First, multiple-choice problem-solving strategies
Mathematics multiple-choice questions have the characteristics of strong generality, wide knowledge, small and flexible, and certain comprehensiveness and depth. Whether candidates can solve multiple-choice questions quickly, accurately, comprehensively and simply has become the key to the success of the college entrance examination.
The basic requirements for solving multiple-choice questions are proficiency, accuracy, flexibility, rapidity, proper methods and surprise. There are generally three ways to solve the problem: one is to consider the root of the problem and explore the results; Second, the stem of the question should be considered together with the selection of branches; The third is to explore the conditions to meet the problem from the choice of expenditure. Multiple choice questions are relatively easy (some are intermediate), and the basic principle of solving problems is "make a mountain out of a molehill".
1, direct method: problems involving mathematical theorems, definitions, rules and formulas often start from the conditions of topic setting and draw conclusions directly through operation or reasoning; And then compared with the selected branch.
Example: It is known that the function y=f(x) has the inverse function y=g(x). If f (3) =- 1, the image of function y = g (x- 1) must pass through () at the following points.
A.(-2，3) B.(0，3) C.(2，- 1) D.(4，- 1)
Solution: We can find the image passing point (3,-1) of function y=f(x) and the image passing point (-1, 3) of its inverse function y=g(x- 1).
2. Screening method (exclusion method and exclusion method): make full use of the characteristics of single choice in multiple-choice questions, eliminate the wrong branches one by one through analysis, reasoning, calculation and judgment, and get the solution of the correct branch.
For example, if x is the smallest internal angle in a triangle, then the range of the function y=sinx+cosx is ().
A.( 1，]B.(0，] C.[，] D .(，]
Solution: Because X is the smallest internal angle in a triangle, x∈(0,), thus Y = sinx+cosx >；; 1, excluding the wrong branch B, C, D C, D, A should be selected.
3. Image method (combination of numbers and shapes): a method to make a quick choice through the combination of numbers and shapes and the intuitive graphic thinking process.
For example, it is known that α and β are both second quadrant angles, cos α >; Cosβ, then ()
a .α& lt； βb . sinα& gt； sinβc tanα& gt； tanβd . cotα& lt； cotβ
Solution: in the second quadrant, through the cosine function line cos α >; Cosβ finds out the positional relationship between α and β, and then makes a judgment to get B.