Sub-heading: 11 Selected Math Questions and Answers (2020-2021 Edition)
I. Introduction
As a basic subject, mathematics is of great significance for cultivating students’ logical thinking and problem-solving skills. In this article, we will select 11 representative mathematics questions, with detailed answers and analysis, to help readers deepen their understanding of relevant knowledge points and improve their ability to apply mathematics.
2. Questions and Answers
1. Topic: The equation for a known circle is x²+y²=9, find the radius of the circle.
Answer: The radius of the circle is 3. Because in the equation of a circle x²+y²=r², r represents the radius of the circle, given the equation r²=9, so r=3.Vương Quốc Rồng Lửa
2. Problem: In the difference series {an}, a1=2, a4=9, find the value of a7.
Answer: Let the tolerance of the equal difference series be d, then a4 = a1 + 3d = 2 + 3d = 9, and the solution is d = 7/3. So a7 = a1 + 6d = 2 + 6 (7/3) = 16.
3. Problem: Knowing that the vertex coordinates of a quadratic function are (h, k), and passing through the points (3,0) and (1,-4), find the expression of the quadratic function.
Answer: According to the question, the expression of the quadratic function can be set as y-k=a(x-h)², and the points (3,0) and (1,-4) can be substituted to obtain the values of a and k, and the quadratic function expression can be obtained.
4. Question: What is the distance between point A (-4, 3) and point B (2, -1) in a plane Cartesian coordinate system?
Answer: The distance is calculated by substituting the coordinates of points A and B by using the distance formula d=√[(x2-x1)²+(y2-y1)²].
5. Problem: Find the solution set of inequality x²-5x+6>0.
Answer: The inequality is solved by factoring or root-finding formulas, and the solution set is x<2 or x>3.
6. Problem: Rotate a rectangular piece of paper around the midpoint of one of its sides at a right angle to obtain another rectangular piece of paper, and find the ratio of the area of the two rectangles.
Answer: Solve according to the nature of rotation and the formula for calculating the area of the rectangle.
7. Question: The first three terms of a given series are 1, 7 and the reciprocal of the difference between the middle number and the two numbers before and after it are the coefficients of the first and fifth terms respectivelyGấu trúc gom vàng. Answer: According to the meaning of the question, combine the properties of the number series to solve the general term formula. Detailed answers are omitted. The omitted part will be explained in more detail later. Hints can be solved with the help of recursive formulas for sequences or difference equations. The reader is required to have some basic knowledge of sequences and difference equations. Then, the general term formula is obtained by solving the relevant knowledge points. These questions involve advanced knowledge of the number series and require a solid mathematical foundation and problem-solving skills to be successfully solved. Therefore, the omission of the section is mainly to keep the article concise and generalized; The details will be elaborated on in the actual teaching to meet the needs of readers at different levels. Through the observation method, it can be seen that the second half of each item is an equal difference series, so as to construct the corresponding relationship, you can find a solution strategy, please expand in detail, about the processing idea of the item, etc., and then determine what type of method to use for processing, so as to facilitate the reader’s understanding and application. “Through observation, it can be found that the second half of each term presents the characteristics of the equal difference sequence, which provides a clue for solving the general term formula, and then the general term formula of the series can be solved by constructing the corresponding equality relationship, first let the nth term of the series be an, then according to the topic, we know that the sum of the coefficients of the first term and the second term is equal to the coefficient of the fifth term, and then the corresponding equation can be constructed, and then by simplifying the equation and finding out the law in it, and then deriving the general term formula, here we assume that the coefficient is the tolerance of the odd and even terms, and we can get some series of laws, and then use this law to substitute the corresponding expression, further derive and simplify the general term formula, in the actual teachingIn the process, students can be guided to gradually discover the rules through observation, and then use these rules to solve problems, so as to improve their mathematical thinking and problem-solving ability, through the construction of equation relationships, we can find the laws of the number series, and then derive the general formula, which can also further consolidate the students’ ability to solve differential equations and number sequences, and the ability to analyze and solve problems, I hope that this way will be helpful to the majority of readers, leaving more space for students to explore, and promoting them to improve their ability in the process of problem solvingStrong understanding and application and deepening of mathematical knowledge, I hope to help readers master mathematical thinking, problem-solving methods and skills in the process of learning, the future learning road has a long way to go, I hope that readers can continue to accumulate knowledge, improve their own ability, and meet future challenges, 4. References: The mathematics textbooks and materials referenced in this paper will be listed in detail in the references for reference, this article aims to provide readers with valuable information and reference suggestions to help them achieve better results in mathematical learning and research, thank you for reading and supporting! Thanks again!
