Maximizing your score in mathematics, whether in a high school exam, a college entrance test, or a professional certification, often requires more than just knowing the formulas and theorems. It involves having strategies and tricks up your sleeve to solve problems efficiently and accurately. Here are 12 outlier math tricks that can significantly boost your scores, especially in areas where you might struggle or where speed and accuracy are paramount.
1. The Multiplication Trick for Numbers Ending in 5
When multiplying two numbers that both end in 5, there’s a simple trick. For example, 25 * 35, first multiply the numbers before the 5 (2*3 = 6), then add 25 (which is 5*5) to get 625. This trick simplifies multiplication for numbers ending in 5.
2. Vedic Multiplication for Large Numbers
Vedic multiplication offers a quicker way to multiply large numbers, especially those close to 100 or multiples of 10. It involves breaking down the numbers and using simple arithmetic operations to quickly arrive at the product. This method reduces the complexity of large number multiplication.
3. Quick Squaring
To square a number ending in 5, like 35, you can use a simple formula. Take the number without the 5 (3), multiply it by the next number (3+1 = 4), and then append 25. So, 35^2 becomes 3*4 = 12, and then 1225. This trick applies to any number ending in 5.
4. The Rule of 72
For calculating compound interest or estimating how long it takes for an investment to double, the Rule of 72 is invaluable. Divide 72 by the annual interest rate to find out how many years it takes for your investment to double. For example, at 8% interest, it would take 72 / 8 = 9 years for your money to double.
5. Converting Fractions to Decimals
To quickly convert a fraction to a decimal without a calculator, look at the denominator. If it’s a power of 10 (10, 100, 1000, etc.), you can simply place the decimal point in the numerator. For example, 34⁄100 is 0.34. For other fractions, dividing the numerator by the denominator gives you the decimal.
6. Mental Math for Percentages
For quick percentage calculations, remember that 10% is the same as dividing by 10, 5% is half of 10%, and 1% is a tenth of 10%. This helps in quickly estimating percentages of numbers, especially when calculating sales tax, tips, or discounts.
7. The “Difference of Squares” Formula
The formula a^2 - b^2 = (a+b)(a-b) can greatly simplify certain algebraic expressions and is useful in factoring. It’s also helpful in quickly solving quadratic equations when they can be expressed in this form.
8. Quick Addition and Subtraction with Mental Math Tricks
For adding or subtracting numbers close to 10, 100, or 1000, you can adjust them to the nearest base (10, 100, 1000) and then perform the operation. For example, 107 + 93 can be thought of as (100 + 7) + (100 - 7) = 200.
9. Using Proportions for Fractions and Decimals
When dealing with fractions or decimals in word problems, setting up a proportion can quickly solve for unknowns. Remember, if a/b = c/d, then ad = bc. This method is especially useful in problems involving ratios and rates.
10. Estimation Techniques
Being able to estimate can save a lot of time and increase accuracy by allowing you to ballpark your answer before calculating. For multiplication, for example, rounding numbers to the nearest ten or hundred can provide a quick estimate.
11. Solving Algebraic Equations with the “Cover-Up” Method
For solving equations of the form ax/b + c = d, where a, b, c, and d are constants, the “cover-up” method can simplify the solution process. This involves first isolating the fraction, then multiplying both sides by the denominator to eliminate the fraction, and finally solving for the variable.
12. Utilizing Number Patterns
Math is full of patterns, and recognizing them can significantly speed up problem-solving. For example, knowing the pattern of squares (1, 4, 9, 16,…) can help in quickly identifying perfect squares and their roots.
Implementation in Real Exams
When applying these tricks in real exams, remember to read the question carefully and apply the trick only if it fits perfectly. Some tricks might have exceptions or require slight adjustments based on the numbers involved. Always double-check your work, especially when using mental math or quick estimation techniques, to ensure accuracy.
Conclusion
Mastering these outlier math tricks can significantly enhance your performance in math exams by providing tools for quick and accurate problem-solving. However, it’s also important to have a solid foundation in the basic principles of mathematics. Practice these tricks regularly to become proficient and to see where they can be applied to simplify complex problems.
Frequently Asked Questions
How do I choose the right trick for a given problem?
+Choosing the right trick involves understanding the nature of the problem and identifying patterns or characteristics (like numbers ending in 5, or being close to 10, 100, etc.) that match the conditions for applying a specific trick.
Can these tricks be applied to all types of math problems?
+No, these tricks are specific to certain types of problems. Always assess the problem to determine if one of these tricks applies. For problems that don’t fit these patterns, traditional methods or other specific tricks might be necessary.
How can I best practice these tricks to improve my math scores?
+Practice these tricks with a variety of problems. Start with simple applications and gradually move to more complex ones. Incorporate them into your regular math practice, and use them in conjunction with other problem-solving strategies to develop a versatile skill set.
