary exploration of new knowledge

1. unequal relationship

The unequal relationship is often represented by _______.

2. Comparative size of real numbers a and b

Literal language Mathematical language Equivalence conditions

a-b is a positive number a-b>0 a>b

a-b is equal to zero a-b=0 a=b

a-b is a negative number a-b＜0 a＜b

3. Important inequalities

Generally, ∀a, b∈R, there is a2+b2　2ab,

The equal sign holds true if and only if ______.

First try

1. The "40-ton weight limit" warning sign erected at the head of the bridge instructs drivers to safely pass the bridge so that the total weight T of vehicles and cargo should not exceed 40 tons. The inequality is expressed as ()

A． T<40

B． T>40

C. T≤40

D. T≥40

2. The maximum speed v of vehicles required to drive on a certain highway is 120 km/h, and the distance d between vehicles on the same lane must not be less than 10 m. The inequality is expressed as ()

A． v≤120 km/h and d≥10 m

B． v≤120 km/h or d≥10 m

C. v≤120 km/h

D. d≥10 m

3. The temperature of lightning is about 28 000 ℃, which is 4.5 times higher than the surface temperature of the sun. Assume that the surface temperature of the sun is t ℃, then the relationship that t should satisfy is ________.

4. Assume M=a2, N=-a-1, then the relationship between M and N is ________.

PPT on the properties of equations and inequalities, the third part: cooperative exploration to improve literacy

Express inequality relations using inequalities (groups)

[Example 1] On the Beijing-Shanghai line, the Fuxing train ran at a speed of 350 km/h. Twice this speed plus 100 km/h does not exceed the minimum speed of civil aviation, but this speed has exceeded the speed of ordinary aircraft. 3 times that of a passenger car. Please use inequalities to express the relationship between the speeds of the three modes of transportation.

[Solution] Suppose the speed of the Fuxing train is v1,

The speed of civil aviation aircraft is v2,

The speed of ordinary passenger cars is v3.

The relationship between v1 and v2: 2v1+100≤v2,

The relationship between v1 and v3: v1>3v3.

regular method

When using inequality group to express an inequality relationship, the quantities to be compared must have the same properties. Two or several  quantities that are not comparable cannot be expressed by inequality group. In addition, when using inequality group When inequalities group represent practical problems, we must pay attention to the unity of units.

Track training

1. Use a 30 m long fence to form a rectangular vegetable garden with one side against the wall. The wall length is 18 m. The area of ​​the vegetable garden is required to be no less than 216 m2. The length of one side against the wall is x m. Use inequalities to express the unequal relationships.

Compare the magnitude of two numbers (expressions)

[Example 2] Given that x≤1, compare the sizes of 3x3 and 3x2-x+1.

[Solution]3x3-(3x2-x+1)＝(3x3-3x2)+(x-1)

=3x2(x-1)+(x-1)＝(3x2+1)(x-1)．

∵x≤1 means x-1≤0, and 3x2+1>0,

∴(3x2+1)(x-1)≤0,

∴3x3≤3x2－x+1.

PPT on the properties of equations and inequalities, part 4: Complying with standards in class and solidifying the bases

1. Thinking and analysis

(1) The meaning of the inequality x≥2 means that x is not less than 2.()

(2) If either a

(3) If a>b, then ac>bc must be true. ()

[Tips] (1) Correct. The inequality x≥2 means x>2 or x=2, that is, x is not less than 2, so this statement is correct.

(2) Correct. The inequality a≤b means a

(3)Error. ac-bc=(a-b)c, which is related to the sign of c.

2. The following expression of the inequality relationship "the difference between a and b is a non-negative number" is ( )

A． a-b>0

B． a-b<0

C. a-b≥0

D. a-b≤0

3. If the real number a>b, then a2-ab________ba-b2. (fill in ">" or "<").

4. To complete a decoration project, the carpenters need to be paid a total salary of 500 yuan per person, and the bricklayers need to be paid a total salary of 400 yuan per person. The existing worker salary budget is 20,000 yuan. Let there be x carpenters and y bricklayers. Use the inequality to express the above relation.

Keywords: Free download of PPT courseware for compulsory course 1 of Mathematics in High School People's Education A version, PPT download of properties of equations and properties of inequalities, PPT download of quadratic function equations and inequalities of one variable, PPT download of inequality relations and inequalities, .PPT format;

For more information about the PPT courseware "Inequality relations and inequalities, quadratic function equations of one variable and inequalities, properties of equality and properties of inequalities", please click on the Inequality relations and inequalities ppt Quadratic function equations of one variable and inequalities ppt Properties of equality and properties of inequalities ppt tag .