1, overall situation
After you get the test paper, you should read the whole volume. Generally speaking, we should answer in the order of easy before difficult, simple before complicated, arrange the time reasonably, and don't type "hold" on a stuck question. There are also points for seemingly difficult questions. Don't be timid when you see the "difficult" problems of new faces. Think calmly and analyze carefully, and you will get the score you deserve.
Step 2 check the problem carefully
Some candidates are not careful enough to write in a hurry, so that they don't fully understand the conditions and requirements of the topic. To learn to dig out the hidden conditions from the questions and inspire the thinking of solving problems, we must examine the questions patiently and carefully, and accurately grasp the keywords and quantities in the questions (such as "at least" and "a>0"). ), get as much information as possible, in order to quickly find the right direction to solve the problem.
3. Fight for it step by step
Turning your problem-solving strategy into a scoring point mainly depends on accurate and complete mathematical language expression, which is often ignored by some candidates. Therefore, there are a lot of "incorrect answers" and "incomplete answers" on the test paper, and the candidates' own evaluation scores are far from the actual scores, such as "jumping questions" in the big topic demonstration, which makes many people lose scores above 1/3.
Advanced mathematics is a difficult course, and it is also a subject that needs extra points in the examinations of colleges and universities in various provinces. How to review high numbers in the sprint stage of college entrance examination? During this period, candidates are required to deepen their understanding, constantly polish their problem-solving skills and improve their test-taking skills. Today I will share some problem-solving skills with you.
Advanced mathematics
1. Given that a function f(x) is derivable at or above the second order, we should immediately think of expanding f(x) into Taylor formula at a specified point.
2. If there is a definite integral expression in the problem setting condition or the conclusion to be proved, the integral expression should be treated with the integral mean value theorem first.
3. If the function f(x) is continuous on [a, b] and derivable on (a, b), and f(a)=0 or f(b)=0 or f(a)=f(b)=0, then we will deal with it by Lagrange mean value theorem first.
4. For definite integral or variable limit integral, if the integrand function or its main part is a composite function, first make variable substitution to make it a simple form f(u).
linear algebra
1. If the condition is related to the algebraic cofactor Aij or A*, it is immediately related to the row (column) expansion theorem with determinant and a * = a * a = | a | e.
2. If it comes to whether A and B are interchangeable, that is, AB=BA, it is immediately associated with the definition of inverse matrix for analysis.
3. If the n-order square matrix A satisfies f(A)=0, to prove that aA+bE is reversible, first decompose the factor aA+bE.
4. Prove a set of vectors a 1, a2,? Because it has nothing to do with linearity, consider using definitions first.
5. If AB=0 is known, take each column of B as the solution of Ax=0.
6. If the parameters are determined according to the requirements of the topic, then think about whether there is a determinant that is zero.
7. If the eigenvector ζ0 of A is known, firstly, it is treated by defining ζ 0 = λ 0 ζ 0.
8. If we want to prove that the abstract N-order real symmetric matrix A is a positive definite matrix, we should use the definition to deal with it.
probability theory
1. If you need the probability of "at least" one of several events, immediately connect it with the probability addition formula; When the event groups are independent of each other, the probability formula of opposing events is used.
2. If the occurrence of an event is accompanied by the occurrence of a complete event group, then the occurrence probability of this event is calculated by the total probability formula. Key: find a complete event group.
3. If the random variable X ~ N is given in the problem, it is immediately associated with the standardized ~ N(0, 1) to deal with the related problems.
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