The AFCAT exam has been scheduled on 26th Feb and candidates have involved themselves completely into the examination preparations. The main part of the exam is to score more in less time. For that, certain tricks of maths can help the aspirants in solving the mathematical problems easily. Some basic tricks that will help the candidates in solving mathematical equations easily are given below.
1. Multiplication Tricks – Multiplication by 11 is commonly seen in the AFCAT exam. To multiply any number by 11, write the first and last letter of the number to be multiplied by 11 and in between them, put the digit which is the sum of the two digits.
Example 1 – 23X11 = 2(2+3)3 = 253
Example 2 – 235X11 = 2(2+3) (3+5)5 = 2585
2. Square of Multiples of 5 = Write 25 at the unit and tens place.
Take the number except the 5 at unit place
Multiply that number by its successor number.
Example 1 – 252 = (2X3)25= 625
Example 2 – 652 = (6X7)25 = 4225
3. Percentage Tricks – For getting some percentage of any number, just fragment the percentage in a simple form.
Example 1 – 150% of 200.
Here, take it as 100% of 200 + 50% of 200 = 200 + 100 = 300
Example 2 – 210% of 150
200% of 150 + 10% of 150 = 300 + 15 = 315
4. Finding Roots of Perfect Squares – For finding out the root of a number, you need to find two things.
Step 1 – The unit digit of the number matches with square of which number (1-9).
Step 2 – The numbers except unit and tens place comes in between the squares of which two numbers.
Example 1 – Root of 324
Sol. 4 comes in the unit place of the square of 22 = 4 and 82 = 64
So the root of 324 will either have 2 or 8 in its unit place
Leaving ones and tens digits of the 324, we get 3
3 comes between the squares of 12 = 1 and 22 = 4
As 1 is the smaller then 2, so 1 will be at the tens place of the square of the number.
So the number could be either 12 or 18. Now, 3 comes closer to 4 which is greater than 1, so the square root among 12 and 18 will be the greater one, i.e. 18.
Example 2 – root of 529
1 comes in the unit place of 32 = 3 and 72 = 49
So the unit digit of the root will be either 3 or 7
Now leaving the unit and tens digits, we get 5
5 comes as the square of 2 = 4 and 3 = 9
But 5 is closer to 4. So the tens place of the root will be 2
So the number could be either 23 or 27.
Now, 5 comes closer to 4 which is smaller than 9, so the square root among 23 and 27 will be the smaller one, i.e. 23
5. Solving Quadratic Equations – Firstly remember the sign conventions.
+ + = – –
-+ = ++
+ – = – +
– – = + –
Let the equation be ax2+bx+c
Step 1 – Multiply the a with c.
Step 2 – Find the factors of the number obtained
Step 3 – Make such an arrangement of 2 numbers using factors of the obtained number that will give you b.
Step 4 – Divide the two numbers with a and apply the above signs as per the signs of the equation.
Example 1 – 6×2 + 11x+3
Multiply 6 and 3 = 18
Factors of 18 = 3,3,2 and we have to get 11 from these factors
9 + 2 = 11
So the roots will be 9/6 and 9/2 OR 3/2 and 9/2
Using the above sign conventions, we will get the signs of the roots i.e. -3/2 and -9/2
Example 2 – x2-9x+20
1X 20 = 20
Factors of 20 = 2,2,5
To get 9 we can arrange them as 4+5 = 9
So the roots will be 4/1 and 5/1
Using sign convention, we will get the signs of the roots. i.e. = + 4/1 and + 5/1
Conclusion – The above mathematical tricks will help the aspirants in solving some of the commonly asked questions in AFCAT and will help them in scoring more in the given time. Well, maths is all about the consistent practice, but using tricks rather than solving as per the concept, will take your scores above the cut-off. So aspirants, work hard and give your best in the examination.
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