The first chapter looks like Class 11 revision. It is actually the vocabulary the rest of the paper is written in.
Updated 3 September 2026 · Delhi Home Tutor
Relations and functions arrives feeling like something already covered, so students skim it. Then inverse trigonometry assumes they understand one-to-one and onto, calculus assumes they understand domain and range, and the marks start going somewhere the student cannot locate. Tightening this chapter early is cheap; repairing it in December is not.
| Class | 12 |
|---|---|
| Subject | Maths |
| Why it matters | Inverse trig and calculus both assume it |
| Where marks go | Proving injective and surjective, and domain errors |
| Board | CBSE, ISC |
| Enquiries | +91 92121 42427 |
What students think they know
Most Class 12 students can define a function. Far fewer can prove one is one-to-one without being prompted, and that proof is where the marks in this chapter actually sit. The gap between recognising a definition and being able to use it in an argument is the whole chapter.
The tell is easy to spot: ask the student to show that a given function is onto. A student who starts by taking an arbitrary element of the codomain has understood it. A student who starts by drawing a graph has not.
The three things to drill
Injective, surjective, bijective as procedures
Each has a standard opening move. For injective, assume two inputs give the same output and show the inputs must be equal. For surjective, take an arbitrary output and construct the input that produces it. Taught as procedures with a fixed first line, students stop freezing.
Domain and range before anything else
Half the errors in the rest of the paper are domain errors imported from here. Insisting the student states the domain before manipulating any expression is a habit that pays for two years.
Equivalence relations
Reflexive, symmetric, transitive — checked in that order, every time, with a counterexample when a property fails. Marks are given for the counterexample, and students routinely just assert the property fails.
A counterexample is worth marks and a claim is not. Writing "not transitive" earns little; writing "not transitive, since (1,2) and (2,3) are in R but (1,3) is not" earns the credit. This is one of the easiest habits to install and one of the most commonly missing.
How a tutor should handle it
Not as revision. Treat it as a new chapter with new demands, because the demand has changed even though the content looks familiar. Two sessions spent here in April save considerably more than two sessions spent on it in January.
- Prove, do not describe — every property gets an argument written out.
- Fixed opening lines for each proof type until they are automatic.
- Domain stated first, always, on every question.
- Counterexamples written in full, not asserted.
Questions parents ask
My child says this chapter is easy and wants to skip ahead.
Test it with a proof rather than a definition. Easy usually means the definitions are familiar, which is not the same as being able to argue with them.
Is this chapter heavily weighted in the board paper?
Moderately on its own, but it is assumed by later chapters that are heavily weighted. The real cost of skipping it appears elsewhere.
How long should it take?
Two to three focused sessions for a student who has the Class 11 background, more if function basics are shaky.
Does ISC treat it differently?
The content overlaps closely; ISC generally expects the reasoning written more fully. Practise to the board your child actually sits.
Home Tuition on the Gurugram Side — Dwarka Expressway
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Do you take students on the Gurugram side of Dwarka Expressway?
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