Chương 4 đai so 10 song ngữ

Preparation date: Teaching date: Chapter IV: INEQUALITIES AND INEQUATIONS PERIOD: 28 §1 INEQUALITIES. (p1) I. AIMS OF THE LESSON To realize concept and properties of inequalities To realize Cauchy’s inequalities and inequalities with absolute value bars Proof some simple inequalities II. TEACHING AIDS Teacher:lesson plan,text book Student: To realize concept and methods in order to proof of inequalities in class 8 and 9 III. TEACHING PROCEDURE 1.Orginization: 2. Checking the previous lesson: NO 3.New lesson: Activity 1: Review of inequalties

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I AIMS OF THE LESSON

-To realize concept and properties of inequalities

-To realize Cauchy’s inequalities and inequalities with absolute value bars

-Proof some simple inequalities

II TEACHING AIDS

-Teacher:lesson plan,text book

-Student: To realize concept and methods in order to proof of inequalities in class 8

Activity 1: Review of inequalties

?1.Which of the following propositions are

true?: a/3,25<4, b/-5>- 41

4, c/- 2≤3

?2 Choose a suitale symbol(=; <; >) such

that we get a true propositions when we fill

in the blank box:

a/2 2 3 b/4 2

3 3 c/3 + 2 2 (1+ 2)2

1.Concept of inequalities :textbook p74

proposition “a > b” or “a < b” are calledinequalties

2.Resulting inequalities and equivalent inequalities:textbook p74

a < b ⇒ a – b < 0 và a – b < 0 => a < b

3.Properties of inequalities: p75

Ex:x > y ⇔x + 2 > y + 2

x > 2 ⇒ x2 > 4Note:page76

Activity 2 :Cauchy’s inequality

II Cauchy’s inequality

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Express theorem cauchy

?Proof

?When does Sign “=” occurs

? a > 0 ,proof: a +1 2

a ≥

?Among all rectangles with the same

perimeter,which has the largest area?

a + b≥2 ab,a,b are lengths 2 sides

when is ab max

If both x and y are positive and their sum is

invariablr then the sum x+y is the smallest if

and only if x=y

Proof: textboob page 76

2.Consequence:

Consequence 1:textbook page76

Activity 3: INEQUALITIES WITH ABSOLUTE VALUE BARS

?Compute absolute value of the following

numbers

a/ 0 b/1,25 c/ 3

4

− d/−π

?State the definition

III INEQUALITIES WITH ABSOLUTE VALUE BARS

State the definition : |A| = A if A ≥ 0 |A| = - A if A < 0Properties: textbook page78

Ex: textbook page78

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- Consolidate concept and properties of inequalities ,Cauchy’s inequalities and

inequalities with absolute value bars

- Consolidate methods in order to proof of inequalities

-Applying methods in order to proof of inequalities in doing exercises

-Student: text book,notebook

III TEACHING PROCEDURE

1.Orginization:

2 Checking the previous lesson:

-State concept and properties of inequalities

- Cauchy’s inequalities.Prove

44

a b c d

abcd

+ + + ≥ ∀a b c d, , , ≥0

3.New lesson

Call student answer Exercise 1

Equation occurs if and only if x = y

Exercise 5Set x = t we have t8 – t5 + t2 – t + 1 = f(t)

0 ≤ t < 1, f(t) = t8 + t2(1- t3) + (1 – t) > 0

t≥ 1, f(t) = t5(t3 – 1) + t(t – 1) + 1 > 0

Exercise 6Call H tangenital point

y

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we can show that

Period 30: Inequations and systems of inequations

with one unknown(p1)

-Introduce concept of inequations and systems of inequations with one

unknown;conditions for an inequation;inequations containing parameters

-To understand some inequation transformations

-Find conditions for an inequation,solve the simple inequations and systems of inequations with one unknown

1.Orginization:

State concept of inequations and systems of inequations with one

3.NEW LESSON

Activity 1: Inequations with one unknown and Conditions for an inequation

Given inequation:2x≤3

Show left side and hand side of

inequation?

I Concept of inequations with one unknown

1 Inequations with one unknown Definition:text book page 80

H2: 2x is the left side, 3 is the right sidea.-2 is the solution to the above inequationThe other numbers are not the solution to the above

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Call people to readdefinition

− ≥

 + ≥



Activity 2 Inequations containing parameters

State equations containing

parameters?To imply inequations

containing parameters

Call people to read definition

People do example

3 Inequations containing parameters

In an inequation,besides letters acting as

unknowns,there may be other letters that are regarded as constants and called parametersEx: (2m – 1)x + 3 < 0

Solving and justify an inequality containing parameters mean considering for which values of parameters the inequality has no solutions or some solutions and finding the solutions

Activity 3 : A systems of inequations with one unknown

People do example

II A systems of inequations with one unknown

Definition:text book page 81

Ex:Solve asystems of inequations: 3x− ≥x2 00

− ≥

 + ≥

Hence,the solution to the system is: [- 2; 3]

IV CONSOLIDATE:

- Find conditions for inequations:

0

x

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x b)1−2 2 > (x−1)(x+3)

x x

V.HOMEWORKS:

Remember concept of inequations and systems of inequations with one unknown

Do the exercise 1,2 page 88

Preparation date:

Teaching date:

Period 31:Review end of term I

-Review propositions,sets,linear and quadratic funtions,equations and system of

equations,inequations;inequalities

- Teacher:syllabus,textbook,exercise

- Students:Review exercises from chapter I to from chapter IV

1.Orginization:

State concept of inequations and systems of inequations with one

3.NEW LESSON

Activity 1:Solve equation contain root

Let students recognize the form of the

equation and state the method to slove

the equation

Ask student to solve equation

Ask 2 students to present on the board

Folow and help student with difficulty

Ask student to comment

Assess and grade

Exercise 4: Solve equationa) 2x− =9 1

Thus,equation has no solution

Activity 2:Solve biquadratic equation:

Let students recognize the form of the

equation and state the method to slove the Exercise 5: Solve equation

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equation

Ask student to solve equation.

Ask 3 students to present on the board

Folow and help student with difficulty.

Remind student to compare conditions to

find the roots.

Ask student to comment.

Assess and grade.

a) x4 – 5x2 + 6 = 0Given x2 = t ( t ≥ 0)

We have

t2 – 5t + 6 = 0 (a = 1; b = - 5 ; c = 6 )

2( 5) 4.1.6 1 0

c) –x4 + 8x2 + 9 = 0Given x2 = t ( t ≥ 0)

Activity 3: Inequalities.

Let student read the question carefully.

Guide student to prove using (A – B )2 0≥

Ask student to present the proof

Folow and help student with difficulty.

Ask student to comment.

Assess and grade.

(satisfy)

(no satisfy)

(satisfy)

(no satisfy)

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IV- Consolidation:

Let student review important knowledge

V- Home work:

Review the forms of above problem.

Prepare for final exam.

Teaching date:

Period 32: Semester 1 Exam.

Question and solution are given by educational council of Vinh Phuc province.

Teaching date:

Period 33: Correct semester 1 exam’s questions

Question and solution are given by educational council of Vinh Phuc province.

Teaching date:

Period 34: Inequations and systems of inequations

with one unknown(p2)

I AIMS OF THE LESSON:

-Introduce concept of inequations and systems of inequations with one

1.Orginization:

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3.New lesson:state concept of inequations, conditions for an inequation

3.NEW LESSON

Activity 1: Equivalent inequations ;Addition/subtracttion

Call a student to read definition

3 Addition/subtracttion

Text book page 83

P(x) < Q(x) ⇔P(x) + f(x) < Q(x) + f(x)

Ex 2 solve inequation (x + 2)(2x - 1) - 2 ≤ x2 + (x - 1)(x + 3)

⇔2x2 +3x – 4 ≤ x2 + x2 + 2x – 3⇔x ≤ 1 Thus the solution set to the inequation(−∞;1]

Activity 2: Multiplication/ division

multiplication

When we square 2 sides of

inequation,What do we must note?

4.Multiplication/ division Text book page 84

P(x) < Q(x)⇔P(x).f(x) < Q(x).f(x) if f(x) > 0 P(x) < Q(x)⇔P(x).f(x) > Q(x).f(x) if f(x) < 0

Ex solve inequation:

2

12

2+

++

x

x x

>

12

2+

+

x

x x

Activity 3: Squaring

When we square 2 sides of

inequation,What do we must note? 5 Squaring P(x) < Q(x)⇔P2(x) < Q2(x) if P(x)≥0, Q(x)≥0, ∀x

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State method to solve inequation

: f (x) > g (x)

Do the example in notebook

Call other student comment and

)()(0

)(

0)(

)()(

x g

x g x f x

g

x f

x g x f

Ex5 solve inequation

6

33444

32

5x+ −x > x − − −x

Note text book page 85

Ex6 solve inequation: 1 1

1

1 ≥+

x và 1 ≥x+ 1

V.HOMEWORKS:

-Remember some inequation transformations

- Do the exercises 1, 2, 3, 4, 5 page 88

Teaching date:

Period 35: Practise

Condisolate concept of inequations and systems of inequations with one unknown;conditions for an inequation;inequations containing parameters

- Củng cố khái nêm bất phương trình một ẩn, các phép biến đổi tương đương, phép biến đổi hệ quả bất phương trình

1.Orginization:

State some inequation transformations

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3.NEW LESSON

Activity 1: Exercise 1 and Exercise 2

1

* Condition of fraction funtion ?

* Condition of funtions contain

root ?

2 a.Compare left side and 0

b Compute min of left side,compare

with hand side

c Compare left side with 1

c VT <1, VP = 1 thus, inequation no solution

Activity 2: Exercise 3 and Exercise 4

3 Show method to change from

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x x

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Period 36:SIGNS OF LINEAR BINOMIALS

- Concept of linear binomials,theorem about signs of linear binomials

-Considering signs of products and quotients of linear binomials

-Using the definition to remove absolute value bars oflinear binomials

-Applications to solving product inequations, inequations containing unknowns

in denominator and inequations containing unknowns inside absolute value bars

-Teacher:lesson plan,text book

-Student: text book,notebook

1.Orginization:

Solve the inequations

a) 5x – 2 > 0 b) - 4x + 3 > 0

3.NEW LESSON

Activity 1: Theorem on signs of linear binomials

Call a student to read definition

Compare signs of linear binomials

with sign of coefficient a

Call a student to read theorem

a.f(x) = a(ax +b) = a2(x +

a

b

)Drawing graphical illustration

A student do H2.Comment and

repeat about theorem

I.Theorem on signs of linear binomials

1 Linear binomials: f(x) = ax + b

a, b are two given numbers, a≠0

2 Signs of linear binomials Theorem:text book page 89

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Ex1 :text book page 90

Activity2: Considering signs of products and quotients of linear binomials

Teacher guides method co

consider f(x)

- Method to solve inequations:

+To takeinequations about form

f(x) > 0 ( <, ≤ ≥, )

+ Considering sign f(x)

+Implying the solution

II Considering signs of products and quotients of linear binomials

Example 2: Consider the signs of binomial

∀ ∈ − ÷ ∪ +∞÷

Activity 3: Applications to solving inequations

Call students do exercise 1

Other student comments and

repairs

III Applications to solving inequations

1 Product inequations and inequations containing unknowns in denominator.

Example3: text book page 92

2 Inequations containing unknowns inside absolute value bars

Example4: text book page 93.

O

1/4 5/3

+ +

-

-x

0

-

-+ +

x

-1 0

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Call students do exercise 2

Other student comments and

2 2

Therefore,the solution to the inequation is:

- Remembertheorem about signs of linear binomials

-Considering signs of products and quotients of linear binomials

-Using the definition to remove absolute value bars of linear binomials

-Applications to solving product inequations, inequations containing unknowns in denominator and inequations containing unknowns inside absolute value bars

Học thuộc định lý về dấu của nhị thức bậc nhất, cách xét dấu của biểu thức, cách giải bất phương trình

-Do the exercise in text book

Teaching date:

Period 37:LINEAR INEQUATION WITH TWO UNKNOWNS(P1)

-+ -

+

-x

3 0

+ +

-

-x -1/3 1/2

1 0

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-To understand concept linear inequations with two unknowns,system of linear

inequations with two unknowns

-To understand concept solution of linear inequations with two unknowns,system of linear inequations with two unknowns

-Representing solution sets of linear inequations with two unknowns,system of linear inequations with two unknowns

-Student: text book,notebook

Students are learned funtion y=ax+b and linear inequations with a unknown

1.ORGINIZATION

2 CHECKING THE PREVIOUS LESSON

1 State theorem on signs of linear binomials

2 Considering signsof products and quotients of linear binomials

3Draw graph funtion 2x + y = 3 hay (y = 3 – 2x)

3.NEW LESSON

Activity1: Linear inequations with two unknowns; Linear inequations with two unknowns

Teacher call a student draw line

(∆): 2x + 3y = 3 ?

Call a student repeat rules for

geometric representation of solution

+The half plane on one side of the

boundary line containing the O is

I Linear inequations with two unknowns

1 Definition in text book 95

II.Linear inequations with two unknowns

1 Definition solution sets of linear inequations withtwo unknowns

2 Rules for geometric representation of solutionsets ax + by < c (≤ > ≥, , )

+ Draw line ax + by = c (∆)+ Take a point M0(x0; y0) ∉ ∆( )+ Compute ax0 + by0 and compare with c

+ Conclusion:

Ex1Produce a geometric representation solution sets

of linear inequations with two unknowns 2x + 3y ≤3

- Draw line (∆): 2x + 3y = 3

- O(0;0) , O∉(∆) và 2* 0 + 0≤3 so the half plane

on one side of the boundary line∆ containing the O

is the solution domain of the given inequation: 2x + y≤3 ?

Ex2Produce a geometric representation solution sets

of linear inequations with two unknowns - 3x + 2y >0

2

3/2

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the solution domain of the given

inequation:

Activity 2: System of linear inequations with two unknowns

Call students representing solution

sets of linear inequations with two

unknowns

III.System of linear inequations with two unknowns

1 Definition in text book 96

2 Produce a geometric representation solution sets

of system of linear inequations with two unknowns:

400

x y

x y x y

- Memorizeconcept linear inequations with two unknowns,system of linear

inequations with two unknowns

≤

−

81252

32

x y x

y x

Teaching date:

Period 38:LINEAR INEQUATION WITH TWO UNKNOWNS(p2)

-To understand concept linear inequations with two unknowns,system of linear inequations with two unknowns

-To understand concept solution of linear inequations with two unknowns,system of linear inequations with two unknowns

-Representing solution sets of linear inequations with two unknowns,system of linear inequations with two unknowns

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