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Functions — Study Plan

ICSE · Class 12 · Mathematics

A step-by-step study plan for Functions, ICSE Class 12 Mathematics: what to learn first, what to practise and when to revise.

101 questions30 flashcards14 formulas & key relations5 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 ideas. Focus on: 1. Basic idea of a function, 2. Standard real functions and their graphs, 3. Domain and range of real functions.

2
Day 3

Practise

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

3
Day 4

Revise & Test

Revise key points without looking at your notes. Take a practice quiz and mark weak areas for another pass.

4
Day 7

Spaced Revision

Come back to Functions after a week. Use flashcards for quick recall and try past exam questions on 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 Basic idea of a function, Standard real functions and their graphs, Domain and range of real functions, Graphical tests. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How should I revise Functions for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 101 practice questions on Functions. Revise 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.

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