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Punjab Board Class 12 Mathematics — Formula Sheet

Punjab Board Class 12 Mathematics formula sheet, chapter by chapter — 25 formulas across 5 chapters. Follows the PSEB syllabus.

How to Use the Formula Sheet

  1. Write, don't just read — writing each formula out helps it stick.
  2. Understand the derivation — you can rebuild a formula you half-remember.
  3. Group related formulas — link the ones that build on each other.
  4. Test yourself — cover the sheet and write the formulas from memory.

Chapter-Wise Formulas — 5 Chapters

1

Relations and Functions

4 entries
Empty Relation: R = φ (no element is related to any other element). Example: R = {(a,b): a – b = 10} in A = {1,2,3,4} is empty.
Universal Relation: R = A × A (every element is related to every element). Example: R = {(a,b): |a – b| ≥ 0} in A = {1,2,3,4} is universal.
One-One (Injective) Function: Different inputs always give different outputs. f(x₁) = f(x₂) ⟹ x₁ = x₂.
Many-One Function: Two or more different inputs can give the same output. Example: f(x) = x² is many-one since f(1) = f(–1) = 1.
The full Relations and Functions formula sheet
2

Inverse Trigonometric Functions

6 entries
sin⁻¹: Domain = [-1, 1], Range = [-π/2, π/2] — closed interval at both ends.
cos⁻¹: Domain = [-1, 1], Range = [0, π] — closed interval at both ends.
For negative values: use identities sin(-θ) = -sin θ, cos(π-θ) = -cos θ, tan(-θ) = -tan θ, cot(π-θ) = -cot θ.
sin⁻¹(1/x) = cosec⁻¹(x) for |x| ≥ 1
cos⁻¹(1/x) = sec⁻¹(x) for |x| ≥ 1
The full Inverse Trigonometric Functions formula sheet
3

Matrices

3 entries
Square Matrix: Number of rows = Number of columns (order n×n). Example: A 3×3 matrix.
If A = [a_ij] and B = [b_ij] are both m×n matrices, then A + B = [a_ij + b_ij]_{m×n} (add corresponding elements).
The (i,k)-th element of AB: c_ik = Σ(j=1 to n) a_ij × b_jk = a_i1×b_1k + a_i2×b_2k + ... + a_in×b_nk.
The full Matrices formula sheet

2 more chapters below

Formula sheets for all 5 chapters with formulas.

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Get chapter-wise help for Punjab Board Class 12 Mathematics

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Frequently Asked Questions

Where can I find Punjab Board Class 12 Mathematics Formula Sheet?

This page has formula sheet for 5 chapters of Punjab Board Class 12 Mathematics for the board exams 2027. Each chapter links to its own page with the full set.

Go through the syllabus first, then work chapter by chapter: learn the ideas, practise questions, and revise with notes and flashcards. Leave time at the end to revise every chapter once more under timed conditions.

Learn the formulas you use most first, and understand what each symbol means so you can apply them. Knowing where a formula comes from helps you rebuild it if you forget it in the exam.

Browse Formula Sheet by Chapter

5 chapters

1

Relations and Functions

2

Inverse Trigonometric Functions

3

Matrices

4

Determinants

5

Continuity and Differentiability

More Mathematics Resources

Punjab Board Class 12

Practice Quiz

Test yourself with quick quizzes

Important Questions

Exam-style questions with answers

Revision Notes

Key concepts and quick revision points

Chapter Summary

Understand each chapter at a glance

Concept Maps

Diagrams showing how topics connect

Flashcards

Quick-fire cards for active recall practice

Syllabus

Chapter list and the topics in each

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