How to solve competency-based questions in Class 10 Maths
A competency-based maths question often creates a strange reaction: the student knows the chapter, knows the formula, and still has no idea what to write. The page mentions a park, a shop, a table of values or a water tank. Suddenly familiar mathematics looks as if it belongs to somebody else.
That reaction is not proof that the student needs more formulas. Usually, the formula is already there. What is missing is the bridge between the situation in the question and the mathematics the student knows.
What CBSE is actually testing
The phrase “competency-based” is used so loosely online that it can sound like a special question type. It is not limited to case studies, long paragraphs or multiple-choice questions. Competency describes the thinking being tested: applying a known idea, analysing information, making a connection, judging a result, or building a solution.
In CBSE’s published 2025–26 Mathematics Standard question-paper design, 19 of 80 theory marks were assigned to applying and 18 to analysing, evaluating and creating. The remaining 43 were assigned to remembering and understanding. That table matters because it shows why memorising one more sheet of formulas cannot be the complete preparation.
The official sample paper separately divides the paper into Sections A to E, including MCQs, short and long answers, and case studies. The two structures are not the same thing. A one-mark MCQ can demand application. A five-mark question can begin with familiar routine work. Do not judge the thinking by the shape of the box around it.
Why a capable student freezes
Chapter exercises quietly provide a clue that disappears in a mixed paper: the chapter heading. If the page says “Arithmetic Progressions”, the student already knows which shelf of the brain to open. A board-pattern question may describe rows of seats increasing by the same number and never use the words arithmetic progression at all.
The calculation may be ordinary. The difficult act happened before the first calculation: noticing what the situation has in common with the chapter.
Students often say, “I knew it after I saw the solution.” That is not a small detail. It means the maths was available, but the route to it was not.
There is a second source of freezing. Context creates noise. Some numbers describe the situation but are not needed for the part being asked. Some words matter mathematically; others make the situation understandable. Students who try to use every number simply because it appears in the question can build a perfectly neat solution to the wrong problem.
The five moves that reveal the maths
Tap through the five moves.
1. Strip away the setting
Read once for the situation. Then read again for the structure. A circular garden may be an area question. A sloping ramp may be a right triangle. Two mobile plans may be a pair of linear equations. The setting explains why the quantities exist; it does not decide the chapter.
2. Name the exact unknown
Write: “I need to find ___.” This takes seconds and prevents a surprising number of wrong starts. “Find the cost” is different from “find which plan is cheaper after a particular number of uses”. “Find the height” is different from “find the remaining height”.
3. Find one relationship
Do not hunt for a formula yet. Ask what connects the given information to the unknown. Equal ratios suggest similarity. A constant difference suggests an arithmetic progression. A tangent and a radius suggest a right angle. Two conditions involving two unknowns suggest simultaneous equations.
4. Do the familiar mathematics
Only after the relationship is visible should a method be chosen. This order prevents formula shopping—the habit of trying whatever formula contains the same letters as the question.
5. Return the answer to the situation
A competency question is not finished when the algebra stops. Put the answer back into the real situation. Is the unit correct? Can a length be negative? Does a probability lie between zero and one? Did the question ask for one part, the total, the difference or the better option?
How to practise without wasting hundreds of questions
Solving more questions helps only when the missing skill is being practised. If a student reads a question, immediately watches the solution, and says “I get it”, the translation was supplied by somebody else again.
Use this three-round routine instead:
- Round one—identify only. Take ten mixed questions. Do not solve them. Write the likely chapter, the unknown and the relationship.
- Round two—write only the first move. Form the equation, mark the right triangle, write the ratio or state the theorem. Then check.
- Round three—solve fully under time. Now combine recognition, execution and interpretation.
This may feel slower than racing through a question bank. It is actually more direct. Round one trains the decision that chapter-wise practice gives away. Round two catches a wrong route before five minutes of algebra are built on top of it. Round three proves the whole chain works.
Keep a translation log, not a “silly mistakes” list
After each practice set, do not write “could not understand question”. That is too broad to fix. Record the exact hidden clue that was missed.
- “Equal increase in every row” should have pointed to an arithmetic progression.
- “Shortest distance from a point to a line” needed a perpendicular.
- “Touches the circle” should have made me look for a tangent fact.
- I found the whole quantity when the question asked for the remaining part.
- I used every number instead of deciding which ones were relevant.
That log becomes a personal dictionary from ordinary language to maths. It is far more useful before the next paper than rereading ten complete solutions.
Use the official free material first
CBSE maintains a Class X competency-based assessment bank aligned to the NCERT/CBSE curriculum. CBSE also hosts a Class X practice resource page with a Maths practice book and a large bank of questions. These are useful not because every future board question will repeat them—it will not—but because they let students practise the kind of transfer the Board says it values.
After that, use the official sample paper and marking scheme together. The paper shows the demand. The marking scheme shows whether the reasoning was complete. Checking only the final answer hides correct methods with arithmetic slips and lucky answers with missing reasoning.
A seven-day reset for a student who keeps going blank
- Days 1–2: identify chapter, unknown and relationship for mixed questions. Do not solve.
- Days 3–4: write the first mathematical move, then check it.
- Days 5–6: solve complete questions and build the translation log.
- Day 7: attempt one mixed set without chapter labels or help.
The goal after seven days is not a magical mark. It is observable: fewer blank starts, faster identification of the underlying chapter, and answers that are interpreted back in context. Those are real changes a parent or student can verify without pretending.
Young Math Brains does not reveal a worked solution and call that practice. The student has to choose the next step, test the choice, and repair any earlier idea that caused the route to break.
Practise making the first moveOfficial sources used for this guide
- CBSE Mathematics Standard question-paper design
- CBSE Class X sample papers and marking schemes
- CBSE competency-based assessment resources
Your turn
Take the last competency question that made you blank. Could you name the unknown and the relationship before choosing a formula? Whichever one was missing is the move to practise next.
Tell us in the comments on YouTube or Instagram, or email connect@youngmathbrains.com. We read every one.
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