CSS Prepare

compulsory · CSS study notes

1. BODMAS (Mathematical Operations)

CSS GSA — Paper 7, Part-II, Section VI, Sub-topic 1 (BODMAS / Order of Operations)

The Rule

BODMAS — the order in which a mathematical expression must be evaluated:

  1. B — Brackets: ( ), { }, [ ] — innermost first
  2. O — Order (powers/roots/"of"): squares, cubes, roots, and the word "of" (treated as multiplication, e.g. "1/2 of 10" = 5)
  3. D — Division and M — Multiplication: same precedence, evaluated left to right
  4. A — Addition and S — Subtraction: same precedence, evaluated left to right
  • Common trap: Division and Multiplication are not always done "D before M" — whichever appears first (left to right) is done first. Same for Addition/Subtraction.
  • "of" ranks with multiplication/division, not with addition — e.g. "12 ÷ 3 of 2" = (12÷3) of 2 = 4×2 = 8, not 12÷(3×2).

Worked Questions (with answers)

  1. 2 + 3 × 4 = 14
  2. 8 ÷ 2 (2 + 2) = 8 ÷ 2 × 4 = 16 (classic ambiguous-looking question — resolved strictly left-to-right after the bracket: 8÷2=4, then 4×4=16)
  3. 2³ – 8 ÷ 4 × 2 + 7 = 8 – 4 + 7 = 11
  4. 12 – 8 ÷ 4 + 25 × 3 = 12 – 2 + 75 = 85
  5. 10 – 3 × 6 + 10² + (6 + 1) × 4 = 10 – 18 + 100 + 28 = 120
  6. 3 + [6 (11 + 1 – 4)] ÷ 8 × 2 = 3 + 48 ÷ 8 × 2 = 3 + 12 = 15
  7. 3 + (18 ÷ 6)² × 2 = 3 + 9 × 2 = 21
  8. (4² – 6 × 2)² ÷ (4 ÷ 2 × 4) + 7 = (16–12)² ÷ 8 + 7 = 16÷8+7 = 9
  9. 4 + 8 ÷ 2 – 5 = 4 + 4 – 5 = 3
  10. 36 + 12 ÷ (8 – 5) = 36 + 4 = 40
  11. 12 + [16 – {5 + (12 – 3)}] = 12 + [16–14] = 14
  12. 4 – [4 – {4 – (4 – 4) – 4}] = 0

Practice Questions (with answers)

  1. 2 + 4 ÷ (22 + 6) × 2 = 2 + (4÷28)×2 = 2 2/7 ≈ 2.29
  2. {15 × 32 ÷ 2 × 5} ÷ 75 = 1200÷75 = 16
  3. 5 × (2 × 34) ÷ 6 + 7 – 8 = 340÷6 – 1 = 55⅔ (≈ 55.67)
  4. 2 × 5 ÷ 5 + 3 = 2 + 3 = 5
  5. [(18 – 6) ÷ 4] + [72 – 12 ÷ 3 of 2] = 3 + [72–8] = 67
  6. 12 + 6 × 27 ÷ 3 + 2 – 16 ÷ 8 × 2 = 12+54+2–4 = 64
  7. 8 ÷ 4 × (6 + 2 × 4) + 32 – 2 = 2×14+30 = 58
  8. [{(45 + 90 ÷ 3 × 6) × 2} × 2] × 56 = [{225×2}×2]×56 = 50,400
  9. 45 + 34 ÷ 2 × 82 ÷ 16 × 3 = 45+17×82÷16×3 = 306.375
  10. 100 – 3[20 + {50 – 40}] = 100–90 = 10

MCQ Traps

  • "8 ÷ 2 (2+2)" style questions are deliberately ambiguous online, but in a strict left-to-right BODMAS convention (used by CSS/FPSC-style tests), the answer is 16, not 1 — always resolve division/multiplication strictly left to right unless brackets dictate otherwise
  • "of" behaves like multiplication/division-tier, not addition-tier
  • A number written immediately outside a closing bracket without an operator (e.g. "(18÷6)²") means that group is squared, not multiplied by that digit

Self-Test Questions

  1. State the BODMAS order of operations in full.
  2. Solve: 15 – (2 + 3) × 2
  3. Solve: 24 ÷ 6 × 2 (do division and multiplication strictly left to right)
  4. Explain how "of" is treated in the order of operations, with an example.

Past-Paper MCQs (FPSC)

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The FPSC MCQ papers you shared (2024 and 2025) had no direct BODMAS question.

Past-Paper Questions with Answers (FPSC)

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Every question below appeared in the FPSC papers you shared; the year and question number are in each title. Answers are worked out by me.

  • CSS 2020 Q6(b): Find the missing number to complete each sum. (5)
    1. (a) 9 + 8 − 5 = 12, so 12 = 2 × ? → 6
    2. (b) 3 × 9 − 14 = 27 − 14 = 13, so 13 = 24 − ? → 11
    3. (c) 15 ÷ 3 × 12 = 5 × 12 = 60, so 60 = 41 + ? → 19
    4. (d) 24 ÷ 4 + 5 = 6 + 5 = 11, so 11 = 66 ÷ ? → 6
    5. (e) 8 × 6 − 13 + 3 = 48 − 13 + 3 = 38, so 38 = 7 × 6 − ? = 42 − ? → 4
    • Method: work out the side with no blank first (BODMAS, left to right), then solve for the unknown

CSS Exam Perspective

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  • Most repeated area: 'find the missing number' equations (2020) built on BODMAS
  • Tip: always evaluate the complete side first, and never skip the left-to-right rule for × and ÷