Competency-based questions in Class 10 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. About half of the questions in Class 10 board papers are competency-focused (case-based, source-based, integrated, data interpretation, situational and application questions); the rest are select-response (MCQ) and constructed-response (short and long answer) questions. (CBSE Secondary 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 case-based question: a garden bed against a wall
A gardener makes a rectangular vegetable bed against a straight wall, so fencing is needed on three sides only. She has \(30\) m of fencing and wants the bed to have an area of \(112\) m\(^2\). Let each side at right angles to the wall be \(x\) m. (i) Write the length of the side parallel to the wall in terms of \(x\). (1) (ii) Show that \(x^2 - 15x + 56 = 0\). (1) (iii) Find the two possible sets of dimensions of the bed. (2)
Show the worked answer
(i) Two sides of \(x\) m use \(2x\) m, so the side parallel to the wall is \((30 - 2x)\) m 1 mark · (i)
(ii) Area: \(x(30 - 2x) = 112\), so \(30x - 2x^2 = 112\), so \(2x^2 - 30x + 112 = 0\); dividing by \(2\), \(x^2 - 15x + 56 = 0\) 1 mark · (ii)
(iii) \((x - 7)(x - 8) = 0\), so \(x = 7\) or \(x = 8\) 1 mark · (iii) solving
\(x = 7\): \(7\) m by \(16\) m; \(x = 8\): \(8\) m by \(14\) m (both use \(30\) m of fencing and have area \(112\) m\(^2\)) 1 mark · (iii) dimensions
Answer: \(7\) m by \(16\) m, or \(8\) m by \(14\) m
Where marks slip: Part (iii) asks for dimensions, not \(x\). Write both sides of the rectangle for each value, and check each against the story.
From the top of a building \(15\) m high, the angle of depression of a parked car is \(30^\circ\). How far is the car from the foot of the building?
Show the worked answer
The angle of elevation of the top from the car is also \(30^\circ\) (alternate angles), so \(\tan 30^\circ = \dfrac{15}{d}\) 1 mark · diagram and ratio
\[\begin{aligned}d &= \dfrac{15}{\tan 30^\circ} \\ &= 15\sqrt{3}\end{aligned}\] m 1 mark · answer
Answer: \(15\sqrt{3}\) m
Where marks slip: Leave the answer as \(15\sqrt{3}\) m: no calculator, and no decimal is asked for. Draw the right triangle first and mark the \(30^\circ\) at the car.
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 10 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 10 maths paper?
CBSE's Secondary School Curriculum 2026-27 says about half of the questions in Class 10 board papers are competency-focused, including case-based and application questions.
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.