Introduction
The best Unit 5, Partial Fractions, solved notes for Class 11 Punjab Boards are now available, with 100 percent of exercises solved using easy, step by step solutions and the marking scheme, based on the new book from PECTAA.
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The Punjab Curriculum and Textbook Board, Ali Brothers. These notes are perfect for the 2026 exams and are built to help students score 90 plus marks.
Ideal for Students, Teachers, and Lecturers Across All Nine Punjab Boards
These notes are used at top registered institutions across all nine Punjab boards, including Aitchison College Lahore, Sadiq Public School Bahawalpur, Army Public Schools and Colleges, Beaconhouse, Forman Christian College Lahore, Government College University Faisalabad, Cadet College Hasan Abdal.
College Petaro, Cadet College Okara, Cadet College Kohat, Cadet College Sargodha, Cadet College Jhang, Cadet College Pasrur, Cadet College Spinkai, Military College Jhelum, Garrison Cadet College Kohat, and many more.
What’s Inside Unit 5, Reversing the Process You Already Know
Unit 5 flips a skill students already have, adding fractions into one, and asks them to run it backward: taking one rational fraction and splitting it back into simpler pieces. This idea, called partial fraction resolution, is one of the most useful tools in calculus for breaking a complicated expression down into something easier to integrate or analyze.
The unit opens with the difference between proper and improper rational fractions, and shows how an improper fraction is first reduced by long division into a polynomial plus a proper fraction, before any partial fraction work begins.
From there, it works through four distinct cases, each covered with fully worked examples:
- Case I, non-repeated linear factors in the denominator, solved using the standard method of equating coefficients, plus a faster alternative method of substituting the roots directly.
- Case II, repeated linear factors, where the same factor appears more than once and needs a partial fraction term for each power.
- Case III, non-repeated irreducible quadratic factors, where a quadratic that can’t be factored further gets its own Ax + B term.
- Case IV, repeated irreducible quadratic factors, combining the logic of Cases II and III.
Exercise 5.1, Linear Factors, Fully Solved
Exercise 5.1 covers both Case I and Case II, resolving rational fractions with non-repeated and repeated linear factors in the denominator. All questions are fully solved, including:
| Question | Fraction | Result |
|---|---|---|
| Q1 | 2 / (x² − 1) | 1/(x − 1) − 1/(x + 1) |
| Q2 | (a − b) / ((x − a)(x − b)) | 1/(x − a) − 1/(x − b) |
The full solved PDF for Exercise 5.1 is available, covering every question in complete detail, including the repeated linear factor questions later in the exercise.
Official Youtube Channel : www.youtube.com/@PECTAAlearnersclub
Exercise 5.2, Quadratic Factors, Fully Solved
Exercise 5.2 covers both Case III and Case IV, resolving rational fractions with non-repeated and repeated irreducible quadratic factors in the denominator, fully solved with complete step by step working.
Exercise 5.3 and Beyond
Exercise 5.3, along with any further cases covered later in the unit, is also fully solved.
Bonus Resources
- A Partial Fractions formula sheet PDF for quick reference.
- The top 30 decomposition shortcuts for faster problem solving.
- Partial Fractions video lectures.
- Unit 6 is coming soon as the next unit in this series.
View the Full Solved PDF
The complete solved PDF for Unit 5 is available to view for free, with no download needed.
Why This Unit Matters for Your Overall Score
Partial Fractions is a shorter unit than Matrices and Determinants, but it’s one you’ll lean on again later, especially in integral calculus, where breaking a complex rational expression into simpler pieces is often the very first step of a solution. Getting comfortable with all four cases here, rather than just the easy non-repeated linear case, saves a lot of time down the line.
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Frequently Asked Questions
Which exercises are covered in these Unit 5 notes? Exercise 5.1 and Exercise 5.2 are covered in full, with complete step by step solutions, alongside every worked example from the unit’s introduction through Case IV.
How do I know which case to use for a given fraction? Factor the denominator first. Non-repeated linear factors use Case I, repeated linear factors use Case II, a non-repeated irreducible quadratic uses Case III, and a repeated irreducible quadratic uses Case IV. Some fractions combine more than one case at once, as shown in the worked examples.
Are past papers included with these notes? Yes, Unit 5 past papers solved from 2018 through 2025 are included as a bonus resource.
Do I need to download the PDF to view these notes? No, the full solved PDF can be viewed directly on the site for free, with no download required.
Conclusion
With Exercise 5.1 and Exercise 5.2 fully solved, alongside every worked example across all four cases, Class 11 students across all nine Punjab boards have a strong, exam ready resource for mastering Partial Fractions ahead of the 2026 exams. Use these notes alongside the bonus formula sheet, shortcuts, and past papers to build both speed and accuracy for your Mathematics exam.
Best of luck for your Class 11 Mathematics exam!