At which grade level is the concept of derivatives introduced in the new curriculum in Vietnam?
At which grade level is the concept of derivatives introduced in the new curriculum in Vietnam?
Based on Subsection 2, Section 5 of the Mathematics General Education Curriculum issued together with Circular 32/2018/TT-BG/DDT, students in grades 11 and 12 are taught about derivatives. The concept of derivatives is introduced in grade 11.
According to the provisions of Article 2 of Circular 32/2018/TT-BGDDT, the implementation of the General Education Curriculum is as follows:
The General Education Curriculum is implemented in the following phases:
1. From the school year 2020-2021 for grade 1.
2. From the school year 2021-2022 for grades 2 and 6.
3. From the school year 2022-2023 for grades 3, 7, and 10.
4. From the school year 2023-2024 for grades 4, 8, and 11.
5. From the school year 2024-2025 for grades 5, 9, and 12.
The most recent program will be applied to students of all grades nationwide from the school year 2024-2025.
Therefore, in the school year 2024-2025, 12th-grade students will continue to learn about derivatives, following the 11th-grade program from the previous year.
At which grade level is the concept of derivatives introduced in the new curriculum in Vietnam? (Photo from the Internet)
What are the content and requirements that 11th-grade students in Vietnam need to achieve when learning about derivatives?
Based on Subsection 3, Section 5 of the Mathematics General Education Curriculum issued together with Circular 32/2018/TT-BG/DDT, the content and requirements for 11th-grade students learning about derivatives are as follows:
| Content | Requirements |
| Concept of derivatives. Geometric meaning of derivatives | - Recognize some problems leading to the concept of derivatives, such as determining the instantaneous velocity of a non-uniformly moving object, determining the rate of temperature change. - Recognize the definition of derivatives. Calculate the derivative of some simple functions using the definition. - Recognize the geometric meaning of derivatives. - Establish the equation of the tangent line to the graph of a function at a point on the graph. - Recognize the number e through banking interest rate modeling problems. |
| Rules for calculating derivatives | - Calculate the derivative of some basic elementary functions (such as polynomial functions, simple radical functions, trigonometric functions, exponential functions, logarithmic functions). - Apply formulas for the derivatives of sums, differences, products, quotients of functions, and the derivative of composite functions. - Solve some problems related to other subjects or practical problems involving derivatives (e.g., determining the instantaneous velocity of a non-uniformly moving object, etc.). |
| Second-order derivatives | - Recognize the concept of second-order derivatives of a function. - Calculate the second-order derivatives of some simple functions. - Solve some problems related to other subjects or practical problems involving second-order derivatives (e.g., determining acceleration from the velocity-time graph of a non-uniformly moving object, etc.). |
What are the content and requirements that 12th-grade students in Vietnam need to achieve when learning about derivatives?
Based on Subsection 3, Section 5 of the Mathematics General Education Curriculum issued together with Circular 32/2018/TT-BG/DDT, the content and requirements for 12th-grade students learning about derivatives are as follows: Application of derivatives to explore and draw specific function graphs:
| Content | Requirements |
| Monotonicity of functions | - Recognize the increasing and decreasing behavior of a function on an interval based on the sign of its first-order derivative. - Represent the increasing and decreasing behavior of the function in a variation table. - Recognize monotonicity, critical points, and extreme values of the function through the variation table or the geometric representation of the function graph. |
| Maximum and minimum values of functions | - Recognize the maximum and minimum values of a function on a given domain. - Determine the maximum and minimum values of a function using derivatives in simple cases. |
| Analysis and graphing of functions | - Recognize the geometric representation of horizontal asymptotes, vertical asymptotes, and oblique asymptotes of the function graph. - Describe the general procedure for exploring a function (finding the domain, examining monotonic behavior, finding critical points, finding asymptotes, preparing the variation table, drawing the graph). - Explore the domain, monotonic behavior, critical points, asymptotes, variation table, and graph of the functions: y = ax^3 + bx^2 + cx + d (a ≠ 0); y = (ax + b)/(cx + d) (c ≠ 0, ad - bc ≠ 0); y = (ax^2 + bx + c)/(mx + n) (a ≠ 0, m ≠ 0, and the numerator not being divisible by the denominator). - Recognize the symmetry (axis of symmetry, point of symmetry) of the graph of the above functions. |
| Application of derivatives to solve practical problems | Apply derivatives and function analysis to solve practical problems. |
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