Remembering trigonometric functions 

Tips and Tricks

A number of students have a tough time while remembering trigonometric functions. To make the trigonometric functions unforgettable for you, we have come up with a mnemonic “SOHCAHTOA”. It will make sure remember to figure out the sine, cosine, tangent of an angle from the sides of a right triangle and vice versa. If you remember this mnemonic, then the questions will be completely on your tips where you are expected to use the functions and determine the length of a missing side.

Cross multiply to find the greater fraction

Tips and Tricks

If you are required to find the greater of two fractions and you are not sure about the right fraction, then Cross multiply to find the greater fraction technique discussed here will simplify the confusion.

  1. Simply multiply the numerator of each fraction with the denominator of the other fraction.
  2. Write the answers to the corresponding numerator.
  3. The fraction which will show a greater value will be bigger.

For Example

If you are given two fractions

5/7 and 2/3

5 multiply by 3 will give 15 and 2 multiply by 7 will give 14

15 5/7  2/3 14

So,

5/7 is the greater equation.

Multiplying larger numbers quickly

Tips and Tricks

One of the common problem in doing mental multiplication is many students forget that multiplying larger numbers quickly requires breaking those larger numbers into more practical pieces. For example, if we see

17 x 6

you might think that 17 is a huge number and difficult to multiply.

To simplify the problem, you can break 17 into two manageable numbers that you can both multiply times 6. To get the right answer, add the result of two numbers. You might take 9 and 8, (9×6)+(9×8). But there is an easier way i.e. to choose a number which ends in a zero as these numbers are easiest to multiply.

Let’s take the example of 17. It can be broken into

7 + 10= 17

Now multiplying the 6 by 10 is quite instantaneous.

10 x 6= 60

That leaves the 7 thus giving us

7 x 6 = 42

Now add both values

42 + 60 =  102

An important point to consider is that not to think of this as a writing exercise. Simply make these equations in your mind and breaking these numbers in this way will make things quite easier for you. While doing this, you multiply 10×6 and then keep 60 on hold, then you multiply 6×7 and finally add both 60 and 42.

Let’s solve another equation with slightly larger number

Suppose we have

32 x 8

One way you can follow is to multiply 10×8 three times. But a faster way is to multiply

30 x 8

We have selected 30 as it ends in zero and closest to 32. This gives us 30×8 which is same as 3×8 with a zero at the end.

3 x 8= 24

Now add zero and it will give

240

Now we will put this number on hold and multiply the 2 left over as our original number was 32 time the 8. So,

2 x 8=16

The final step is to add this number to the on-hold number i.e. 240

240+16=256

Have a great test day with making the complex multiplications way too simpler for you.

Solving Algebraic Simultaneous Equations

Tips and Tricks

For solving algebraic simultaneous equations, the first step you should follow is to add or subtract the given equation. In case you are not able to find the required result, multiple one of the equation by a number. Make sure to select a number that eliminates one of the variables when you add or subtract the equation.

Solving Algebraic Equations

Tips and Tricks

To keep the students, stay on the right track with their exam preparation, here we have listed some of the key tips for solving algebraic equations more quickly without facing any error.

  1. While solving algebraic equations, treat both equations equally. What you do on one side, you must do on the other side of equations to keep it balanced. For example, if you apply square on one side, you must apply square on the other side too. Remember the algebraic equation with a Seesaw. As balancing a seesaw requires equal weight on both sides.
  2. While solving an expression, keep in mind to quickly manipulate the equation to get the desired expression.
  3. If two expressions are required to set equal to each other, cross multiply them or multiply by using a common denominator.
  4. While multiplying or dividing an expression by a negative number, remember to switch the direction of the inequality sign or else your minor mistake will ultimately give wrong results.

Greater than vs Less than

Tips and Tricks

Greater than vs Less than makes us confused several times while operating the equations because of common looking signs.

Here we have listed two ways that will make you remember them throughout your life.

  1. It’s a very common example that we have learned in our childhood that an alligator always eats the bigger number. It will completely make sense if you turn the inequality sign into an alligator.
  2. Another trick is that you can simply grow up by learning “less than three” i.e. <3. In this way, you will never forget the less than sign which will definitely make you remember the greater than sign.

Multiplication of a two-digit number with 11

Tips and Tricks

Multiplication of a two-digit number with 11 is a challenging and time consuming task. Therefore, keeping in mind the following tricks and practice a few times will effectively help you in saving your precious time and solve equation within seconds.

It’s not a difficult task to multiply two-digit numbers with 11 once you know the trick. Let’s solve the following problem

For example Lets multiply 13 by 11

13 x 11

To solve this, simply add the two digits

1+3=4

Put the 4 between 1 and 3

143 is a correct answer

Now consider another example where we multiply 34 by 11

34 x 11

Adding both digits of 34

3 + 4= 7

Now putting 7 between 3 and 4 will give us

374, and that is a correct answer

Let’s move towards a bit complex problem and make it simple than ever before. Here we will multiply 78 with 11

78 x 11

Adding both 7 and 8 will give

7 + 8 = 15

Now put 15 between 7 and will give us

7158, now add 7 and 1 which will result 8

Now the final outcome will be

858, which is the correct answer

Practice of this trick will surely increase the speed of solving complex equations and expressions enabling students to focus more on the complex parts of calculations.

How to calculate the square of number ending with 5

Tips and Tricks

Students in their exam can save enormous amount of time solving complex problems if they know how to calculate the square of number ending with 5. This quick technique is very easy to learn and handy to apply Lets say you have a Number n5 (Where n can be any digit) then the square of the number can be calculated in these simple four steps

  1. Extract the trailing 5 and consider the remaining digit as n. E.g You have the number 45 then n=4.
  2. To calculate the square put  n(n+1) E.g n=4(4+1) =20
  3. Put 25 for trailing 5
  4. Concatenating them will give the correct square E.g square of 45=2025

For example calculating square for 35

  • Step 1: Here n=3
  • Step 2: n(n+1) =  3(3+1) =3*4 =12
  • Step 3 : 25 for trailing 5
  • Step 4: Concatenating 12 and 25 will give us 1225 which is the correct answer.

To understand the trick more lets take another example of calculate square for 155

  • Step 1: Here n=15
  • Step 2: n(n+1) =  15(15+1) =15*16 =240
  • Step 3 : 25 for trailing 5
  • Step 4: Concatenating 240 and 25 will give us 24025 which is the correct answer.

However we can use the technique described here where we calculate the square of any number in mind but the trick given above is easier for the case where the number’s ending digit is 5.

For example square of 35 can be calculated as x = 35

  • Step 1 :  y=30
  • Step 2 : z= 5
  • Step 3 : (35+5) *(35-5) + 52 =   40*30+25 =  40 *10 *3 +25
  • breaking up 20=2*10 for easier and quick calculation
    400*3+25 =   1200+25 =  1225 is the correct answer

How to calculate the square of any number in your mind

Tips and Tricks

How to calculate the square of any number in your mind is the most interesting question by the students who are planning to attempt any prep test, the technique discuss in this post help those students while saving their time in solving complex problems.

This technique contains following steps which can be followed in mind to calculate the square of any number quickly.

Lets consider  x is the number which square is to be calculated.

  1. Find the absolute value of number to the nearest multiple of 10. Lets consider  y is that absolute value of the number x from the nearest multiple of 10.
  2. Calculate the difference of the absolute value of the number with the number itself. E.g z is the difference between the number from its absolute value than z=|y-x|
  3. Now the solution expression will be  (x+z) * (x-z) + z2

Lets take an example,

We need to find the square of  22

so x=22

Step 1 :  y=20

Step 2 : z= 2

Step 3 : (22+2) *(22-2) + 22

=   24*20+4

=  24 *10 * 2 +4    breaking up 20=2*10 for easier and quick calculation

=    240*2+4

=   480+4

=  484 is the correct answer

Lets take another example,

We need to find the square of  96

so x=96

Step 1 :  y=100

Step 2 : z= 4

Step 3 : (96-4) *(96+4) + 42

=   92*100+4

=    9200+16

=  9216 is the correct answer

However there is a quicker technique for calculating square of number ending with 5 which is discussed in this post

Refer to the table below for some more examples, and examples given above

x y z (x+z) (x-z) z2 (x+z)*(x-z) +z2
1 22 20 2 24 20 4 484
2 36 40 4 40 32 16 1296
3 43 40 3 46 40 9 1849
4 57 60 3 60 54 9 3249
5 96 100 4 100 92 16 9216

Dealing with alternative information

Tips and Tricks

Deal with alternative with extra care containing more than one bit of data – ensure both or all bits are right.