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Before the midterm exam, say a few more words about the math exam. Limited by space, here are only some basic questions, so that students can "watch a movie" in their minds before the exam and sort out their mathematical thinking.

1. About filling in the blanks. Students generally think that reviewing today is a piece of cake. I advise students not to underestimate their enemies. It is not so easy to get full marks when filling in the questions. Among them, the binary solution problem, the rotation problem of graphics, the application problem of percentage and so on. It is easy to lose points, so be careful.

Also, judging the type of numbers (especially irrational numbers) is often wrong, such as comparing the size of π. -32 and (-3) 2 are two different powers with different results. When finding the median, don't forget to arrange the known data in order from small to large before solving it.

As a set of data is known in statistics, the average value of x 1, x2…xn is x, and the variance is s2. To master the following rules, use them flexibly and save time.

(1) A new set of data, X 1+B, X2+B … XN+B, with an average of X+B and a variance of S2;

(2) A new set of data AX 1, ax2...AXN has an average value of ax and a variance of a2s2；;

(3) A new set of data AX 1+B, AX2+B … AXN+B has an average value of AX+B, a variance of a2s2 and a standard deviation of |as|.

2. About multiple-choice questions. Multiple-choice questions are often the easiest to lose points, which requires students to carefully analyze and calculate when choosing, not to be confused by some superficial phenomena, and to understand the relationship between several function images, special quadrangles and the positional relationship between graphics.

3. Misunderstanding of score calculation. The most common mistake in the problem is to mistake the calculation of the score for the calculation of the equation and remove the denominator, which leads to the loss of points in the whole problem. But the operation of fractional equation often forgets to check whether it is the root of the original equation.

4. The formula in quadratic function is also a problem that often makes mistakes. Sometimes the whole question will lose points because of the wrong formula. Note that the vertex coordinates are calculated twice (using formula and formula respectively).

5. For the equation with letter coefficient, we should not only change the equation into a standard form, but also discuss the letter coefficient in categories.

6. Solve the quadratic equation of one variable by using the relationship between roots and coefficients. Firstly, the equation is required to have a range of real roots, which is a prerequisite and an implicit condition. Pay attention to solving some parameters (such as the values of k and m) from known conditions, and then determine these values under the condition that the equation has real roots.

7. When solving binary quadratic equations, we should pay attention to the characteristics of the topic, distinguish the types and choose the appropriate method to solve the problem. When solving equations by substitution method, the key is to set auxiliary elements. After finding a new unknown quantity (auxiliary element), students often mistakenly think that this is the final result, but forget to substitute it into the set relation, and then find the solution of the original unknown quantity.

8. When solving a linear inequality (group), the most common mistake is that both sides of the inequality are divided by or multiplied by a negative number, and the inequality will change direction.

9. About the application. First of all, we should carefully examine the questions. There are two ways to find out the equivalence relationship according to the meaning of some topics: one is to express it through some keywords in the topic or give it directly in the topic design, and the other is to find the implicit equivalence relationship which is not clearly given in the topic and needs further investigation. List the equations, the unknown values obtained should be tested, and those that do not meet the meaning of the question should be discarded. When answering questions, we should also pay attention to the units involved.

10. The range of letters in the function. In the function, the range of letters is also a problem that students easily ignore. What needs to be reminded here is that in addition to the meaning of the corresponding resolution function, we should also consider the implicit restrictions that make the actual problem meaningful.

1 1. On the correct division of figures in polygons. In rectangular coordinate system, when calculating the area of polygon, students often feel at a loss because they can't find a special quadrilateral. In fact, it is the key to solve the problem to divide the graphics reasonably and correctly. In general, a polygon can be divided into several triangles or right-angled trapeziums, so that one side of the divided triangle or right-angled trapezium falls on the coordinate axis as much as possible. In drawing, the coordinates of intersection points often play the role of the bottom and height of triangle or right-angled trapezoid.

12. Apply trigonometric ratio to solve practical problems. The key is to transform the actual problem into a mathematical problem to solve the triangle, and to classify the known conditions and unknown elements in the actual problem into a right triangle for calculation. If some figures are not right triangles, they can be solved by adding appropriate auxiliary lines according to conditions. When solving this kind of problems, we have a clearer understanding of related concepts such as slope angle, slope, elevation angle, depression angle, direction angle and azimuth angle.

13. The acute triangle ratio is often combined with functions and equations to form a comprehensive problem. To solve this kind of problem, we should pay attention to separate the single item from the comprehensive one, break one by one, and then from the single item to the comprehensive one.

14. When proving that two triangles are similar, we should pay attention to the corresponding relationship between edges and angles in the graph. When using the properties of similar triangles to solve the area problem, don't forget that it is often combined with the formula for calculating the area of a triangle.

15. When proving the line segment proportion formula, don't forget the bridge function of "middle ratio".

16. There are generally two ways to prove that a straight line is tangent to a circle:

(1) If a straight line passes through a point on a circle, connect the point with the center of the circle, just prove the vertical radius of the straight line;

(2) If the straight line and the circle are not sure whether there is a common point, make a double line with a straight line passing through the center of the circle, and prove that the distance from the center of the circle to the straight line is equal to the radius;

17. Two solutions of circle. This is also something that students often ignore and thoughtless. Similarly, two solutions of the circle can be found in five situations:

Two parallel chords in a circle (1) may be on the same side or on different sides of the center;

(2) The tangency of two circles can be inscribed or circumscribed.

But when the center distance is less than the radius, there will be two situations;

(3) Two circles are separated from each other, and there are also two cases where two circles are separated from each other.

(4) When two circles intersect, there are two cases where the centers of the two circles are on both sides or the same side of the common chord;

(5) There are two kinds of arcs subtended by the inner chord of a circle: optimal arc and differential arc.