What are the numbers and formulas of error-prone knowledge points in junior one mathematics?
1: The concepts of rational number, irrational number and real number are misunderstood, and the concepts of inverse number, reciprocal number and absolute value are confused. And the classification of absolute value and quantity. Choose a compulsory exam every year.
2. The key to real number operation is to master the concepts and properties related to real numbers and use various algorithms flexibly. In more complex operations, the order of operations is not paid attention to or the algorithm is used unreasonably, which leads to errors in operations.
3. The difference between square root, arithmetic square root and cubic root. Fill in the blanks must be tested.
4. When the fractional value is zero, students often ignore that the denominator cannot be zero.
5. Pay attention to the change of arithmetic and symbol when decimal operation. When the denominator of a fraction is a polynomial, factorization should be carried out first, and then factorization should be carried out until it can no longer be decomposed. Pay attention to the calculation method, you can't remove the denominator and turn the fraction into the simplest fraction. Fill in the blanks must be tested.
6. The nature of non-negative numbers: the sum of several non-negative numbers is 0, and each formula is 0; Integral replacement method; A completely smooth road.
7. The calculation of the first question must be tested. Calculation of five basic numbers: 0 exponent, trigonometric function, absolute value, negative exponent and simplification of quadratic root.
8. Scientific symbols. Precision, significant number. I haven't taken the exam in Shanghai yet. It's good to know!
9. Alternative evaluation should make the formula meaningful. To master the calculation methods of various numbers, we must pay attention to the calculation order.
Equations (groups) and inequalities (groups)
1: The solution of various equations (groups) should be mastered skillfully. An equation (group) has no solution, which means that the conditions for the equation to be established cannot be found.
2. When using the properties of the equation, we should pay attention to the situation that both sides are divided by a number, and also pay attention to solving the equation and the basic idea of the equation. The main trap is to eliminate a common factor with x, and then check it back!
3. When using the property of inequality 3, it is easy to forget to change the direction of the invariant sign, which leads to the wrong result.
4. It is easy to ignore that the quadratic coefficient is not 0 on the topic of the range of the quadratic equation of one variable, which leads to errors.
5. The equality of one-dimensional linear inequalities with and without solutions is easily ignored.
6. When solving the fractional equation, the first step is to remove the denominator, and the fractional phase is equivalent to brackets, so it is easy to forget the root test and lead to errors in the operation results.
7. To solve the inequality (group) problem, we must first determine the solution set, and the method of determining the solution set uses the number axis.
8. Using function images to find inequality solution sets and equation solutions.
function
1: the meaning of each undetermined coefficient.
2. Mastering the solutions of various analytic functions skillfully, several undetermined coefficients need several point values.
3. Use the image to find the solution set of inequality and the solution of equation (group), and use the image properties to determine the increase or decrease.
4. Two variables use function models to solve practical problems, and pay attention to the differences between equation, function and inequality models to solve problems in different fields.
5. Using function image classification (parallelogram, similarity, right triangle, isosceles triangle) and the solution of classification.
6. You must find the coordinates of the intersection with the coordinate axis. The solution of maximum area, minimum distance sum and maximum distance difference.
7. The application of the thinking method of combining numbers and shapes should also pay attention to solving problems by combining the essence of images. The combination of function images and graphics can learn the method of decomposing complex graphics into simple graphics, and graphics provide data for images or images provide data for graphics.
8. The range of independent variables is: the square root of the quadratic root is non-negative, the denominator of the fraction is not 0, the exponential base of 0 is not 0, and all others are real numbers.
triangle
1: The concept of triangle, and the characteristics and differences of angle bisector, median line and height line of triangle.
2. The unequal relationship between the three sides of a triangle, pay attention to "any two sides". The shortest distance method.
3. Sum of interior angles of triangles, classification of triangles, and properties of interior angles and exterior angles of triangles, with special attention to "non-adjacency" in the properties of exterior angles.
4. Integration, congruent triangles and its nature, triangle congruence judgment. Focus on learning and demonstrating the congruence of triangles, the comprehensive application of triangle similarity and congruence, line segment equality as congruence feature, line segment doubling as similarity feature, and the combination of similarity and trigonometric function. Two triangles with edges and angles are not necessarily exactly the same.
5. Equal parallelism of two angles is often the basic element of similarity. The ratio of heights corresponding to similar triangles is equal to similarity ratio, the corresponding line segments are proportional, and the ratio of areas is equal to the square of similarity ratio.
6. The definition of isosceles (equilateral) triangle, the judgment and properties of isosceles (equilateral) triangle, and the calculation and proof problems are solved by using the judgment and properties of isosceles (equilateral) triangle. Here, we need to pay attention to the infiltration of ideas.
7. Use Pythagorean theorem and its inverse theorem to calculate the length of line segments, prove the quantitative relationship of line segments, and solve problems related to area and simple practical problems. (Question 2065438+25 in 2002)
8. Combine right triangle, plane right coordinate system, function, open question and exploratory question, and explore various problem-solving methods.
9. The induction of midpoint, midline, midline and semitheorem and their respective properties.
10: right triangle determination method: determination of triangle area and height on the bottom (especially obtuse triangle)
1 1: the ratio of the corresponding line segment in the definition of trigonometric function is often wrong, and the trigonometric function value of special angle.
Statistics and probability
1: The concepts of median, mode and average are not fully understood, and the calculation of median, mode and average is wrong.
2. To obtain information from the statistical chart, we must first judge the accuracy of the statistical chart. Irregular statistical charts often give people the illusion and get inaccurate information.
3. The concepts of general survey and sampling survey and their scope of application are unclear, which leads to errors.
4. The concepts of range and variance are not clearly understood, so the range and variance of a set of data cannot be calculated correctly.
5. The meanings of probability and frequency are not clearly understood, and the probability of an event cannot be correctly calculated.
How to improve junior high school math scores? To learn mathematics well, first of all, junior high school students should change their learning methods, cultivate their own mathematics learning ability, and learn to learn to learn by accepting learning and inquiry learning, cooperative learning, experiential learning and other ways.
In the process of mathematics learning, we should develop good review habits. Knowledge has the law of forgetting. After a while, it is easy to forget new knowledge without reviewing it. Mathematics review needs timely review and reflection. If you have a thorough grasp of the knowledge and methods you have learned; What mathematical thinking methods have been learned and how to use them; Review and consolidate typical problems frequently, and don't make mistakes again and again.
It is suggested that junior one students prepare a "wrong problem book" of mathematics, write down the "typical mistakes" they usually make, and think about where they are wrong, why they are wrong and how to correct them, so that there will be fewer and fewer wrong problems and problems that they can't do.
Mathematics learning is a process of thinking transformation, but any thinking training can't be immediate and needs a step-by-step process. We should master the concept of basic knowledge skillfully, and use this knowledge to achieve the purpose of deepening understanding and cultivating thinking, avoid using "practice" instead of "complex" tactics, learn to draw inferences from others and use them skillfully, and finally improve our math scores.