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Functions

ICSE · Class 12 · Mathematics

Step-by-step guide to study Functions in ICSE Class 12 Mathematics. Topics to cover, practice strategy, and time allocation.

101 questions30 flashcards5 concepts

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A comprehensive infographic comparing different types of functions: one-one (injective), onto (surjective), many-one, into, and bijective, using set diagrams and clear definitions.
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Study Plan

1
Day 1–2

Learn the Theory

Read the textbook chapter carefully. Note down definitions, formulas, and key concepts.

2
Day 3

Practice Problems

Solve textbook exercises and additional practice questions. There are 101 questions available for this chapter.

3
Day 4

Revise & Test

Revise key formulas and concepts without looking at notes. Take a practice quiz to test your understanding. Mark weak areas for re-revision.

4
Day 7

Spaced Revision

Revisit Functions after a week. Use flashcards for quick recall. Solve previous year questions from this chapter.

What to Focus On

  • A function gives exactly one image to every element of the domain.
  • Domain is the input set A.
  • Co-domain is the target set B.

  • f(A) denotes the range.
  • Every domain element has exactly one image.
  • If n(A) = p and n(B) = q, then number of functions from A to B is q^p.

  • Real-valued means outputs are real numbers.
  • Real function means both domain and co-domain are subsets of R.
  • Square root needs non-negative expression inside the root.

Common Mistakes to Avoid

A relation is a function even if one input has no image or has two images.

Domain, co-domain, and range mean the same thing.

If a function is one-one, then it must also be onto, and if it is onto, then it must also be one-one in every case.

Memory Tips

Function means every element of the domain has exactly one image

Domain, co-domain, and range

Range is always a subset of the co-domain

Total number of functions from A to B

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Frequently Asked Questions

What are the important topics in Functions for ICSE Class 12 Mathematics?
Key topics in Functions include Functions Concept Hierarchy, Functions — Complete Chapter Overview, Functions - Concept Hierarchy and Classification. These are the concepts ICSE Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Functions — ICSE Class 12 Mathematics?
Understand the core concepts first, then work through the 101 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Functions

All 13 chapters — ICSE Class 12 Mathematics Study Plan

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