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If you search for ISC maths "sections A, B and C", most of what you find describes a structure that no longer applies. For years, ISC Class 12 students chose between two optional sections. CISCE's syllabus for ISC 2027 removes that choice. This post explains what changed, how the new paper is organised, how the 20 project marks work, and one linear programming problem worked in full.
What were the old sections A, B and C?
An earlier Class XII syllabus, still on the CISCE site as Mathematics XII (Revised), split the 80-mark theory paper like this:
Section A, 65 marks, compulsory: relations and functions (10), algebra (10), calculus (32), probability (13).
Section B, 15 marks: vectors (5), three-dimensional geometry (6), applications of integrals (4).
Section C, 15 marks: application of calculus (5), linear regression (6), linear programming (4).
Candidates answered Section A and "EITHER Section B OR Section C."
How is ISC 2027 maths structured instead?
The ISC 2027 Mathematics syllabus, dated February 2025, keeps Paper I (theory, 3 hours, 80 marks) and Paper II (project work, 20 marks), but lists one set of units for everyone:
Relations and Functions: 10 marks
Algebra: 10 marks
Calculus: 35 marks
Vector Algebra: 5 marks
Three-Dimensional Geometry: 6 marks
Linear Programming: 5 marks
Probability: 9 marks
Check: 10 + 10 + 35 + 5 + 6 + 5 + 9 = 80. Three things follow. Vectors, 3D geometry and linear programming are now compulsory for every candidate. Linear regression does not appear in the unit list. And area under curves now sits inside calculus, which on its own is almost half the paper. The syllabus also notes that Mathematics (860) may not be taken with Applied Mathematics. Check the document for your own examination year.
What do Sections A to D mean now?
The letters survive, but they now sort questions by length. The ISC 2027 Mathematics specimen paper has twenty questions, all compulsory:
Section A: 1-mark questions, 20 marks in all.
Section B: seven 2-mark questions, 14 marks.
Section C: seven 3-mark questions, 21 marks.
Section D: five 5-mark questions, 25 marks.
That adds to 20 + 14 + 21 + 25 = 80. Internal choice is offered in three questions each of 2, 3 and 5 marks. Many parts are tagged with the skill they test, such as Understand, Apply or Analyse, and Section A includes statement-based and graph-based items, not just routine calculations.
How are the 20 project marks given?
You complete two projects, each marked out of 10: overall format 1, content 4, findings 2, and a viva-voce of 3 based on the project. Your teacher and a Visiting Examiner both mark the written work, and only the Visiting Examiner conducts the viva. Suggested topics include showing a one-one function that is not onto using a graph, and finding the area bounded by two curves.
Worked example: linear programming by corner points
Maximise Z = 3x + 2y subject to x + y ≤ 4, x + 3y ≤ 6, x ≥ 0, y ≥ 0.
Draw the boundary lines. x + y = 4 meets the axes at (4, 0) and (0, 4). x + 3y = 6 meets them at (6, 0) and (0, 2).
Find where they cross. Subtract the first equation from the second: 2y = 2, so y = 1 and x = 3. The point is (3, 1).
List the corners of the feasible region: (0, 0), (4, 0), (3, 1) and (0, 2). Points such as (6, 0) and (0, 4) break one of the constraints, so they are not corners.
Evaluate Z. (0, 0): 0. (4, 0): 12. (3, 1): 9 + 2 = 11. (0, 2): 4.
Answer. The maximum is Z = 12 at x = 4, y = 0.
Common mistakes: including axis intercepts that lie outside the region; solving the pair of lines wrongly; and stating a maximum for an unbounded region without checking it exists. Our post on the corner point method in linear programming has more practice, and for probability, worth 9 marks, see probability distributions with mean and variance.
A practice routine for the term
Daily, 30 minutes: calculus problems, since the unit carries 35 of 80 marks. Mix differentiation, integration and differential equations.
Twice a week: one vectors or 3D question, now compulsory for everyone.
Weekly: one timed Section D question in 12 minutes.
Fortnightly: work on a project, so that findings and the viva are ready well before the Visiting Examiner arrives.
When you get stuck on the first step of a calculus or 3D problem, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
This week, download the 2027 specimen paper, find every question that would have been in the old Section B or C, and solve those first.
