Vietnam: What is the maximum value of an expression? What are the levels of general education?

What is the maximum value of an expression? What are the levels of general education in Vietnam?

What is the maximum value of an expression?

The maximum value of an expression is the value that the expression reaches when the variables within the expression assume optimal values or reach their maximum. In mathematics, the concept of the "maximum value" often pertains to functions, especially in extremum problems.

What is the maximum value of an expression?


Example:

Expression: A = -x² + 4x + 3

The maximum value of A will occur at a specific value of x that makes A reach its maximum value.

Expression: B = 1/(x² + 1)

The maximum value of B will occur when the denominator (x² + 1) reaches its minimum value (since 1 divided by a smaller number gives a larger result).

Methods to find the maximum value:

Depending on the form of the expression, various methods can be used to find the maximum value, such as:

Completing the square: Transform the expression into a perfect square plus a constant. Squares are always non-negative, so the maximum value is achieved when the square is zero.

Using inequalities: Apply familiar inequalities like Cauchy-Schwarz or Bunyakovsky to evaluate the expression.

Derivative (for functions): Find the derivative of the function and set it to zero to find extremum points.

Graphing the function: Plot the function's graph and observe its maximum point.

Note:

Not every expression has a maximum value. Some expressions can increase infinitely.

To find the maximum value, it is necessary to clearly define the domain of the expression.

Specific Example:

Find the maximum value of the expression A = -x² + 4x + 3.

Method 1: Completing the square: A = -(x² - 4x + 4) + 7 = -(x - 2)² + 7 Since -(x - 2)² ≤ 0 for all x, A ≤ 7. The "=" occurs when x = 2. Therefore, the maximum value of A is 7 when x = 2.

Method 2: Derivative: A'(x) = -2x + 4 Set A'(x) = 0 => x = 2 Checking shows that x = 2 is a maximum point of the function. Hence, the maximum value of A is A(2) = 7.

*Note: The information about the maximum value of an expression is for reference only./.

What is the largest value of an expression? What are the levels of general education?

What is the maximum value of an expression? What are the levels of general education? (Image from the Internet)

What are the levels of general education in Vietnam?

Under Clause 1, Article 28 of the Education Law 2019, the levels of general education in Vietnam are stipulated as follows:

Educational levels and entry ages

1. Educational levels and age groups of general education are regulated as follows:

a) Primary education lasts for 05 school years, from the first to the fifth grade. The entry age for the first grade is 06;

b) Lower secondary education lasts for 04 school years, from the sixth to the ninth grade. Students must complete the primary educational programme before entering the sixth grade. The entry age for the sixth grade is 11;

c) Upper secondary education lasts for 03 school years, from the tenth to the twelfth grade. Students must complete the lower secondary educational programme before entering the tenth grade. The entry age for the tenth grade is 15;

...

Thus, general education comprises three levels: primary education, lower secondary education, and upper secondary education.

What are the 04 objectives of general education in Vietnam?

According to Article 29 of the Education Law 2019, the objectives of general education are as follows:

- The objectives of general education are to help learners develop comprehensively by acquiring morals, knowledge, physical health, aesthetic values and other basic skills, develop personal abilities, flexibility and creativeness, with a view to forming the socialist Vietnamese personality and the civic duty, to preparing them for further studies of higher education, vocational education or entering the workforce, participating in the building and defending of the Fatherland.

- Primary education aims to help students form initial foundations for moral, intellectual, physical and aesthetic development and capacity, preparing them for entering lower secondary education.

- Lower secondary education is directed towards students' consolidation and development of the outcomes of primary education, provision of general and basic knowledge along with introductory understanding on techniques and career orientation to enter upper secondary education or vocational education.

- Upper secondary education is directed towards the provision of civic knowledge; students' consolidation and development of the outcomes of lower secondary education; completion of general education and acquisition of common understanding on techniques and career orientation; provision of opportunities for students to develop their personal abilities in order to choose their development direction, to enter higher education, vocational education or the workforce, contributing to the building and defending of the Fatherland.

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