At a glance
- Subject code
- 041
- Board paper
- 80 marks, 3 hours
- Internal assessment
- 20 marks: periodic tests 10, activities 10
- Calculus weighting
- 35 of 80 marks
- Grading
- Positional: A1 is the top 1/8 of passing candidates
Units and marks for the 2027 board paper
| Unit | Chapters | Marks |
|---|---|---|
| I Relations and Functions | Types of relations and functions; inverse trigonometric functions | 8 |
| II Algebra | Matrices; determinants (up to 3 x 3), adjoint, inverse, solving linear systems | 10 |
| III Calculus | Continuity and differentiability; applications of derivatives; integrals; applications of integrals; differential equations | 35 |
| IV Vectors and 3D Geometry | Vectors, dot and cross products; lines in space, skew lines, shortest distance | 14 |
| V Linear Programming | Graphical method, feasible regions, up to three non-trivial constraints | 5 |
| VI Probability | Conditional probability, multiplication theorem, independent events, total probability, Bayes' theorem | 8 |
| Total | 80 |
Source: CBSE Mathematics (041) curriculum for Classes XI-XII, 2026-27. Question mix: 55% remembering and understanding, 25% applying, 20% analysing and evaluating.
Where Class 12 marks are lost
- Integration: choosing the wrong method (substitution, partial fractions or by parts) and running out of time. The standard forms, such as the integral of 1/(x^2 + a^2), must be instant.
- Definite integrals: forgetting to change the limits after a substitution, or not using the property that the integral from 0 to a of f(x) equals that of f(a - x).
- Differential equations: not separating variables fully, or writing the integrating factor for dy/dx + Py = Q incorrectly.
- Applications of derivatives: finding a stationary point but not proving it is a maximum or minimum with the first or second derivative test.
- Three-dimensional geometry: the shortest distance between skew lines, where one sign error in the cross product spoils the answer.
- Bayes' theorem: setting up the events and the tree before calculating, which students often skip.
How one-to-one Class 12 Maths lessons work
Lessons are 60 minutes, one to one, in LiveTutor's online classroom with video and a shared whiteboard. Calculus is taught by working each problem fully on the board, with the tutor stopping at the step where your child hesitates; over a few weeks that builds a short list of personal weak points to drill. A tutor who teaches CBSE senior secondary maths uses NCERT and exemplar problems first, then the CBSE sample question paper and marking scheme, so that your child learns how many steps each mark band expects.
From the pre-board exams onwards, lessons are mostly timed practice. Many students know the methods but cannot finish the paper; the tutor sets section-by-section time targets and shows where to take the internal choices.
When to start
Ideally at the start of Class 12, before Continuity and Differentiability, since every later calculus chapter uses it. Students who struggled with Class 11 trigonometry or limits should fix those first, in the summer before Class 12 if possible. Starting after the pre-boards still helps, with lessons focused on calculus and vectors, which together make up 49 of the 80 marks.
Common questions
Which chapter carries the most marks?
Calculus as a unit carries 35 of the 80 theory marks. Within it, integrals, applications of derivatives and differential equations together make up most of the questions.
How is the CBSE Class 12 grade worked out?
CBSE ranks all passing candidates in a subject and awards grades by eighths: A1 to the top eighth, A2 to the next, down to D2. Marks are also shown, and a student needs 33% separately in the board paper and in internal assessment to pass.
Is random variable and probability distribution still in the syllabus?
Not in the 2026-27 syllabus. The probability unit covers conditional probability, the multiplication theorem, independent events, total probability and Bayes' theorem.
What are the 20 internal marks for?
Ten marks are from periodic tests (the best two of three, averaged) and ten from mathematics activities recorded during the year. Both are assessed by the school.
How much do Class 12 Maths lessons cost?
$15 a lesson, the same for every subject and level, on a weekly plan of 1 to 5 lessons billed monthly. The first lesson is a free trial, and there is a 7-day money-back guarantee on your first paid month before the first paid lesson.
Sources
Dates and figures on this page come from these official and published sources. Always confirm deadlines on the official page before acting on them.