"End of Chapter Review Lesson" Equality and Inequality PPT

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"End of Chapter Review Lesson" Equality and Inequality PPT

Question type exploration

The relationship between the roots and coefficients of a quadratic equation

[Example 1] If the quadratic equation (k-1)x2-2x+1=0 about x has two unequal real roots, then the value range of k is ()

A． k＜2 and k≠1　B． k<2 and k≠0

C． k>2 D. k<-2

A[∵The quadratic equation (k-1)x2-2x+1=0 with respect to x has two unequal real roots,

∴k-1≠0 and Δ=(-2)2-4(k-1)×1>0,

Solution: k<2 and k≠1, so choose A.]

regular method

According to the definition of a quadratic equation and the discriminant of the roots, k-1≠0 and Δ=-22-4k-1×1＞0.

solution set of a system of equations

[Example 2] If the solution of the system of linear equations of two variables a1x+b1y=-2 and a2x-b2y=4 with respect to x and y is x=1, y=2, then the solution set of the system of equations a1x+b1y=-2+a1a2x-b2y=4+a2 for()

A． {(x,y)|(2,1)} B． {(x,y)|(2,3)}

C． {(x,y)|(2,2)} D． {(x,y)|(1,2)}

regular method

Commonly used methods to find the solution set of a system of linear equations of two variables include addition, subtraction, elimination, and substitution and elimination. You must be able to select the appropriate method according to the characteristics of the system of equations to be solved, and pay attention to the representation form of the solution set.

Track training

2. It is known that the prices of three kinds of books are 10 yuan, 15 yuan, and 20 yuan respectively. A school plans to spend exactly 500 yuan to purchase 30 of the above books, with at least one of each kind of book. How many different book purchasing plans are there ()

A． 10B． 9C. 12D． 11

B [ Suppose you purchase copy a for 10 yuan and copy b for 15 yuan, then (30-a-b) for 20 yuan,

According to the question: 10a+15b+20(30-a-b)=500,

After sorting, we get 2a+b=20.

①When b=2, a=9,

②When b=4, a=8.

③When b=6, a=7.

④When b=8, a=6.

⑤When b=10, a=5.

⑥When b=12, a=4.

⑦When b=14, a=3.

⑧When b=16, a=2.

⑨When b=18, a=1.

There are 9 different book purchasing plans.

So choose B.]

Solution to Quadratic Inequality of One Variable

[Example 3] Solve the inequality about x: x2+(1-a)x-a<0.

[Solution] The solution of the equation x2+(1-a)x-a=0 is x1=-1, x2=a.

The graph of function y=x2+(1-a)x-a opens upward, so

(1) When a<-1, the solution set of the original inequality is {x|a

(2) When a=-1, the solution set of the original inequality is ∅;

(3) When a>-1, the solution set of the original inequality is {x|-1

regular method

When solving quadratic inequalities of one variable, you must pay attention to the combination of numbers and shapes, and make full use of the relationship between the corresponding quadratic function image and the solution of the quadratic equation. If it contains parameters, the parameters need to be classified and discussed according to certain standards.

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Update Time: 2024-09-20

This template belongs to Mathematics courseware People's Education High School Mathematics Edition B Compulsory Course 1 industry PPT template

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