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Are you struggling to review the National High School Mathematics exam, especially the knowledge of exponential and logarithmic functions? Do not worry! This article will be a full and detailed handbook, helping you conquer this tough topic most effectively, thereby confidently entering the exam and achieving high scores.
Topic of exponential and logarithmic functions in the national high school math exam structure 2024
According to the latest information, synthesized from the national high school reference test of 2024 Math subjects published by the Ministry of Education and Training, the structure of the National High School Mathematics Examination 2024 has the same difficulty as the 2023 exam. In which, the content of the exponential and logarithmic function, the power account for about 8 of the total of 50 questions included in the exam, with 5 sentences at the basic level and 3 sentences of the level of understanding. Therefore, if you want to achieve high scores, candidates need to grasp the thematic knowledge of the logarithmic function from theory to the exercise.
Functions
1. What is the definition of excess power?
2. Some properties of excess:
For a, b ≠ 0 and m, n ∈ Z, we have:
3. Learn about N and N units in excess:
Definition: Give real number b and positive integer N (n ≥ 2). Number A is called the n units of the number b if an = b.
Some important notes:
Logarithmic function
1. What is logarithmic definition?
2. Properties of logarithmic:
3. Natural logarithmic and decimal logarithms:
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Natural logarithmic (also known as logarithm) is the base logarite e, written as: logb = lnb.
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The decimal logarithm is the number 10 logarithm, written as: log10b = logb = LGB.
Exponential function and logarithmic function
Below is a summary of the theory of the logarithmic function that the candidates should “pocket”:
1. End function:
2. Logarite function:
Exponent equation, logarithmic equation
In addition to the exponent and logarithmic review section, this is the same amount of knowledge about the logarithmic equation in the university exam questions (under the testing function of the exam review), including:
Uncompleted – logarithmic
Overview of the theory of logarithmic inequalities in the national high school exam that candidates need to review such as:
1. Definition:
Basic exponential inequalities have ax> b (or ax ≥ b, ax 0, a ≠ 1.
2. Theorem, rule:
3. Method of bringing back the same number:
4. Hidden placement method:
5. Method of function, evaluation:
See also: Topic of the National High School Examination Function Mathematics: Theory & Exercise Form!
The type of interest rate problem in the exponent and logarithmic function
1. The problem in the form of dual interest P, deposit A dong, interest rate r per period in the form of double interest. Calculate the money collected after the period.
-> Fast calculation formula: an = a (1 + r) n
2. The problem is in the form of double interest, at the beginning of each period deposit a dong, interest rates r a period. Calculate the proceeds after n periods (including principal and interest).
-> Fast calculation formula: an = a (1 + r)[((1 + r)n – 1)/r]
3. The problem in the form of dual interest, borrowing a dong, interest rate r, repaying debt regularly per period m. Ask how many periods, then pay off the debt including the principal and interest.
-> Fast calculation formula: m = [Ar(1 + r)n ]/[(1 + r)n -1]
4. The problem is in the form of double interest, sending A dong to the savings account, interest rate r a period. After a period of drawing m and the next period. Ask the remaining money in the account after n?
-> Fast calculation formula: an = a (1 + r) n – m[((1 + r)n -1)/r]
Note: Above are some general formulas. In the process of solving math, candidates need to flexibly transform the quantities that the problem requires based on the fast solution formula. At the same time, combining the problems in case the problem is complicated.
With the full system of knowledge, effective solutions and diverse exercises, hopefully this article has helped you master the exponent and logarithmic function – one of the important topics in the National High School Mathematics exam. Wishing students the highest results!
Nguồn: https://mncatlinhdd.edu.vn/ Tác giả: Nguyễn Lân dũng
Giáo sư Nguyễn Lân Dũng là một trong những nhà khoa học hàng đầu Việt Nam trong lĩnh vực vi sinh vật học, với hơn 50 năm cống hiến cho giáo dục và nghiên cứu (Wiki). Ông là con trai của Nhà giáo Nhân dân Nguyễn Lân, xuất thân từ một gia đình nổi tiếng hiếu học. Trong sự nghiệp của mình, Giáo sư đã đảm nhiệm nhiều vị trí quan trọng như Chủ tịch Hội các ngành Sinh học Việt Nam, Đại biểu Quốc hội và được phong tặng danh hiệu Nhà giáo Nhân dân vào năm 2010.