Title: 5 out of 11 math problems and answers 2020
1. Fill in the blanks
Question: If you divide an integer by a non-zero integer, does the quotient you get must be an integer? Please give the answer and explain why.
Answer: Not necessarily. For example, when the dividend is an integer and the divisor is a decimal, the quotient may be a decimal. For example, if you divide the integer 5 by the decimal place 0.2, the quotient is 25, which is a non-integer number. Or when both the dividend and the divisor are integers but not divisible, the quotient is also a non-integer. For example, if you divide the integer 7 by the integer 3, the quotient is a number with a remainder (i.e., a false fraction), not an integer.
2. Multiple choice questions
Question: Knowing that the area of a square is 9 square centimeters, what is the length of its sides? Please select the correct answer from the options below.
Options: A. 3 cm B. Root number 9 cm C. Unsure D. None of the above is correct
Answer: A.3 cm. The area of the square is equal to the square of the side length, and the known area is 9 square centimeters, so the side length is directly squared to get the root number 9, which is 3 centimeters. So choose A.
3. Calculation questions
Problem: Calculate the circumference and area of a circle. The radius of the circle is known to be r centimeters. Please give the formula and calculation process. Let’s assume r = 5 cm. Please calculate the results and give the answers.
Answer: The formula for perimeter is C=2πr and the formula for area is S=πr². Substituting r=5 cm for calculation. The circumference is obtained about: C = 2π (5) = 31.4 cm; The area is approximate: S = π (5²) = 78.5 square centimeters. So the answer is that the circumference is about 31.4 centimeters and the area is about 78.5 square centimeters. The calculation process can be adjusted for appropriate accuracy according to rounding or other approximation methods.
4. Geometry questions
Problem: In a planar Cartesian coordinate system, there is a point A with coordinates of (x,y). Knowing that the distance from point A to the origin is √(x²+y²), what coordinate is the closest position to the origin if the coordinates of point A are integer values? At least three such sets of coordinate values are given as possible answers. Answer: (omitted) 5. Practical question: Knowing that the length of a rectangle is l meters and the width is w meters, what is the formula for calculating the area and perimeter of the rectangle and the difference and connection between the two? Please give detailed explanations and examples to deepen understanding. Answer: The formula for calculating the area of a rectangle is S=lw (length times width), which indicates the total area of the rectangleGAME BÀI NOHU90. The circumference of a rectangle is calculated as P=2(l+w) (twice the length and width), which represents the total length around the rectangle. Both involve two variables, length and width, but the results are calculated in different meanings, one is the size of the area and the other is the length of the perimeter. For example, if the length of the rectangle is 4 meters and the width is 3 meters, then the area is S=lw=12 square meters; Circumference P = 2 (l + w) = 14 m. 6. Extended Question: If a piece of paper is rolled into a conical container and placed upside down on a horizontal surface, is the amount of liquid that the container can hold related to its bottom radius and height? Please give an explanation and possible calculation process or ideas. Answer: Yes. The volume of liquid that the container is capable of holding is related to its bottom radius and height. According to the formula for calculating the volume of the cone, V=(πr²h)/3 (where r is the base radius and h is the height), it can be known that if the radius or height changes, the volume will also change. However, due to the fact that the actual paper container may have errors such as deformation under the influence of practical factors such as forming and gravity, the capacity in practical application will change and the specific value may be more complex, and its accuracy needs to be further determined by experiments and other means. 7. Multiple choice question: If the diameter of one circle is twice the radius of another circle, what is the relationship between the areas of the two circles? Please select the correct answer from the following options and explain why. Options: ABig Bass Secrets of the…. Equal area B. Twice the difference in area C. Twice as much difference in area D. Proportional relationship of area Answer: D. Proportional relationship of area. According to the formula for calculating the area of a circle S=πr² (where r is the radius), if the diameter of one circle is twice the radius of another circle, the ratio of the radii of the two circles is a fixed proportional relationship (i.e., a double relationship), so their area is also a proportional relationship of two times rather than a simple relationship such as equality or multiples. 8. Practical questions: There is a batch of goods that have been sold for a total of four sales cycles (i.e., one quarter). In the first quarter, the sales situation was good, more than 70% of the sales plan was completed, and the second quarter declined slightly, but still reached more than two-thirds of the sales target, and the total sales grew steadily and has been showing an upward trend, indicating that the market sales trend continues to improve; At the end of the second quarter, the total sales are expected to reach about 70% of the total target, and the market feedback is good, and it is expected to continue to maintain growth in the future. The reason is that the market sales trend continues to improve, and the total sales have been growing steadily, and the market feedback is good, and the future is expected to continue to maintain a growth trend, indicating that the market demand is still strong, and the competitiveness of the company’s products continues to improve, can meet the needs of consumers, and continue to achieve competitive advantages in the market, which also indicates that the company’s sales revenue will continue to achieve steady growth in the coming period, so it is predicted that the sales in the third quarter will maintain a growth trend, and is expected to achieve a high sales target level. In triangle ABC, it is known that the degree of angle A is α if the length of the middle line on the side of AB is less than or equal to twice the difference between the two sides of the triangle, then whether the triangle is an acute triangle or a right triangle, and the reason is given, and the answer is analyzed: (It is necessary to draw conclusions through a detailed proof process, and cannot be fully expanded in this short answer) It is necessary to judge an acute triangle and a right triangle in combination with the geometric properties and property theorems of the triangle, and there is not enough evidence or conclusion to judge the accurate relationship and inference of the condition that if the difference between the two sides of this triangle is less than twice the length of the middle line, the conclusion should be drawn in conjunction with the specific proof process 10Fill-in-the-blank question: The top angle of an isosceles triangle is an acute angle, and the sum of its two base angles is equal to what is the answer and explain the reasonAnswer: (omitted) Explain the reason: The two base angles of the isosceles triangle are equal, and the sum of the two base angles plus the degree of the top angle is equal to the sum of the inner angles of the triangle, that is, equal to a flat angle, that is, equal to one hundred and eighty degrees, so it can be calculated that the sum of the two base angles of the isosceles triangle is equal to the degree of the flat angle minus the top angle, the above questions introduce ten mathematics-related questions selected from the exam questions this year, and the analysis of each problem reflects the understanding and mastery of the corresponding mathematical knowledge, in order to get good results, in addition to the accumulation of knowledge itself, the accumulation of training and analysis ability of solving problems can not be ignored, it will be of great help to future learning, and will also help to exercise the improvement and development of mathematical thinking ability, I wish you allHave good performance and gains in mathematics studies and exams
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