CSS Optional Subjects · Group II 2016 – 2026

CSS Pure Mathematics Past Papers (2016–2026): Free PDF Download

CSS Pure Mathematics past papers are useful for understanding how FPSC turns abstract mathematics into a timed competitive-exam paper. This page collects the original Pure Mathematics question papers from 2016 through 2026, with a free PDF for each year and one combined archive for offline study. The papers are especially useful for candidates comparing Pure Mathematics with other Group-II options or building a topic-by-topic revision plan.

Coverage2016 – 2026Eleven consecutive years of papers
Papers included11 filesOne original paper for each year
FormatOriginal, unsolvedQuestion papers without added solutions
Marks100 totalThree-hour paper with Sections A, B and C

Download CSS Pure Mathematics past papers

Use the combined file if you want the full archive in one place. For focused revision, download individual years and solve them under the same time limit used in the examination.

CSS Pure Mathematics Past Papers 2016–2026All eleven original papers in one downloadable PDF
Download Combined PDF

The files below are the same archive separated by year. Each link opens the corresponding Pure Mathematics question paper in PDF format.

CSS Pure Mathematics past papers by year

Start with the most recent paper to understand the current style, then work backwards. Older papers are still useful because they show how the subject has tested algebra, analysis, geometry and complex variables over time.

What the Pure Mathematics paper tests

Each supplied paper is a three-hour, 100-mark question paper divided into three sections. The instructions require candidates to attempt five questions: two from Section A, two from Section B and one from Section C. All questions carry equal marks, and the papers state that a calculator is allowed.

Section A: Algebra and linear mathematicsRecent papers include group theory, homomorphisms, rings, subgroups, matrices, rank, linear transformations and related proof-based questions.
Section B: Calculus and geometryQuestions cover limits, continuity, differentiation, integration, critical points, areas, conic sections, planes and coordinate-based problems.
Section C: Complex analysisThe archive includes complex-variable questions involving analytic functions, contour or path integrals, Cauchy’s Integral Formula and Taylor or related series work.
Important: The paper is not only a calculation test. The questions also ask for proofs, definitions and explanations. Practise writing a complete mathematical argument, not just reaching a final answer.
Group theorySubgroups, cyclic groups, normalisers, homomorphisms and Lagrange’s theorem
Linear algebraMatrices, echelon form, rank and linear transformations
CalculusLimits, continuity, differentiation, critical points and integration
Analytic geometryPlanes, coordinates, conics, parabolas and related geometric forms
Complex variablesAnalytic functions, Cauchy’s formula, path integrals and series
Proof writingClear definitions, logical steps and complete justifications under time pressure

How to use these CSS Pure Mathematics past papers

Do not begin by solving eleven papers without a plan. Use the archive in three passes.

First, map the syllabus. Mark every question by topic: group theory, linear algebra, calculus, geometry or complex analysis. This shows which parts of the subject you can already handle and which areas need a fresh review.

Next, practise by section. Solve two Section-A questions, two Section-B questions and one Section-C question in a single sitting. This mirrors the paper’s selection rule and prevents you from preparing only the topics you find comfortable.

Finally, repeat the paper under exam conditions. Use the three-hour limit. Leave time to check notation, missing steps and signs. In Pure Mathematics, a correct idea can still become an incomplete answer if the working is unclear.

Related CSS past-paper resources

Pure Mathematics sits within the wider optional-subject preparation system. These internal resources can help you compare papers and organise the rest of your preparation:

Frequently asked questions

Where can I download CSS Pure Mathematics past papers?

You can download the 2016–2026 CSS Pure Mathematics past papers from the year-by-year links on this page. A combined PDF is also provided for candidates who want the complete archive in one file.

How many marks is CSS Pure Mathematics?

Each supplied Pure Mathematics paper is worth 100 marks and has a three-hour time limit. The paper is divided into Sections A, B and C.

How many questions should I attempt?

The instructions in the supplied papers require five questions: two from Section A, two from Section B and one from Section C. All questions carry equal marks.

Is a calculator allowed in the Pure Mathematics paper?

Yes. The instructions printed on the supplied 2016–2026 papers state that the use of a calculator is allowed.

Are these Pure Mathematics papers solved?

No. These are original, unsolved question papers. Use them for topic mapping, timed practice and answer-writing review. Solutions should be checked against a reliable teacher, textbook or verified preparation resource.

What is the difference between Pure Mathematics and Applied Mathematics past papers?

Pure Mathematics focuses on areas such as algebra, calculus, geometry and complex analysis. Applied Mathematics uses mathematical methods in applied or physical contexts. Candidates should compare the official syllabus and recent papers before selecting either subject.

Source and verification

The year-by-year PDFs and combined archive on this page were supplied for publication on CSS Bureau and checked for their printed FPSC examination title, subject name, marks, time limit and section instructions. The topic summary above is based on the questions visible in the 2016–2026 papers. For current rules, syllabus changes and official notices, always confirm details through FPSC before making a final subject decision.