The key points to be explained in this book are: 1. Able to solve one-dimensional linear inequalities (groups) and list one-dimensional linear inequalities (groups) to solve simple practical problems; 2. To understand the significance of factorization, we will use common factor method, square difference formula and complete square difference formula to decompose factors; 3. Understand the concepts of fractions and fractional equations, master the basic properties of fractions, perform four operations of fractions, general fractions, addition, subtraction, multiplication and division, solve fractional equations that can be transformed into linear equations of one variable, test the roots of fractional equations, and solve some practical problems related to fractions and fractional equations. 4. Understand the line segment ratio, proportional line segment and golden section, and know that the angles corresponding to similar triangles are equal. 5. Understand the concepts of population, individual and sample, frequency and frequency, understand the significance and function of frequency distribution histogram, draw the corresponding frequency distribution map, master the concepts of range, variance and standard deviation, and calculate the range, variance and standard deviation of a group of data; 6. Knowing the meaning of definitions, propositions and theorems will distinguish the conditions and conclusions of propositions, know the significance and function of counterexamples, and preliminarily master the format of proof, which will prove relevant judgment theorems and property theorems, triangle interior angle sum theorems and their inferences.
Third, pay attention to error-prone points
1. The application of basic property 3 of attention inequality. When multiplying and dividing a negative number on both sides of inequality, the direction of inequality should be changed; Note that when solving inequalities (groups), when removing the denominator, every term on both sides of the inequality must be multiplied, and multiplication cannot be omitted.
2. Pay attention to the difference between factorization and algebraic expression multiplication; Note that when there are common factors, we must mention them first; Note that factorization must be carried out until each item can no longer be decomposed; Pay attention to the application of square difference formula and complete square difference formula.
3. Note that the score is meaningless and the value of the score is 0; Pay attention to the differences and connections between scores, general scores and simplified scores; Pay attention to the four operations of skilled fractional equation; Pay attention to how to remove the denominator when solving fractional equations, and remember to test the roots of fractional equations (because they may increase roots); Pay attention to writing in strict accordance with the steps when solving application problems, and remember to bring your unit.
4. Pay attention to the application of proportion and golden section; Pay attention to the similarity conditions when the certificates are similar, and what conclusions can be drawn according to the similarity; Note that when similar triangles is similar, the corresponding line segments are proportional, and the corresponding fixed points must be written in the corresponding positions.
5. Pay attention to the differences and connections between whole and individual, sample and sample size, spot check and general survey; Pay attention to frequency and frequency, range and variance calculation.
6. Pay attention to the conditions and conclusions of distinguishing propositions; Pay attention to the writing steps and format of proving a proposition (draw a figure according to the meaning of the question, write what is known and verified according to the conditions and conclusions, and write the proof process in the proof item); Pay attention to the difference between parallel judgment and nature; Pay attention to the theorem of triangle interior angle sum and its inference application.