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## Maths Tricks And Shortcut For Competitive Exams PDF Free Download

### Maths Shortcut Tricks PDF

**1. Square Root**

Finding the square root of a number by estimating and multiplying can be a long procedure. Given below is a simpler method to find the square root of a number:

**Example:****Find the square root of 2116**

To find the square root of 2116:

**Step 1:** See the digit in one’s place. In this case, it is 6. Now, check between 1-9, the square of what all numbers have “6” at one’s place. The answer is 42 = 16 and 62 = 36.

**Step 2:** Now, check the square of which number between 1 to 9 is closest to the first two digits of the given number. In this case, the sum of the number between 1 to 9 is closest to 21. The answer is 42 = 16 and 52 = 25.

So, one number among 44, 46, 54 and 56 is the square root of 2116.

**Step 3:** For the two numbers you got in step 2, multiply each of them with the next number in the number series. That is, 4×5 = 20 and 5×6 = 30. Since 20 is a closer number to 21, the answer has to be either 46 or 44. Multiply and check your answer.

Check yourself with the below-mentioned example:

**Example: What is the square root of 1024?**

**Solution:**

**Step 1:** 22 = 4 and 82 = 64

**Step 2:** 32 = 9

**Step 3:** 3×4 = 12. Since 12 is greater than 10, the square root will be 32.

**2. Cube Root**

Follow the steps given below to find out the cube root of a number quickly.

**Example: What is the cube root of 9261?**

**Step 1: **Find the numbers between 1 to 9 whose cube is equal to the digit present at the one’s place; here, it is 1. So, we get 1×1×1 = 1.

**Step 2:** See the first digit of the number, in this case, 9. 9 lies between the cube of 2 (2×2×2 = 8) and (3×3×3 = 27). Since 8 is closest to 9, the cube root of 9261 is 21.

**Note: To find the cube root of 5 digit number, use the first two digits instead of the first digit in step 2**

Try one example by yourself to understand the trick even better:

**Example: What is the cube root of 32768?**

**Step 1: **23 = 8

**Step 2:** 33 = 27 and 43 = 64

Since 27 is closer to 32, the cube root of 32768 will be 32.

**3. Quadratic Equations**

Given below are two examples of quadratic equations solved with easy tricks to find the answer quickly:

**Example: x² – 18x + 45 = 0**

**Step 1: **Multiply the coefficient of x² and the constant in the equation. In this case, 1×45 = 45

**Step 2: **Multiply “-1” with the coefficient of x. In this case, -1× (-18) = 18

**Step 3: **Hence, the value of x will be 15 and 3 (3+15=18 & 3×15=45). Remember, for signs, **if the answer obtained in both step 1 & 2 is positive, then both values of x will be positive. If even one is negative, then values of x will be negative. **

Here, the value obtained in step 1 & 2 is positive hence the value of x will be positive. So, the answer is x = 15, 3

**Example:** **x²-5x-6 = 0**

**Step 1: **Multiply the coefficient of x² and the constant in the equation. In this case, 1×(-6) = (-6)

**Step 2:** Multiply “-1” with the coefficient of x. In this case, (-1)× (-5) = 5

**Step 3:** Hence, the value of x will be 6 and 1 (6-1=5 & 6×1=6). Remember, for signs, **if the answer obtained in both step 1 & 2 is positive, then both values of x will be positive. If even one is negative, then one of the values of x will be negative.**

**Step 4: **Here the answer in step 1 is negative. Thus, one value of x will be negative. If the answer in step 1 is negative, the smaller value of x will be negative. If the answer in step 2 is negative, the larger value will be negative.

So, x= 6, -1

**4. Compound Interest**

Given below are a few formulas that may save you some time during the exam while solving the compound interest problems:

**(a) **If compound interest is x% for 1st interval of time and is y% for the second interval of time, Then,

**Net Effective Rate of Interest after the 2 intervals = x + y + (xy/100)**

**Note:** This is applicable if both the time intervals are equal)

**(b)** If a sum of money, say P, amounts to A1 in a certain duration of time, say T, at Compound Interest and the same sum of money amounts to A2 in “2T” time at Compound Interest,

Then,

**P/A1 = A1/A2**

**(c) **If a sum of money, say P, amounts to A1 in a certain time duration, say T, at compound interest and the same sum of money amounts to A2 after T+1 years at compound interest

Then,

**Rate of Interest = {(A2-A1) / A1} × 100**

**For example: Raj pays compound interest at 16% per annum to Shyam, which is compounded quarterly. What is the effective rate of interest per annum paid by Raj?**

**Solution: **

Annual interest rate = 16%

So, the interest is paid quarterly, which makes a 4 time installment. Therefore, the rate of interest per quarter = 16/4 = 4%

Using (a) x + y + (xy/100).

4 + 4 + {(4×4)/100} = 8 + 0.16 = 8.16% for two quarters

For four quarters, 8.16% + 8.16% = 16.32%

**5. Simple Interest**

Take reference from the formulas given below and save some time while solving the questions in the final exam for the quantitative section:

**(a)** Difference between simple and compound interest for 2 years = {(PR)^{2}/ (100)^{2}}

**(b)** Difference between simple and compound interest for 3 years = {PR2 (300+R) / 100^{3}}

**For example: The difference between simple interest and compound interest for two years, on a certain sum of money at 4% per annum is Rs.800, when compounded annually. What is the sum of money on which the interest has been gained?**

**Solution:**

Following (a) CI-SI = {(PR)^{2}/ (100)^{2}}

⇒800 = {(P×4)^{2}/ (100)^{2}}

⇒P = Rs. 707.11

**6. Time & Work**

Given below is a simpler way to find out the time taken to complete a piece of work done by three people, when working together:

**Example: Three labourers, Ajit, Sumit & Ramesh take 10, 8 and 20 days respectively to complete the same piece of work. How long will it take for all three of them if they work together?**

**Solution:**

LCM of 10, 8 and 20 = 40

Efficiency of Ajit = 40/10 = 4

Efficiency of Sumit = 40/8 = 5

Efficiency of Ramesh = 40/20 = 2

Time Taken by all three together = {(LCM) / (Efficiency of all three)} = 40/11 days

**So to calculate the time taken to complete the same work by 3 people = (Total Unit of Work) / Efficiency of all the works)**

**7. Approximation**

Simple multiplication is something that consumes maximum of our time while solving maths questions in competitive exams. Given below is a shortcut to multiply two numbers which may help you in questions related to approximation and simplification.

**Example:** Solve 32 × 34

**Step 1:** Multiply the first number (in this case, 32) with the digit at ten’s place in second number (in this case, 3)

We get, 32×3 = 96

**Step 2:** Add a “0” to the answer obtained in step 1. So the number now becomes “960”

**Step 3:** Multiply 32 with the one’s digit in the second number, we get, 32×4 = 128

**Step 4:** Add the result obtained in step 2 & step 3.

So answer is 960 + 128 = 1088

Language | English |

No. of Pages | 64 |

PDF Size | 2 MB |

Category | Education |

Source/Credits | Drive.com |

Maths Tricks and Shortcut For Competitive Exams PDF Free Download