Shortcut Methods and Tricks to Solve Numerical problems:

• Estimation or Order of Magnitude Calculation: Many problems can be estimated approximately by using order of magnitudes or by neglecting small quantities. This approach can provide quick and reasonable answers.

• Dimensional Analysis: Dimensionally correct equations ensure the consistency of units in calculations. Check if both sides of an equation have the same units; this can identify potential errors and serves as an initial check.

• Finding Patterns and Symmetries: Look for symmetrical patterns, periodic trends, or special cases in the problem. This might lead to simpler solutions.

-Graphical Representation: Plotting graphs or visualizing the behavior of functions or equations can provide insights and simplify complex calculations.

• Special Formulas and Identities: Remember key mathematical identities, trigonometric formulas, and properties of numbers and shapes to simplify expressions.

• Logarithms and Exponents: Utilize logarithmic properties to simplify calculations, convert products to sums, and rewrite expressions in a manageable form.

• Approximation Techniques: Use series expansions (like Taylor series) or approximations like the binomial theorem to simplify complicated expressions or functions.

• Limits and Continuity: Apply limit concepts to evaluate indeterminate forms or handle equations with discontinuities.

• Case Analysis: In some problems, cases might arise based on specific conditions. Analyze each case separately and combine the results.

• Guess-and-Check or Trial-and-Error: Make initial guesses and observe patterns to improve your guesses iteratively until the correct solution is found.

-Bounds and Inequalities: Use inequalities to set bounds or ranges for the unknown variables, which can help narrow down the solution space.

Remember that these methods are not exhaustive, and different techniques might be applicable to specific problems. Practice and familiarity with various mathematical techniques will enhance your problem-solving skills.