Competency-based questions in Class 12 Maths, explained
What CBSE means by competency-based, how to take a case study apart, and where to practise them for every chapter.
What they are
A competency-based question tests whether you can use a piece of maths, not only recall it: the same skill as a textbook question, set in a situation you have not seen. CBSE says Class 12 board papers will have more questions based on real-life situations that ask students to apply, analyse, evaluate and synthesise, with the core competencies taken from the prescribed syllabus. It gives no percentage for Class 12. (CBSE Senior School Curriculum 2026-27)
In the maths paper they appear as:
Case studies (Section E): a short passage, often with a table or figure, then parts of 1, 1 and 2 marks.
Real-life short and long answers: a word problem in Sections B to D.
Assertion–reason questions and data questions (a table, a graph, a frequency distribution) in Section A.
How to approach one
Read the parts first, then the passage, so you know which numbers matter.
Name the chapter. Once you know it is quadratic equations or Bayes' theorem, the story is a question you have practised.
Write down what is given and what is asked, with units. Draw a figure if there is any geometry.
Turn the words into maths: one equation, expression or event per sentence of the passage.
Answer the question asked. If it asks for dimensions, give dimensions, not \(x\); if it asks "how far", give a distance with units.
Check against the story: a negative length or a probability over 1 means a slip.
Use the internal choice wisely on the 2-mark part: read both options before you start one.
Two worked examples
Our own questions. Try each one first, then open the worked answer.
A packaging firm makes open-top boxes with a square base from \(108\) cm\(^2\) of sheet. The base has side \(x\) cm and the height is \(h\) cm. (i) Express \(h\) in terms of \(x\). (1) (ii) Show that the volume is \(V(x) = \dfrac{108x - x^3}{4}\). (1) (iii) Find the value of \(x\) that gives the greatest volume, and that volume. (2)
Show the worked answer
(i) Area of sheet: \(x^2 + 4xh = 108\), so \(h = \dfrac{108 - x^2}{4x}\) 1 mark · (i)
(ii) \[\begin{aligned}V &= x^2 h \\ &= x^2 \cdot \dfrac{108 - x^2}{4x}\end{aligned}\] \(= \dfrac{108x - x^3}{4}\) 1 mark · (ii)
(iii) \(V'(x) = \dfrac{108 - 3x^2}{4} = 0\), so \(x^2 = 36\) and \(x = 6\) (as \(x > 0\)) 1 mark · (iii) critical point
\(V''(x) = -\dfrac{3x}{2}\), and \(V''(6) = -9 < 0\), so a maximum: \(V(6) = \dfrac{648 - 216}{4} = 108\) cm\(^3\) (with \(h = 3\) cm) 1 mark · (iii) maximum justified
Where marks slip: The second-derivative test (or a sign change of \(V'\)) is the reasoning mark in part (iii). Without it, \(x = 6\) is not shown to give a maximum.
A factory has two machines. Machine \(A\) makes \(60\%\) of the bulbs and machine \(B\) makes \(40\%\). Of the bulbs from \(A\), \(2\%\) are defective; of those from \(B\), \(5\%\) are defective. A bulb picked at random is defective. Find the probability that machine \(B\) made it.
Show the worked answer
Let \(E_1\): made by \(A\), \(E_2\): made by \(B\), \(D\): defective. \(P(E_1) = \dfrac{3}{5}\), \(P(E_2) = \dfrac{2}{5}\), \(P(D \mid E_1) = \dfrac{1}{50}\), \(P(D \mid E_2) = \dfrac{1}{20}\) 1 mark · events and probabilities
Where marks slip: Define the events in words first. Working in fractions keeps the arithmetic short without a calculator.
Practise them chapter by chapter
The questions themselves live on the chapter pages. "Competency-based questions" opens the chapter's practice with the Competency-based filter already on; the free case studies need no sign-in.
For more, CBSE publishes its own sample papers with marking schemes: Class 12 sample papers 2026-27 (cbseacademic.nic.in).
Questions students ask
Are competency-based questions harder than other questions?
They use the same chapters and skills. The extra step is turning the situation into maths, which gets quicker with practice on case studies from every chapter.
How many competency-based questions are in the Class 12 maths paper?
CBSE's Senior School Curriculum 2026-27 says board papers will have more questions based on real-life situations, but gives no percentage for Class 12. Section E always has three case studies.
Where can I practise competency-based questions?
On every chapter page of this site (the Competency-based filter in Practice questions), in our free MCQ and case-study sets, and in CBSE's own sample papers.
Official facts on this page were last checked against CBSE's own documents on 5 October 2026. CBSE Math Revision is independent and not affiliated with CBSE or NCERT. If a newer CBSE notice or your school says something different, follow CBSE and the school. Worked examples are written by CBSE Math Revision and checked twice (by computer algebra and by hand); the mark splits are our illustration, not CBSE's scheme for any paper.