Syllabus
What CBSE covers
Class 10 — 7 Units (80 marks)
- Number Systems: the Fundamental Theorem of Arithmetic and irrationality proofs (6 marks)
- Algebra: polynomials, pairs of linear equations, quadratic equations and arithmetic progressions (20 marks)
- Coordinate Geometry: distance and section formulae (6 marks)
- Geometry: similar triangles and circle tangents (15 marks)
- Trigonometry: trig ratios, identities and heights & distances (12 marks)
- Mensuration: areas of circle sectors and surface area/volume of combined solids (10 marks)
- Statistics & Probability: mean/median/mode of grouped data and classical probability (11 marks)
Class 12 — 6 Units (80 marks)
- Relations & Functions: types of relations, one-one/onto functions, inverse trig functions (8 marks)
- Algebra: matrices and determinants up to 3×3 (10 marks)
- Calculus: continuity, differentiability, applications of derivatives, integrals and differential equations — the largest unit (35 marks)
- Vectors & 3D Geometry: vector algebra and Cartesian/vector forms of lines (14 marks)
- Linear Programming: the graphical method and feasible regions (5 marks)
- Probability: conditional probability, Bayes' theorem and the total probability theorem (8 marks)
Exam Pattern
How CBSE is assessed
Section A
20 one-mark objective questions.
Section B
5 short-answer questions.
Section C
6 questions with some internal choice.
Section D
4 multi-step questions with internal choice.
Section E
3 multi-part, case-study based questions.
Internal Assessment
Periodic tests, a portfolio and a lab-practical component, on top of the 80-mark written paper.
Required Materials
What you'll need
NCERT Mathematics Textbook
The prescribed textbook for the relevant class (Class 10, or Part I & II for Class 12) — the primary source for board exam questions.
NCERT Exemplar Problems
Higher-order practice questions officially published alongside the textbook, closely mirroring case-study and long-answer question styles.
CBSE Mathematics Laboratory Manual
The official activities and lab-practical guide that feeds the internal assessment component.
Try It Yourself
Sample questions, solved step by step
Scroll into view to watch each solution build itself, one step at a time, exactly how our tutors walk students through it.
Sample question
5 years ago, a father's age was 7 times his son's age. 10 years from now, the father's age will be twice the son's age. Find their present ages.
Animated solution
Define variables
Let the father's present age be F and the son's present age be S
Translate the first condition
F − 5 = 7(S − 5) → F = 7S − 30
Translate the second condition
F + 10 = 2(S + 10) → F = 2S + 10
Solve the system
7S − 30 = 2S + 10 → 5S = 40 → S = 8, then F = 2(8) + 10 = 26
Answer: Father = 26 years, Son = 8 years
Sample question
Bag A has 3 red and 2 black balls. Bag B has 2 red and 3 black balls. A bag is chosen at random and a ball is drawn — it is red. Find the probability the ball came from Bag A.
Animated solution
Write the prior probabilities
P(Bag A) = P(Bag B) = 1/2
Write the conditional probabilities
P(red | A) = 3/5, P(red | B) = 2/5
Apply the law of total probability
P(red) = (1/2)(3/5) + (1/2)(2/5) = 3/10 + 2/10 = 1/2
Apply Bayes' theorem
P(A | red) = [P(A) × P(red|A)] / P(red) = (3/10) / (1/2) = 3/5
Answer: 3/5 = 0.6