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# BODMAS Rule-Sainik School Class 9 Math Study Material Notes pdf download free-Sainik School Coaching Center In Jalandhar-ANAND CLASSES

Sainik School Entrance Exam for Class 9 Math Study Material Notes helps students face the competition in the current education system. For NDA exam, students must be well prepared and score satisfactory marks in the 10th and 12th exams. It is observed that almost 90 percent of the Class 9th syllabus is repeated in Class 10th. So, students should clear the basics in Class 9 to understand the concepts easily in Class 10 for foundation of NDA exam. In this case, the ANAND CLASSES is the best study tool to get a clear idea about the basics and gain a strong knowledge of the syllabus.

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# What is BODMAS Rule ?

BODMAS is an acronym and it stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction.

In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is used, which is the synonym of BODMAS. Thus, the order of operations of BODMAS and PEMDAS is shown in the below figure.

According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by ‘order’ (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right. Solving the problem in the wrong order will result in a wrong answer.

## BODMAS Rule Full form

As we mentioned earlier, the full form of BODMAS is Brackets, Orders, Division, Multiplication, Addition, Subtraction. While applying the BODMAS rule we should follow the order of these operations.

 B Brackets ( ), { }, [ ] O Order of Square roots, indices, exponents and powers D Division ÷, / M Multiplication ×, * A Addition + S Subtraction –

## Tips to Remember BODMAS Rule:

The rules to simplify the expression using BODMAS rule are as follows:

• First, simplify the brackets
• Solve the exponent or root terms
• Perform division or multiplication operation (from left to right)
• Perform addition or subtraction operation (from left to right)

This order must be followed to get accurate results.

## Best Sainik School Exam Coaching Institute Near me In Jalandhar

Here’s how you apply the BODMAS rule in mathematics:

1. Brackets: First, perform any calculations within parentheses, brackets, or braces. Solve expressions inside the innermost set of brackets first. For example:
• (3 + 4) × 2 = 7 × 2 = 14
2. Orders (Exponents and Roots): After dealing with the brackets, address exponents and roots (like square roots or cube roots).For example:
• 23 = 2 × 2 × 2 = 8
3. Division and Multiplication: From left to right, perform any division or multiplication operations. Both of these operations have the same level of precedence.For example:
• 6 ÷ 2 × 3 = 3 × 3 = 9
4. Addition and Subtraction: Finally, from left to right, perform any addition or subtraction operations. Like division and multiplication, these have the same level of precedence.For example:
• 5 + 4 – 2 = 9 – 2 = 7

Using the BODMAS rule ensures that you perform calculations in the correct order, preventing errors in your math problems. This rule is particularly important in more complex mathematical expressions to maintain consistency and accuracy in your solutions.

# Types of Brackets

Sometimes we need to use more than one type of bracket. The brackets which are used are –

• Vinculum or bar bracket —
• Parentheses ()
• Braces {}
• Square brackets []

We should start solving from the innermost bracket. Generally, vinculum is used as innermost bracket, then parentheses, then braces, then square brackets.

### Simplification of Brackets

Simplification of terms inside the brackets can be done directly. That means we can perform the operations inside the bracket in the order of division, multiplication, addition and subtraction.

Note: The order of brackets to be simplified is (), {}, [].

## Example 1: Simplify the expression: 4 + 3 × (5 – 2)²

Step 1: First, we simplify what’s inside the parentheses.

• 5 – 2 = 3

Step 2: Now we square the result from step 1.

• 3² = 9

Step 3: Finally, we perform multiplication and addition.

• 3 × 9 = 27
• 4 + 27 = 31

So, 4 + 3 × (5 – 2)² = 31.

## Example 2: Evaluate the expression: 12 ÷ 3 + 5 × (2 – 1)

Step 1: We begin with the multiplication inside the parentheses.

• 2 – 1 = 1

Step 2: Now we perform multiplication and division from left to right.

• 5 × 1 = 5
• 12 ÷ 3 = 4

Step 3: Finally, we perform the addition.

• 4 + 5 = 9

So, 12 ÷ 3 + 5 × (2 – 1) = 9.

## Example 3: Calculate the value of: (6 + 3)² ÷ 3 – 4

Step 1: First, we calculate the sum inside the parentheses.

• 6 + 3 = 9

Step 2: Now, we square the result.

• 9² = 81

Step 3: Then, we perform the division.

• 81 ÷ 3 = 27

Step 4: Finally, we perform the subtraction.

• 27 – 4 = 23

So, (6 + 3)² ÷ 3 – 4 = 23.

## Example 4: Simplify the expression: 2 + 3 × (4 – 1)² ÷ 5

Step 1: First, perform the subtraction inside the parentheses.

• 4 – 1 = 3

Step 2: Then, square the result.

• 3² = 9

Step 3: Next, perform multiplication and division from left to right.

• 3 × 9 = 27
• 27 ÷ 5 = 5.4

Step 4: Finally, perform the addition.

• 2 + 5.4 = 7.4

So, 2 + 3 × (4 – 1)² ÷ 5 = 7.4.

## Example 5: Evaluate the expression: (8 ÷ 2) × 3 – 4²

Step 1: First, perform the division inside the parentheses.

• 8 ÷ 2 = 4

Step 2: Next, square the result.

• 4² = 16

Step 3: Finally, perform the multiplication and subtraction.

• 4 × 3 = 12
• 12 – 16 = -4

So, (8 ÷ 2) × 3 – 4² = -4.

## Example 6: Evaluate the expression: 5 + 4 × 2² – (6 + 3)

Step 1: First, calculate what’s inside the parentheses.

• 6 + 3 = 9

Step 2: Then, square the result.

• 2² = 4

Step 3: Next, perform the multiplication.

• 4 × 4 = 16

Step 4: Finally, perform the addition and subtraction.

• 5 + 16 – 9 = 12

So, 5 + 4 × 2² – (6 + 3) = 12.

## Example 7: Simplify the expression: 10 – 2 × (3 + 5) ÷ 4

Step 1: First, calculate what’s inside the parentheses.

• 3 + 5 = 8

Step 2: Then, perform the multiplication and division from left to right.

• 2 × 8 = 16
• 16 ÷ 4 = 4

Step 3: Finally, perform the subtraction.

• 10 – 4 = 6

So, 10 – 2 × (3 + 5) ÷ 4 = 6.

## Example 8: Evaluate the expression: 2 × (3 + 4)² ÷ 6 – 5

Step 1: First, calculate what’s inside the parentheses.

• 3 + 4 = 7

Step 2: Then, square the result.

• 7² = 49

Step 3: Next, perform the multiplication and division from left to right.

• 2 × 49 = 98
• 98 ÷ 6 = 16.33 (approximately)

Step 4: Finally, perform the subtraction.

• 16.33 – 5 ≈ 11.33

So, 2 × (3 + 4)² ÷ 6 – 5 is approximately 11.33.

## Example 9: Simplify the expression: (10 + 4) × 2 – (5² ÷ 5)

Step 1: First, calculate what’s inside the parentheses.

• 10 + 4 = 14

Step 2: Then, calculate the expression inside the second set of parentheses.

• 5² ÷ 5 = 25 ÷ 5 = 5

Step 3: Next, perform the multiplication and subtraction from left to right.

• 14 × 2 = 28
• 28 – 5 = 23

So, (10 + 4) × 2 – (5² ÷ 5) = 23.

## Example 10: Evaluate the expression: (6 – 2) × (4 + 3)² ÷ 7

Step 1: First, calculate what’s inside the first set of parentheses.

• 6 – 2 = 4

Step 2: Then, calculate what’s inside the second set of parentheses.

• 4 + 3 = 7

Step 3: Now, square the result from step 2.

• 7² = 49

Step 4: Next, perform the multiplication.

• 4 × 49 = 196

Step 5: Finally, perform the division.

• 196 ÷ 7 = 28

So, (6 – 2) × (4 + 3)² ÷ 7 = 28.

## Example 11: Simplify the expression: 12 + 2 × (6 + 4²) – 3

Step 1: First, calculate what’s inside the second set of parentheses.

• 4² = 16

Step 2: Then, calculate the sum inside the parentheses.

• 6 + 16 = 22

Step 3: Now, perform the multiplication and addition from left to right.

• 2 × 22 = 44
• 12 + 44 = 56

Step 4: Finally, perform the subtraction.

• 56 – 3 = 53

So, 12 + 2 × (6 + 4²) – 3 = 53.

## Example 12: Simplify the expression: 8 × (5 – 2) + 7² ÷ 14

Step 1: First, calculate what’s inside the parentheses.

• 5 – 2 = 3

Step 2: Next, square the result.

• 7² = 49

Step 3: Now, perform the multiplication and division from left to right.

• 8 × 3 = 24
• 49 ÷ 14 ≈ 3.5

Step 4: Finally, perform the addition.

• 24 + 3.5 = 27.5

So, 8 × (5 – 2) + 7² ÷ 14 ≈ 27.5.

## Example 13: Evaluate the expression: (15 – 3) × 2² + 4 × 3

Step 1: First, calculate what’s inside the first set of parentheses.

• 15 – 3 = 12

Step 2: Next, square the result.

• 12² = 144

Step 3: Now, perform the multiplication and addition from left to right.

• 144 × 4 = 576
• 4 × 3 = 12

Step 4: Finally, perform the addition.

• 576 + 12 = 588

So, (15 – 3) × 2² + 4 × 3 = 588.

## Example 14: Simplify the expression: (4 + 3) × (5 + 6) ÷ 7 – 9

Step 1: First, calculate what’s inside the first set of parentheses.

• 4 + 3 = 7

Step 2: Then, calculate what’s inside the second set of parentheses.

• 5 + 6 = 11

Step 3: Now, perform the multiplication and division from left to right.

• 7 × 11 = 77
• 77 ÷ 7 = 11

Step 4: Finally, perform the subtraction.

• 11 – 9 = 2

So, (4 + 3) × (5 + 6) ÷ 7 – 9 = 2.

## Example 15: Evaluate the expression: 2² × (8 ÷ 2) + 4 – 3

Step 1: First, calculate the division inside the second set of parentheses.

• 8 ÷ 2 = 4

Step 2: Then, square the result from step 1.

• 4² = 16

Step 3: Next, perform the multiplication and subtraction from left to right.

• 2² × 16 = 4 × 16 = 64
• 64 – 3 = 61

So, 2² × (8 ÷ 2) + 4 – 3 = 61.

## Example 16: Simplify the expression: 9 – 2 × (3 + 2)² ÷ 5

Step 1: First, calculate what’s inside the first set of parentheses.

• 3 + 2 = 5

Step 2: Then, square the result from step 1.

• 5² = 25

Step 3: Now, perform the multiplication and division from left to right.

• 2 × 25 = 50
• 50 ÷ 5 = 10

Step 4: Finally, perform the subtraction.

• 9 – 10 = -1

So, 9 – 2 × (3 + 2)² ÷ 5 = -1.

## Example 17: Evaluate the expression: (10 – 2) × (4 + 1)² ÷ 5

Step 1: First, calculate what’s inside the first set of parentheses.

• 10 – 2 = 8

Step 2: Then, calculate what’s inside the second set of parentheses.

• 4 + 1 = 5

Step 3: Now, square the result from step 2.

• 5² = 25

Step 4: Next, perform the multiplication and division from left to right.

• 8 × 25 = 200
• 200 ÷ 5 = 40

So, (10 – 2) × (4 + 1)² ÷ 5 = 40.

## Example 18: Simplify the expression: 15 ÷ 3 + 5 × (3² – 2)

Step 1: First, calculate what’s inside the second set of parentheses.

• 3² – 2 = 9 – 2 = 7

Step 2: Then, perform the multiplication and division from left to right.

• 5 × 7 = 35
• 15 ÷ 3 = 5

Step 3: Finally, perform the addition.

• 5 + 35 = 40

So, 15 ÷ 3 + 5 × (3² – 2) = 40.

## Example 19: Evaluate the expression: (6 – 2) × 2² + 5

Step 1: First, calculate what’s inside the first set of parentheses.

• 6 – 2 = 4

Step 2: Then, square the result.

• 4² = 16

Step 3: Now, perform the multiplication and addition from left to right.

• 16 × 4 = 64
• 64 + 5 = 69

So, (6 – 2) × 2² + 5 = 69.

## Example 20: Simplify the expression: 12 ÷ (4 + 1) × 2 – 3

Step 1: First, calculate what’s inside the parentheses.

• 4 + 1 = 5

Step 2: Then, perform the division and multiplication from left to right.

• 12 ÷ 5 = 2.4
• 2.4 × 2 = 4.8

Step 3: Finally, perform the subtraction.

• 4.8 – 3 = 1.8

So, 12 ÷ (4 + 1) × 2 – 3 = 1.8.

## Example 21: Evaluate the expression: (7 – 3) × (2 + 1)² ÷ 6

Step 1: First, calculate what’s inside the first set of parentheses.

• 7 – 3 = 4

Step 2: Then, calculate what’s inside the second set of parentheses.

• 2 + 1 = 3

Step 3: Now, square the result from step 2.

• 3² = 9

Step 4: Next, perform the multiplication and division from left to right.

• 4 × 9 = 36
• 36 ÷ 6 = 6

So, (7 – 3) × (2 + 1)² ÷ 6 = 6.

## Example 22: Simplify the expression: 9 – 2 × (3 + 2)² ÷ 5

Step 1: First, calculate what’s inside the first set of parentheses.

• 3 + 2 = 5

Step 2: Then, square the result from step 1.

• 5² = 25

Step 3: Now, perform the multiplication and division from left to right.

• 2 × 25 = 50
• 50 ÷ 5 = 10

Step 4: Finally, perform the subtraction.

• 9 – 10 = -1

So, 9 – 2 × (3 + 2)² ÷ 5 = -1.

## Example 23: Evaluate the expression: (10 – 2) × 2² + 4 – 3

Step 1: First, calculate what’s inside the first set of parentheses.

• 10 – 2 = 8

Step 2: Then, square the result from step 1.

• 8² = 64

Step 3: Now, perform the multiplication and addition from left to right.

• 64 × 4 = 256
• 256 – 3 = 253

So, (10 – 2) × 2² + 4 – 3 = 253.

## Example 24: Simplify the expression: 20 ÷ (5 – 3) × 2 + 7

Step 1: First, calculate what’s inside the parentheses.

• 5 – 3 = 2

Step 2: Then, perform the division and multiplication from left to right.

• 20 ÷ 2 = 10
• 10 × 2 = 20

Step 3: Finally, perform the addition.

• 20 + 7 = 27

So, 20 ÷ (5 – 3) × 2 + 7 = 27.

## Example 25: Evaluate the expression: (12 – 3) × 3² + 5

Step 1: First, calculate what’s inside the first set of parentheses.

• 12 – 3 = 9

Step 2: Then, square the result from step 1.

• 9² = 81

Step 3: Now, perform the multiplication and addition from left to right.

• 81 × 3 = 243
• 243 + 5 = 248

So, (12 – 3) × 3² + 5 = 248.

Example 26: Simplify the expression: 8 × (6 – 2) + 4² ÷ 4

Step 1: First, calculate what’s inside the parentheses.

• 6 – 2 = 4

Step 2: Then, perform the subtraction inside the second set of parentheses.

• 4² ÷ 4 = 16 ÷ 4 = 4

Step 3: Now, perform the multiplication and addition from left to right.

• 8 × 4 = 32
• 32 + 4 = 36

So, 8 × (6 – 2) + 4² ÷ 4 = 36.

## Example 27: Evaluate the expression: (9 – 2) × 2² – 3

Step 1: First, calculate what’s inside the first set of parentheses.

• 9 – 2 = 7

Step 2: Then, square the result from step 1.

• 7² = 49

Step 3: Now, perform the multiplication.

• 49 × 4 = 196

Step 4: Finally, perform the subtraction.

• 196 – 3 = 193

So, (9 – 2) × 2² – 3 = 193.

## Example 28: Simplify the expression: (4 + 3) × (6 – 2)² ÷ 8

Step 1: First, calculate what’s inside the first set of parentheses.

• 4 + 3 = 7

Step 2: Then, calculate what’s inside the second set of parentheses.

• 6 – 2 = 4

Step 3: Now, square the result from step 2.

• 4² = 16

Step 4: Next, perform the multiplication and division from left to right.

• 7 × 16 = 112
• 112 ÷ 8 = 14

So, (4 + 3) × (6 – 2)² ÷ 8 = 14.

## Example 29: Evaluate the expression: 3 × (8 – 2)² + 7

Step 1: First, calculate what’s inside the parentheses.

• 8 – 2 = 6

Step 2: Then, square the result from step 1.

• 6² = 36

Step 3: Now, perform the multiplication and addition from left to right.

• 3 × 36 = 108
• 108 + 7 = 115

So, 3 × (8 – 2)² + 7 = 115.

## Example 30: Simplify the expression: 15 – 4 × (7 – 3)² ÷ 2

Step 1: First, calculate what’s inside the first set of parentheses.

• 7 – 3 = 4

Step 2: Then, square the result from step 1.

• 4² = 16

Step 3: Now, perform the multiplication and division from left to right.

• 4 × 16 = 64
• 64 ÷ 2 = 32

Step 4: Finally, perform the subtraction.

• 15 – 32 = -17

So, 15 – 4 × (7 – 3)² ÷ 2 = -17.

## Example 31: Evaluate the expression: (9 – 2) × 2² + 5

Step 1: First, calculate what’s inside the first set of parentheses.

• 9 – 2 = 7

Step 2: Then, square the result from step 1.

• 7² = 49

Step 3: Now, perform the multiplication and addition from left to right.

• 49 × 4 = 196
• 196 + 5 = 201

So, (9 – 2) × 2² + 5 = 201.

## Example 32: Simplify the expression: 6 + 3 × (7 – 2)² ÷ 4

Step 1: First, calculate what’s inside the first set of parentheses.

• 7 – 2 = 5

Step 2: Then, square the result from step 1.

• 5² = 25

Step 3: Now, perform the multiplication and division from left to right.

• 3 × 25 = 75
• 75 ÷ 4 = 18.75

Step 4: Finally, perform the addition.

• 6 + 18.75 = 24.75

So, 6 + 3 × (7 – 2)² ÷ 4 ≈ 24.75.

## Example 33: Evaluate the expression: (10 – 3) × 2² + 7

Step 1: First, calculate what’s inside the first set of parentheses.

• 10 – 3 = 7

Step 2: Then, square the result from step 1.

• 7² = 49

Step 3: Now, perform the multiplication and addition from left to right.

• 49 × 4 = 196
• 196 + 7 = 203

So, (10 – 3) × 2² + 7 = 203.

## Example 34: Simplify the expression: 12 ÷ (3 + 1) × 2 + 6

Step 1: First, calculate what’s inside the parentheses.

• 3 + 1 = 4

Step 2: Then, perform the division and multiplication from left to right.

• 12 ÷ 4 = 3
• 3 × 2 = 6

Step 3: Finally, perform the addition.

• 6 + 6 = 12

So, 12 ÷ (3 + 1) × 2 + 6 = 12.

## Example 35: Evaluate the expression: (6 – 2) × 2² – 4

Step 1: First, calculate what’s inside the first set of parentheses.

• 6 – 2 = 4

Step 2: Then, square the result from step 1.

• 4² = 16

Step 3: Now, perform the multiplication.

• 16 × 4 = 64

Step 4: Finally, perform the subtraction.

• 64 – 4 = 60

So, (6 – 2) × 2² – 4 = 60.

## Example 36: Simplify the expression: 15 – 4 × (6 – 3)² ÷ 3

Step 1: First, calculate what’s inside the first set of parentheses.

• 6 – 3 = 3

Step 2: Then, square the result from step 1.

• 3² = 9

Step 3: Now, perform the multiplication and division from left to right.

• 4 × 9 = 36
• 36 ÷ 3 = 12

Step 4: Finally, perform the subtraction.

• 15 – 12 = 3

So, 15 – 4 × (6 – 3)² ÷ 3 = 3.

## Example 37: Evaluate the expression: (8 – 2) × 2² + 6

Step 1: First, calculate what’s inside the first set of parentheses.

• 8 – 2 = 6

Step 2: Then, square the result from step 1.

• 6² = 36

Step 3: Now, perform the multiplication and addition from left to right.

• 36 × 4 = 144
• 144 + 6 = 150

So, (8 – 2) × 2² + 6 = 150.

## Example 38: Simplify the expression: 18 ÷ (6 – 3) × 3 + 7

Step 1: First, calculate what’s inside the parentheses.

• 6 – 3 = 3

Step 2: Then, perform the division and multiplication from left to right.

• 18 ÷ 3 = 6
• 6 × 3 = 18

Step 3: Finally, perform the addition.

• 18 + 7 = 25

So, 18 ÷ (6 – 3) × 3 + 7 = 25.

## Example 39: Evaluate the expression: (11 – 4) × 2² + 5

Step 1: First, calculate what’s inside the first set of parentheses.

• 11 – 4 = 7

Step 2: Then, square the result from step 1.

• 7² = 49

Step 3: Now, perform the multiplication and addition from left to right.

• 49 × 4 = 196
• 196 + 5 = 201

So, (11 – 4) × 2² + 5 = 201.

## Example 40: Simplify the expression: 14 – 3 × (8 – 4)² ÷ 2

Step 1: First, calculate what’s inside the first set of parentheses.

• 8 – 4 = 4

Step 2: Then, square the result from step 1.

• 4² = 16

Step 3: Now, perform the multiplication and division from left to right.

• 3 × 16 = 48
• 48 ÷ 2 = 24

Step 4: Finally, perform the subtraction.

• 14 – 24 = -10

So, 14 – 3 × (8 – 4)² ÷ 2 = -10.

## Example 41: Evaluate the expression: (7 – 2) × 2² – 6

Step 1: First, calculate what’s inside the first set of parentheses.

• 7 – 2 = 5

Step 2: Then, square the result from step 1.

• 5² = 25

Step 3: Now, perform the multiplication.

• 25 × 4 = 100

Step 4: Finally, perform the subtraction.

• 100 – 6 = 94

So, (7 – 2) × 2² – 6 = 94.

## Example 42: Simplify the expression: 10 ÷ (2 + 1) × 3 – 5

Step 1: First, calculate what’s inside the parentheses.

• 2 + 1 = 3

Step 2: Then, perform the division and multiplication from left to right.

• 10 ÷ 3 ≈ 3.33 (approximately)
• 3.33 × 3 ≈ 9.99 (approximately)

Step 3: Finally, perform the subtraction.

• 9.99 – 5 ≈ 4.99 (approximately)

So, 10 ÷ (2 + 1) × 3 – 5 ≈ 4.99 (approximately).

## Example 43: Evaluate the expression: (8 – 2) × 2² – 2

Step 1: First, calculate what’s inside the first set of parentheses.

• 8 – 2 = 6

Step 2: Then, square the result from step 1.

• 6² = 36

Step 3: Now, perform the multiplication.

• 36 × 4 = 144

Step 4: Finally, perform the subtraction.

• 144 – 2 = 142

So, (8 – 2) × 2² – 2 = 142.

## Example 44: Simplify the expression: 16 – 2 × (9 – 3)² ÷ 4

Step 1: First, calculate what’s inside the first set of parentheses.

• 9 – 3 = 6

Step 2: Then, square the result from step 1.

• 6² = 36

Step 3: Now, perform the multiplication and division from left to right.

• 2 × 36 = 72
• 72 ÷ 4 = 18

Step 4: Finally, perform the subtraction.

• 16 – 18 = -2

So, 16 – 2 × (9 – 3)² ÷ 4 = -2.

## Example 45: Evaluate the expression: (12 – 2) × 2² – 1

Step 1: First, calculate what’s inside the first set of parentheses.

• 12 – 2 = 10

Step 2: Then, square the result from step 1.

• 10² = 100

Step 3: Now, perform the multiplication.

• 100 × 4 = 400

Step 4: Finally, perform the subtraction.

• 400 – 1 = 399

So, (12 – 2) × 2² – 1 = 399.

## Example 46: Simplify the expression: 20 ÷ (5 – 2) × 2 + 4

Step 1: First, calculate what’s inside the parentheses.

• 5 – 2 = 3

Step 2: Then, perform the division and multiplication from left to right.

• 20 ÷ 3 ≈ 6.67 (approximately)
• 6.67 × 2 ≈ 13.33 (approximately)

Step 3: Finally, perform the addition.

• 13.33 + 4 ≈ 17.33 (approximately)

So, 20 ÷ (5 – 2) × 2 + 4 ≈ 17.33 (approximately).

## Example 47: Evaluate the expression: (10 – 2) × 2² – 3

Step 1: First, calculate what’s inside the first set of parentheses.

• 10 – 2 = 8

Step 2: Then, square the result from step 1.

• 8² = 64

Step 3: Now, perform the multiplication.

• 64 × 4 = 256

Step 4: Finally, perform the subtraction.

• 256 – 3 = 253

So, (10 – 2) × 2² – 3 = 253.

Step 1: First, calculate what’s inside the first set of parentheses.

• 6 – 3 = 3

Step 2: Then, square the result from step 1.

• 3² = 9

Step 3: Now, perform the multiplication and division from left to right.

• 2 × 9 = 18
• 18 ÷ 3 = 6

Step 4: Finally, perform the subtraction.

• 15 – 6 = 9

So, 15 – 2 × (6 – 3)² ÷ 3 = 9.

## Example 49: Evaluate the expression: (9 – 2) × 2² – 2

Step 1: First, calculate what’s inside the first set of parentheses.

• 9 – 2 = 7

Step 2: Then, square the result from step 1.

• 7² = 49

Step 3: Now, perform the multiplication.

• 49 × 4 = 196

Step 4: Finally, perform the subtraction.

• 196 – 2 = 194

So, (9 – 2) × 2² – 2 = 194.

## Example 50: Simplify the expression: 14 – 2 × (8 – 4)² ÷ 2

Step 1: First, calculate what’s inside the first set of parentheses.

• 8 – 4 = 4

Step 2: Then, square the result from step 1.

• 4² = 16

Step 3: Now, perform the multiplication and division from left to right.

• 2 × 16 = 32
• 32 ÷ 2 = 16

Step 4: Finally, perform the subtraction.

• 14 – 16 = -2

So, 14 – 2 × (8 – 4)² ÷ 2 = -2.

## Example 51: Evaluate the expression: (8 – 2) × 2² – 3

Step 1: First, calculate what’s inside the first set of parentheses.

• 8 – 2 = 6

Step 2: Then, square the result from step 1.

• 6² = 36

Step 3: Now, perform the multiplication.

• 36 × 4 = 144

Step 4: Finally, perform the subtraction.

• 144 – 3 = 141

So, (8 – 2) × 2² – 3 = 141.

## Example 52: Simplify the expression: 24 ÷ (6 – 3) × 2 + 5

Step 1: First, calculate what’s inside the parentheses.

• 6 – 3 = 3

Step 2: Then, perform the division and multiplication from left to right.

• 24 ÷ 3 = 8
• 8 × 2 = 16

Step 3: Finally, perform the addition.

• 16 + 5 = 21

So, 24 ÷ (6 – 3) × 2 + 5 = 21.

## Example 53: Evaluate the expression: (10 – 2) × 2² – 4

Step 1: First, calculate what’s inside the first set of parentheses.

• 10 – 2 = 8

Step 2: Then, square the result from step 1.

• 8² = 64

Step 3: Now, perform the multiplication.

• 64 × 4 = 256

Step 4: Finally, perform the subtraction.

• 256 – 4 = 252

So, (10 – 2) × 2² – 4 = 252.

## Example 54: Simplify the expression: 18 ÷ (4 – 2) × 2 + 6

Step 1: First, calculate what’s inside the parentheses.

• 4 – 2 = 2

Step 2: Then, perform the division and multiplication from left to right.

• 18 ÷ 2 = 9
• 9 × 2 = 18

Step 3: Finally, perform the addition.

• 18 + 6 = 24

So, 18 ÷ (4 – 2) × 2 + 6 = 24.

## Example 55: Evaluate the expression: (7 – 2) × 2² – 5

Step 1: First, calculate what’s inside the first set of parentheses.

• 7 – 2 = 5

Step 2: Then, square the result from step 1.

• 5² = 25

Step 3: Now, perform the multiplication.

• 25 × 4 = 100

Step 4: Finally, perform the subtraction.

• 100 – 5 = 95

So, (7 – 2) × 2² – 5 = 95.

## Example 56: Simplify the expression: 30 ÷ (6 – 3) × 3 + 8

Step 1: First, calculate what’s inside the parentheses.

• 6 – 3 = 3

Step 2: Then, perform the division and multiplication from left to right.

• 30 ÷ 3 = 10
• 10 × 3 = 30

Step 3: Finally, perform the addition.

• 30 + 8 = 38

So, 30 ÷ (6 – 3) × 3 + 8 = 38.

# Frequently Asked Questions (FAQs) related to studying for the Sainik School Class 9 Math entrance exam

To help you prepare for Sainik School Class 9 Math, it’s important to use appropriate study materials. Here are some frequently asked questions (FAQ) related to studying for the Sainik School Class 9 Math entrance exam:

1. What is the syllabus for the Sainik School Class 9 Math entrance exam?

• The syllabus for the entrance exam may vary slightly from one Sainik School to another. However, it generally covers topics from the standard Class 9 mathematics curriculum, including arithmetic, geometry, algebra, and basic mathematical concepts.

2. Where can I find official information about the exam pattern and syllabus?

• You can find official information about the exam pattern and syllabus on the official website of the specific Sainik School you’re applying to. Each school may have its own admission criteria.

3. Which textbooks should I use for Class 9 Math preparation?

• You should primarily use the NCERT Class 9 Math textbook. It covers the fundamental concepts and is widely accepted in Indian schools. Additionally, consider supplementary Math textbooks that are designed for competitive exams.

4. Are there any online resources for Sainik School Class 6 Math preparation?

• Yes, you can find online resources such as video tutorials, practice questions, and mock tests on educational websites. Websites like ANAND CLASSES offer free Math materials that can be helpful for your preparation.

5. Where can I get sample papers and previous year’s question papers?

• You can find sample papers and previous year’s question papers at online bookstore of ANAND CLASSES that sell competitive exam preparation materials. Additionally, ANAND CLASSES website offer downloadable PDFs of these papers for free or at a minimal cost.

6. Should I consider enrolling in coaching classes for Sainik School Math preparation?

• Enrolling in coaching classes is a personal choice. While they can provide structured guidance and additional practice, they are not mandatory. You can achieve success through self-study and the use of appropriate study materials.

7. How should I manage my study time effectively for Class 9 Math preparation?

• Create a study schedule that allocates specific time for Math preparation daily. Focus on understanding concepts, practicing regularly, and taking regular breaks to avoid burnout. Consistency is key.

8. Is there any specific advice for tackling the Math section of the Sainik School entrance exam?

• Pay close attention to the BODMAS rule (Order of Operations) and practice solving a variety of math problems. Make sure you’re familiar with the types of questions that are commonly asked in the entrance exam.

Remember to check the specific requirements and guidelines provided by the Sainik School you are applying to, as these may vary from school to school.

To prepare effectively for the Sainik School Class 9 Math entrance exam, you should consider the following general sources:

1. Sainik School Official Website: Visit the official website of the Sainik School you are applying to. They often provide information about the exam pattern, syllabus, and sample question papers.

2. NCERT Textbooks: The National Council of Educational Research and Training (NCERT) textbooks are widely used in Indian schools and are a valuable resource for exam preparation. Ensure you have the NCERT Math textbook for Class 9.

3. Solved Sample Papers and Previous Year Question Papers: You can find solved sample papers and previous year question papers for Sainik School entrance exams at bookstores or online at ANAND CLASSES website. These papers can give you an idea of the exam pattern and types of questions asked.

4. Math Study Guides: The Math study guides and reference books are publish under publication department of ANAND CLASSES and are designed to help students prepare for entrance exams. Look for books specifically tailored to the Sainik School entrance exam.

5. Online Resources: www.anandclasses.co.in

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