Civil Service Exam (Subprofessional) Numerical Ability — Integers, PEMDAS & DivisibilityExam Answer Templates

Marks

2

Topic

Integers

Difficulty

easy

Template Id

T1

Examiner Tip

Include the phrase 'cannot be a fraction' to show complete understanding

Model Answer

An integer is a whole number that can be positive, negative, or zero, but cannot be a fraction or decimal. Examples: -5, 0, 7 (any two appropriate examples)

Question Type

short_answer

Answer Structure

• Line 1: Define integer clearly [1 mark]
• Line 2: Provide two correct examples [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incomplete definition missing key elements
• Giving fractional or decimal examples
• Only one example provided

Key Phrases To Include

• whole number
• positive, negative, or zero
• cannot be a fraction

Marks

3

Topic

Integer Operations

Difficulty

medium

Template Id

T2

Examiner Tip

Always convert double negatives to positive immediately to avoid confusion

Model Answer

(-8) + (+3) - (-5) = (-8) + (+3) + (+5) [Converting subtraction of negative to addition] = -8 + 3 + 5 = -8 + 8 = 0 Answer: 0

Question Type

numerical

Answer Structure

• Line 1: Write the original expression [no marks, but essential]
• Line 2: Apply sign rules correctly [1 mark]
• Line 3: Perform addition/subtraction step by step [1 mark]
• Line 4: State final answer clearly [1 mark]

Scoring Breakdown

Common Mark Deductions

• Sign errors when handling negative numbers
• Not showing intermediate steps
• Arithmetic mistakes

Key Phrases To Include

• subtracting negative equals adding positive
• step-by-step working

Marks

3

Topic

PEMDAS

Difficulty

medium

Template Id

T3

Examiner Tip

Label each PEMDAS step to show you understand the correct order

Model Answer

2 + 3 × (4 - 1)² Step 1 - Parentheses: 4 - 1 = 3 2 + 3 × (3)² Step 2 - Exponents: (3)² = 9 2 + 3 × 9 Step 3 - Multiplication: 3 × 9 = 27 2 + 27 Step 4 - Addition: 2 + 27 = 29 Answer: 29

Question Type

numerical

Answer Structure

• Line 1: Identify and solve parentheses [1 mark]
• Line 2: Apply exponents [1 mark]
• Line 3: Perform multiplication and addition [1 mark]

Scoring Breakdown

Common Mark Deductions

• Wrong order of operations
• Calculation errors
• Not labeling each step clearly

Key Phrases To Include

• PEMDAS order
• parentheses first
• exponents second
• multiplication before addition

Marks

2

Topic

Divisibility Rules

Difficulty

easy

Template Id

T4

Examiner Tip

Always state the rule first, then apply it systematically

Model Answer

Rule for divisibility by 8: A number is divisible by 8 if its last three digits form a number divisible by 8. Last three digits of 2,376 = 376 376 ÷ 8 = 47 (exactly) Therefore, 2,376 is divisible by 8.

Question Type

short_answer

Answer Structure

• Line 1: State the divisibility rule for 8 [1 mark]
• Line 2: Apply the rule and show calculation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not stating the rule
• Wrong rule application
• Calculation errors

Key Phrases To Include

• last three digits
• divisibility rule
• exactly divisible

Marks

5

Topic

PEMDAS

Difficulty

hard

Template Id

T5

Examiner Tip

Show every single step and state which PEMDAS rule you're applying at each stage

Model Answer

48 ÷ 6 + 2³ × (10 - 7) - 5 Step 1 - Parentheses first: (10 - 7) = 3 Expression becomes: 48 ÷ 6 + 2³ × 3 - 5 Step 2 - Exponents: 2³ = 2 × 2 × 2 = 8 Expression becomes: 48 ÷ 6 + 8 × 3 - 5 Step 3 - Multiplication and Division (left to right): 48 ÷ 6 = 8 8 × 3 = 24 Expression becomes: 8 + 24 - 5 Step 4 - Addition and Subtraction (left to right): 8 + 24 = 32 32 - 5 = 27 Final Answer: 27

Question Type

long_answer

Answer Structure

• Step 1: Handle parentheses [1 mark]
• Step 2: Calculate exponents [1 mark]
• Step 3: Perform multiplication and division [2 marks]
• Step 4: Complete addition and subtraction [1 mark]

Scoring Breakdown

Common Mark Deductions

• Wrong order of operations
• Calculation errors in exponents
• Not working left to right for same-level operations
• Missing intermediate steps

Key Phrases To Include

• PEMDAS order
• parentheses first
• left to right
• step by step

Marks

3

Topic

Integer Operations

Difficulty

medium

Template Id

T6

Examiner Tip

Grouping like signs first makes the problem much easier and reduces errors

Model Answer

(-12) + (+8) + (-15) + (+20) Group positive and negative integers: Positive integers: +8 + 20 = +28 Negative integers: (-12) + (-15) = -27 Combine results: +28 + (-27) = +28 - 27 = +1 Answer: +1 or 1

Question Type

numerical

Answer Structure

• Line 1: Group like signs together [1 mark]
• Line 2: Add within each group [1 mark]
• Line 3: Combine final results [1 mark]

Scoring Breakdown

Common Mark Deductions

• Sign errors
• Not grouping systematically
• Final combination errors

Key Phrases To Include

• group like signs
• add positive integers
• add negative integers

Marks

3

Topic

Divisibility Rules

Difficulty

medium

Template Id

T7

Examiner Tip

Always test both conditions (divisibility by 2 AND 3) to show complete understanding

Model Answer

Divisibility rule for 6: A number is divisible by 6 if it is divisible by both 2 and 3. Testing 234: For divisibility by 2: Last digit is 4 (even), so 234 is divisible by 2 ✓ For divisibility by 3: Sum of digits = 2 + 3 + 4 = 9, and 9 ÷ 3 = 3, so 234 is divisible by 3 ✓ Since 234 is divisible by both 2 and 3, it is divisible by 6.

Question Type

short_answer

Answer Structure

• Line 1: State divisibility rule for 6 [1 mark]
• Line 2: Test divisibility by 2 [1 mark]
• Line 3: Test divisibility by 3 and conclude [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incomplete rule statement
• Wrong divisibility tests
• Not testing both conditions

Key Phrases To Include

• divisible by both 2 and 3
• even number
• sum of digits

Marks

1

Topic

Absolute Value

Difficulty

easy

Template Id

T8

Examiner Tip

Use proper absolute value notation with the vertical bars

Model Answer

|-25| = 25

Question Type

very_short_answer

Answer Structure

• Direct answer with proper notation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Wrong notation
• Negative answer
• Missing absolute value bars

Key Phrases To Include

• absolute value notation | |
• positive value

Marks

2

Topic

Integer Operations

Difficulty

easy

Template Id

T9

Examiner Tip

State the sign rule you're using at each step to show understanding

Model Answer

(-6) × (+4) × (-2) Apply multiplication rules for integers: Negative × Positive = Negative: (-6) × (+4) = -24 Negative × Negative = Positive: (-24) × (-2) = +48 Answer: +48 or 48

Question Type

numerical

Answer Structure

• Line 1: Apply sign rules step by step [1 mark]
• Line 2: Calculate final answer [1 mark]

Scoring Breakdown

Common Mark Deductions

• Sign errors
• Wrong multiplication rules
• Calculation errors

Key Phrases To Include

• sign rules
• negative × positive = negative
• negative × negative = positive

Marks

2

Topic

Divisibility Rules

Difficulty

easy

Template Id

T10

Examiner Tip

Double-check your addition of digits as this is where most errors occur

Model Answer

Divisibility rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9. Sum of digits of 5,427: 5 + 4 + 2 + 7 = 18 18 ÷ 9 = 2 (exactly) Therefore, 5,427 is divisible by 9.

Question Type

short_answer

Answer Structure

• Line 1: State the divisibility rule for 9 [1 mark]
• Line 2: Apply rule and conclude [1 mark]

Scoring Breakdown

Common Mark Deductions

• Wrong rule
• Addition errors
• Incorrect conclusion

Key Phrases To Include

• sum of digits
• divisible by 9
• divisibility rule

Marks

4

Topic

PEMDAS

Difficulty

medium

Template Id

T11

Examiner Tip

Remember that multiplication and division have equal priority - work left to right

Model Answer

15 - 3 × 2² + 8 ÷ 4 Step 1 - Exponents: 2² = 4 Expression becomes: 15 - 3 × 4 + 8 ÷ 4 Step 2 - Multiplication and Division (left to right): 3 × 4 = 12 8 ÷ 4 = 2 Expression becomes: 15 - 12 + 2 Step 3 - Addition and Subtraction (left to right): 15 - 12 = 3 3 + 2 = 5 Final Answer: 5

Question Type

long_answer

Answer Structure

• Step 1: Handle exponents [1 mark]
• Step 2: Perform multiplication and division [2 marks]
• Step 3: Complete addition and subtraction [1 mark]

Scoring Breakdown

Common Mark Deductions

• Wrong order of operations
• Exponent calculation errors
• Not working left to right

Key Phrases To Include

• PEMDAS order
• exponents first
• left to right

Marks

3

Topic

Divisibility Rules

Difficulty

easy

Template Id

T12

Examiner Tip

Be specific about which digits qualify as 'even' to avoid ambiguity

Model Answer

Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8). Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.

Question Type

short_answer

Answer Structure

• Line 1: Rule for divisibility by 2 [1 mark]
• Line 2: Rule for divisibility by 3 [1 mark]
• Line 3: Rule for divisibility by 5 [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incomplete rules
• Mixing up rules
• Not mentioning all required digits

Key Phrases To Include

• even digit
• sum of digits
• ends in 0 or 5

Marks

2

Topic

Scientific Notation

Difficulty

medium

Template Id

T13

Examiner Tip

Remember: moving decimal right gives negative exponent, left gives positive

Model Answer

0.00456 Move decimal point to create a number between 1 and 10: 0.00456 → 4.56 Decimal moved 3 places to the right, so exponent is -3 Scientific notation: 4.56 × 10⁻³

Question Type

numerical

Answer Structure

• Line 1: Identify decimal movement [1 mark]
• Line 2: Write in proper scientific notation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Wrong exponent sign
• Incorrect decimal placement
• Wrong format

Key Phrases To Include

• move decimal point
• between 1 and 10
• negative exponent

Marks

2

Topic

Absolute Value

Difficulty

easy

Template Id

T14

Examiner Tip

Remember absolute value always gives the positive distance from zero

Model Answer

|−8| + |+5| − |−3| Evaluate each absolute value: |−8| = 8 |+5| = 5 |−3| = 3 Substitute and calculate: 8 + 5 − 3 = 13 − 3 = 10 Answer: 10

Question Type

numerical

Answer Structure

• Line 1: Evaluate each absolute value [1 mark]
• Line 2: Perform final calculation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Wrong absolute values
• Sign errors in final calculation
• Arithmetic mistakes

Key Phrases To Include

• absolute value
• positive value
• distance from zero

Marks

3

Topic

Properties of Zero

Difficulty

medium

Template Id

T15

Examiner Tip

Always mention that division BY zero is undefined - this is a key distinction

Model Answer

Zero Property in Multiplication: Any number multiplied by zero equals zero. Example: 7 × 0 = 0, (-5) × 0 = 0 Zero Property in Division: Zero divided by any non-zero number equals zero, but division by zero is undefined. Example: 0 ÷ 8 = 0, but 8 ÷ 0 is undefined

Question Type

short_answer

Answer Structure

• Line 1: State multiplication property with example [1 mark]
• Line 2: State division property [1 mark]
• Line 3: Provide correct examples [1 mark]

Scoring Breakdown

Common Mark Deductions

• Missing the undefined division case
• Wrong examples
• Incomplete explanations

Key Phrases To Include

• any number times zero equals zero
• zero divided by non-zero equals zero
• division by zero is undefined