Mathematics gives answers to unknown questions and is the pillar of science. But memorizing the formula and theorem is not sufficient to solve maths problems. You need to understand the important cycle which is learn -> analysis -> improvise. Learning will include theory section along with memorizing concepts and formulas. Next step comes with Analyzing the situation in which you need to understand each step and reason behind the step. Also during analyzing categorize the problem so that if similar problem comes in future you can handle it smoothly. Finally for completely new set of problems you need to improvise your knowledge and enter into unknown (to you) problem sets. A smart and intelligent engineer and scientist are expert in improvising technique which help them in making unknown as known.
Understanding the theme of question (Analyze)
- The higher the math class, the more types of problems: in earlier classes, problems often required just (just in case definition) one step to find a solution. Increasingly, you will tackle problems which require several steps to solve them. Break these problems down into smaller pieces and solve each piece – divide and conquer!
- Problem types:
- Problems testing memorization- Formula based (like Trigonometry, AP, GP)
- Problems requiring application of skills to familiar situations – Practice (like Binomial Theorem)
- Problems requiring that you extend the skills or theory you know before applying them to an unfamiliar situation. – Concept based (like P&C)
- When you work problems on homework, write out complete solutions, as if you were taking a test. Don’t just scratch out a few lines and check the answer in the back of the book. If your answer is not right, rework the problem; don’t just do some mental gymnastics to convince yourself that you could get the correct answer. If you can’t get the answer, get help.
- The practice you get doing homework and reviewing will make test problems easier to tackle.
Tips on Problem Solving
- Problem solving approach/technique
- The first and most important step in solving a problem is to understand the problem, that is, identify exactly which quantity the problem is asking you to find or solve for (make sure you read the whole problem).
- Next you need to devise a plan, that is, identify which skills and techniques you have learned can be applied to solve the problem at hand.
- Carry out the plan.
- Look back: Does the answer you found seem reasonable? Also review the problem and method of solution so that you will be able to more easily recognize and solve a similar problem.
- Some problem-solving strategies: use one or more variables, complete a table, consider a special case, look for a pattern, guess and test, draw a picture or diagram, make a list, solve a simpler related problem, use reasoning, work backward, solve an equation, look for a formula, use coordinates.