What the board asks

We went through the ISC board papers, question by question, and matched each question to a topic. Here is what was asked, how often, and what was never asked.

Mathematics: 309 topics in the 2027 syllabus, across 11 units. The board has asked 255 of them at least once. 54 were never asked in the papers we checked.

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M1 Relations and Functions

This unit carries about 10 marks in the paper. We split it into 31 topics: each is one thing an examiner can ask, and you can practise it on paper in 5 to 25 minutes. The board has asked 29 of them. 2 were never asked. The top 5 topics make 30% of all the times this unit was asked. Last asked: Specimen 2027.

The syllabus says: Composite and invertible functions: algebraic functions only.

29asked by the board at least once

2in the syllabus, never asked

69times a topic of this unit was asked

5.5hours for one attempt at every topic

What the papers ask most

  • Find the inverse of an invertible algebraic function and verify5 times, last 2026
  • Principal value of expressions and nested inverse trig5 times, last 2026
  • Apply the double-angle formulae to evaluate or solve4 times, last 2026
  • Equations solved with the complementary identities4 times, last 2025 improvement
  • Domain and range of a real-valued function3 times, last Specimen 2027
  • Test a listed relation for reflexive, symmetric, transitive3 times, last 2026
  • Convert one inverse trig function into another3 times, last 2026
  • tan^-1 sum and difference formula: evaluate or prove3 times, last 2026
  • Simplify or prove by trig substitution for x3 times, last 2026
  • Write relations on a set: identity, empty, universal, inverse3 times, last 2025 improvement

In the syllabus, never asked (2)

They can still come, because they are in the syllabus. Give each one clean attempt. Your plan has two practice questions for each.

  • Prove a relation is an equivalence relationProof
  • Show a function is not one-one or not ontoGive reason

All the topics in Mathematics: Relations and Functions →

The 10 topics Mathematics papers ask most

Counted on the board papers from 2018 to the 2027 specimen paper, which every unit has been checked against.

  1. 1.Formulate an LPP from a word problemM10 Linear Programming · asked 7 times since 2018
  2. 2.Scalar and vector projection of one vector on anotherM8 Vector Algebra · asked 6 times since 2018
  3. 3.Mean (expected value) of a random variableM11 Probability · asked 6 times since 2018
  4. 4.Find the inverse of an invertible algebraic function and verifyM1 Relations and Functions · asked 5 times since 2018
  5. 5.Principal value of expressions and nested inverse trigM1 Relations and Functions · asked 5 times since 2018
  6. 6.Evaluate or show zero without expanding, using propertiesM2 Algebra: Matrices and Determinants · asked 5 times since 2018
  7. 7.Prove a determinant equals a factorised expression using propertiesM2 Algebra: Matrices and Determinants · asked 5 times since 2018
  8. 8.Definite integral of a modulus functionM5 Calculus: Integrals · asked 5 times since 2018
  9. 9.Case study or linked parts on lines and planesM9 Three-Dimensional Geometry · asked 5 times since 2018
  10. 10.Equations solved with the complementary identitiesM1 Relations and Functions · asked 4 times since 2018

See when each unit comes in your plan