Introduction: I will bring you six inspection methods to get high marks in mathematics in the senior high school entrance examination, hoping to help you.
Method 1: Check the basic concepts.
Basic concepts, rules and formulas are the most easily overlooked by students when checking, so it is easy to make small mistakes when solving problems, but you can't find them after checking several times. Therefore, after completing the first step of the examination paper, when checking the basic questions, we should read the questions carefully, return to the definition of concepts, and prescribe the right medicine.
For example, multiple-choice questions in the senior high school entrance examination, questions asked? What is the square root of 8? If students choose 2? 2, it is easy to check again (2? 2) 2 = 8, you take it for granted that the answer is right. At this point, we should start with the concept and think about what is? Square root? , you will recall such an equation x 2 = 8, and the quadratic equation should have two solutions, so the answer should have positive and negative solutions.
Method 2: Symmetry test
The condition of symmetry will inevitably lead to the symmetry of the conclusion, and the answer can be quickly tested by using this symmetry principle.
For example: factorization, the conclusion of (xy+1) (x+1) (y+1)+xy = (xy-y+1) (xy+x+1) is obviously wrong.
The left end is symmetrical about x.y, so the right end should be symmetrical about x.y. The correct answer should be: (xy+1) (x+1) (y+1)+xy = (xy+y+1) (xy+x
Method 3: Invariant test
Some mathematical problems are changeable and deformed, while others are unchangeable. For example, the shape and size of a graph remain unchanged when it is translated, rotated and folded, and the basic quantity remains unchanged. Using the invariants in this changing process, we can directly verify the correctness of some answers.
Method 4: Special case test
Special cases of problems are often easier to solve than general cases, so it is a very quick way to test the answers through special values and special cases.
For example, in the power operation in the senior high school entrance examination, such as (-A 2) 3 in 20 14, I can go to a=2, first calculate -A 2 =-4, and then calculate -4 3, so it is easy to check whether the original answer is correct or not.
Method 5: Inverse derivation of the answer.
I believe many students will use this method. After finding the answer to the question, they can replace the answer back to the question and test whether the conditions of the question are still valid.
But we must pay attention to this method and think about whether there may be multiple solutions.
In short, in order to improve the frequency and efficiency of inspection and avoid boring repetition, it is necessary to solve multiple problems.
A problem, done in the original way, of course, can also find mistakes, but people are inertial thinking, it is easy to ignore some small mistakes.
If everyone tries to come up with some new methods when checking, then first, we can check whether the answers are right or wrong, second, we can reduce the boredom caused by mechanical repetition, third, thinking about new solutions is also a means to exercise our thinking, and fourth, we can maximize the role of the questions in the test paper, which can be said to be a good measure to kill two birds with one stone.
Method 6: Direct test method
As the most basic method, direct inspection should pay attention to skills.
The direct test method is to check, check and test the problem-solving process and related conclusions around the original problem-solving method. In order to cooperate with the inspection, we must first use the draft paper correctly. I suggest you fold the draft paper out of the mark, calculate it in order, and mark it with the title number to facilitate inspection and comparison. Second, be careful. Every detail needs careful scrutiny, doesn't it? Take it for granted? Remember? The safest place is sometimes the most dangerous place? .
Extended reading: the complete set of knowledge points and formulas for reviewing mathematics in senior high school entrance examination
1. Merge similar projects
When merging similar items, the rule cannot be forgotten, only the sum of coefficient, letter and index remains unchanged.
2. Constantly changing
When two numbers are subtracted, the exchange position is the most common, and the positive or negative only depends on its index, and the odd number becomes the even number. (a-b)2n+ 1 =-(b-a)2n+ 1(a-b)2n =(b-a)2n
3. Variance formula
There are two square difference formulas with opposite signs. Remember to be firm, and multiply the head and tail by the head and tail to avoid confusion with the complete formula.
4. Perfect square
There are three complete squares, the first and last symbols are hometown, the first and last squares, and the first and last two times are placed in the middle; First of all? The closing bracket is square, and the final bullet follows the center.
5. Factorization
Give two sets (formulas) and three groups, and look at several items carefully. Two items only use square difference, three items are cross multiplication, and the array method is skillful and careless, and four items are carefully looked at. If there are three square numbers (terms), use one or three to group, otherwise, use two or two to group, and try to group five or six or more terms, two or three. If none of the above works,
6.？ Substitution? Oral decision
Dig out the letters and replace them with numbers (formulas), numbers and letters; Replace it with fractions or negative numbers, enclose it in parentheses, put the (present) brackets in the original brackets, and gradually change the brackets (small? Medium? Big)
7. Single operation
Addition, subtraction, multiplication, division and multiplication (on), the three-level operation is clear, the coefficient is calculated at the same level, and the exponential operation is degraded.
8. General steps to solve the one-dimensional linear inequality problem
Delete denominator, brackets and symbols when moving items, and similar items. After the merger, remove the coefficient, and don't forget to change the inequality sign when dividing (dividing) the negative number on both sides.
9. Solution set of linear inequality system with one variable
Take the big ones, the small ones take the small ones, the small ones take the middle ones, and the small ones are nowhere to be found.
10. One-dimensional quadratic inequality. Solution set of one-dimensional linear absolute value inequality
The big fish takes both sides, and the small fish takes the middle.
1 1. Fractional hybrid algorithm
Fraction four operations, sequential multiplication, division, addition and subtraction, multiplication and division at the same level, the division sign must be changed (multiplied); Multiplication simplification, factorization first, numerator and denominator meet, and then operation; The addition and subtraction of denominator should be consistent, and denominator integration is the key; It is not difficult to find the simplest common denominator. The sign must be changed in two places, and the result is the simplest.
12. Steps to Solve Fractional Equation
Multiply the simplest common denominator into algebraic expressions and write them clearly. After the solution is obtained, the root must be tested, leaving the original (root). Add (root) to avoid ambiguity.
13. The condition of the simplest root
The simplest three conditions of the root formula, the denominator contains no sign, the power exponent (number) and the root exponent (number) are coprime, and the power exponent is a little smaller than the root exponent.
14. Coordinate characteristics of special points
Coordinate plane points (x, y), transverse to the front and longitudinal to the back; (+,+), (-,+), (-,-) and (+,-), the four quadrants are divided into front and back; Y is 0 on the x axis, and x is 0 on the y axis.
15. Quadrant angle bisector
The quadrant bisector has its own characteristics: 1. All three directions are equal, 2. All four directions are opposite.
16. Lines parallel to the axis
A straight line parallel to an axis, the coordinates of points are particular, the straight line is parallel to the X axis, and the ordinate is different; The straight line is parallel to the Y axis, and the abscissa of the point remains unchanged.
17. Symmetric point coordinates
Keep in mind the coordinates of symmetrical points, and the positions of opposites should not be confused. X-axis symmetry, Y-axis symmetry, Y-axis symmetry, with negative sign in front of X; It is best to remember that the origin is symmetrical, and the abscissa and ordinate are signed.
18. Range of independent variables
Fraction denominator is not zero, and it must be negative under even roots; The zeroth power base is not zero, and the odd roots of algebraic expressions can be used.
19. Motion law of function image
If the first analytic function is written as y = k (x+0)+B. The analytic formula of the quadratic function is written as y=a(x+h)2+k, then use the following formula? Pan left and right in brackets, and pan up and down at the end. The opposite of Zuo Zheng's right deviation must be borne in mind that it is wrong.
20. Linear function image and property formula
The linear function is a straight line, and the image passes through three quadrants; The proportional function is simpler, and the straight line passes through the origin; These two coefficients, k and b, play a great role. K is the inclination angle, B intersects with the Y axis, K is positive and right oblique, X increases or decreases, and Y increases or decreases; K is negative to the lower left, and the change law is just the opposite; The greater the absolute value of k, the farther the straight line is from the horizontal axis.
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