Error-prone point 1: The concepts of rational number, irrational number and real number are misunderstood, and the meanings of reciprocal, reciprocal and absolute value are confused. And the classification of absolute value and quantity. Choose a compulsory exam every year.

Error-prone point 2: The key to real number operation is to master the concepts and properties related to real numbers and flexibly use various algorithms. 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.

Error-prone point 3: the difference between square root, arithmetic square root and cubic root. Fill in the blanks must be tested.

Error-prone point 4: When the score value is zero, students tend to ignore that the denominator cannot be zero.

Error-prone point 5: Pay attention to the change of algorithm and symbol when calculating the score. 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.

Error-prone point 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.

Error-prone point 7: The first calculation question must be tested. Calculation of five basic numbers: 0 exponent, trigonometric function, absolute value, negative exponent and simplification of quadratic root.

Error-prone point 8: scientific notation. Precision, significant number. I haven't taken the exam in Shanghai yet. It's good to know!

Error-prone point 9: Substitution 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)

Error-prone point 1: The solution of various equations (groups) should be mastered skillfully, and the meaning of no solution of equations (groups) is that the conditions for the establishment of equations cannot be found.

Error-prone point 2: When using the properties of equations, we must pay attention to the situation that both sides are divided by the same number, and pay attention to the basic idea of solving equations and equations. The main trap is to eliminate a common factor with x, and then check it back!

Error-prone point 3: when using the property 3 of inequality, it is easy to forget to change the direction of the symbol, resulting in errors in the results.

Error-prone point 4: It is easy to ignore the value range of quadratic equation with one variable, and the coefficient of quadratic term is not 0, which leads to errors.

Error-prone point 5: One-dimensional linear inequalities are easy to ignore when there are solutions and no solutions.

Error-prone point 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.

Error-prone point 7: the solution of inequality (group) must be determined first, and the method of determining the solution set uses the number axis.

Error-prone point 8: Use the function image to find the solution set of inequality and the solution of equation.

function

Error-prone point 1: the meaning of each undetermined coefficient.

Error-prone point 2: master the solution of various analytical functions skillfully, and several undetermined coefficients need several points.

Error-prone point 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.

Error-prone point 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.

Error-prone point 5: image classification by function (parallelogram, similarity, right triangle, isosceles triangle) and the solution of classification.

Error-prone point 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.

Error-prone point 7: the application of the thinking method of combining numbers and shapes should also pay attention to solving problems in combination with the nature 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.

Error-prone point 8: The range of independent variables is: the square root of quadratic form is non-negative, the denominator of fraction is not 0, the exponential base of 0 is not 0, and the rest are real numbers.

triangle

Error-prone point 1: the concept of triangle and the characteristics and differences of angle bisector, median line and height line of triangle.

Error-prone point 2: the unequal relationship between the three sides of a triangle, and pay attention to the "any two sides". The shortest distance method.

Error-prone point 3: the sum of the internal angles of the triangle, the classification of the triangle and the nature of the internal and external angles of the triangle, paying special attention to the "non-adjacent" nature of the external angles.

Error-prone point 4: congruence, congruent triangles and its properties, 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.

Error-prone point 5: The equality and parallelism of two angles are often the basic elements of similarity. The ratio of heights corresponding to similar triangles is equal to the similarity ratio, the corresponding line segments are proportional, and the ratio of areas is equal to the square of the similarity ratio.

Error-prone point 6: the definition, judgment and properties of isosceles (equilateral) triangle. We should use the judgment and properties of isosceles (equilateral) triangles to solve the calculation and proof problems. Attention should be paid to the infiltration of classified discussion ideas here.

Error-prone point 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.

Error-prone point 8: Combining right triangle, plane rectangular coordinate system, function, open question and exploratory question, explore various problem-solving methods.

Error-prone point 9: midpoint, midline, midline, semi-theorem and their respective properties are summarized.

Error-prone point 10: Right triangle judgment method: determination of triangle area and height on the bottom (especially obtuse triangle).

Error-prone point 1 1: In the definition of trigonometric function, the ratio of corresponding line segments and the trigonometric function value of special angle are often wrong.

quadrilateral

Error-prone point 1: the nature and judgment of parallelogram, and how to apply it flexibly and appropriately. The stability of triangle and the instability of quadrilateral.

Error-prone point 2: the difference between parallelogram attention and triangle area solution. Transformation relation between parallelogram and special parallelogram.

Error-prone point 3: The parallelogram is a central symmetrical figure, which is divided into two parts with equal area by a straight line at the symmetrical center. The diagonal divides the quadrilateral into four parts with equal area.

Error-prone point 4: Apply the knowledge of congruent triangles and similar triangles to solve problems in parallelograms, and highlight the infiltration of transformation ideas.

Error-prone point 5: the concepts, properties, judgments and relationships of rectangles, diamonds and squares, mainly focusing on the calculation of side length, diagonal length and area. Folding of rectangles and squares.

Error-prone point 6: hands-on operation problems such as folding, translation, rotation and cutting of quadrilateral, and master some properties of invariance and rotation.

Error-prone point 7: the main method of making auxiliary lines for trapezoidal questions

circle

Error-prone point 1: I don't have a deep understanding of the concepts of arc, chord and circumferential angle, especially in the case of circumferential angle with chord-to-chord, and the distance between the two chords should also be considered.

Error-prone point 2: I don't understand the vertical diameter theorem enough, I can't add auxiliary lines correctly, and I can't solve problems with right triangles.

Error-prone point 3: I don't have a deep understanding of the definition and nature of tangent, and I can't accurately use the nature of tangent to solve problems. I use two methods to judge whether tangent is unskilled.

Error-prone point 4: When investigating the positional relationship between circles, there are two cases of tangency and circumscribed, and there are also two cases where the centers of two circles are on the same side and different sides of the common chord, so students can easily ignore one of them.

Error-prone point 5: the position relationship with the circle, grasp the relationship between D and R and R+r, R-r and apply the above method to solve it.

Error-prone point 6: the theorem of circle angle is the key point. The circumferential angle of the same arc (equal arc) is equal, the circumferential angle of the diameter is a right angle, the chord of the 90-degree circumferential angle is a diameter, and the circumferential angle of an arc is equal to half the central angle it faces.

Error-prone point 7: We must keep in mind several formulas: the area formula of triangle, parallelogram, rhombus, rectangle, square, trapezoid and circle, the circumference formula of circle, the lateral area and total area of arc length, sector area, cone, the transformation relationship between arc length and bottom circumference, and the radius of bus length and sector.

symmetric figure

Error-prone point 1: the concepts and properties of axisymmetric and axisymmetric figures, central symmetry and central symmetry figures are uncertain.

Error-prone point 2: To solve the problem of axial symmetry or rotation of a graph, we should make full use of its properties, that is, to make use of the "invariance" of the graph, the size of the angle remains the same in axial symmetry and rotation, and the length of the line segment remains the same.

Error-prone point 3: confuse axial symmetry and congruence, and confuse linear symmetry and axial symmetry.

Statistics and probability

Error-prone point 1: the concepts of median, mode and average are not thoroughly understood, and the calculation of median, mode and average is wrong.

Error-prone point 2: when obtaining information from statistical charts, we must first judge the accuracy of statistical charts. Irregular statistical charts often give people the illusion and get inaccurate information.

Error-prone point 3: The concepts of general survey and sampling survey and their scope of application are unclear, which leads to errors.

Error-prone point 4: the concepts of range and variance are not clearly understood, and the range and variance of a set of data cannot be correctly calculated.

Error-prone point 5: the meaning of probability and frequency is not clearly understood, and the probability of an event cannot be correctly calculated.

Error-prone point 6: average, weighted average, variance formula, the relationship between central angle and frequency of fan-shaped statistical chart, and the relationship between frequency and total number. The weight of the weighted average can be data, score, percentage or probability (or frequency).

Error-prone point 7: the method of finding probability;

(1) Simple event.

(2) Probability calculation method of two or more simple events: a tree or a list is used to represent the ratio of all equally possible situations to the possibility of events.

(3) The calculation method of the probability of complex events uses frequency to estimate the probability.

Error-prone point 8: the method to judge whether it is fair uses equal probability and pays attention to the integration of frequency and probability.