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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M2 Algebra: Matrices and Determinants

This unit carries about 10 marks in the paper. We split it into 33 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 23 of them. 10 were never asked. The top 5 topics make 43% of all the times this unit was asked. Last asked: Specimen 2027.

The syllabus says: Restricted to matrices of order up to 3 and determinants up to 3 x 3. Systems solved by inverse are those having a unique solution; conditions for consistency are to be covered.

23asked by the board at least once

10in the syllabus, never asked

49times a topic of this unit was asked

6.3hours for one attempt at every topic

What the papers ask most

  • Prove a determinant equals a factorised expression using properties6 times, last Specimen 2027
  • Evaluate or show zero without expanding, using properties5 times, last 2026
  • Symmetric or skew-symmetric matrix: find unknown entries4 times, last 2025
  • Word problem: put data in a matrix and multiply3 times, last Specimen 2027
  • Word problem or case study: form 3 equations, matrix method3 times, last Specimen 2027
  • Standard properties of determinants (|kA|, |A'|, |AB|, row operations)3 times, last 2026
  • Non-commutativity: AB vs BA, (A+B)(A-B), commuting matrices2 times, last Specimen 2027
  • Area of a triangle by determinant; find unknown vertex2 times, last Specimen 2027
  • Inverse of a 3x3 matrix by the adjoint method2 times, last Specimen 2027
  • Types and order of matrices; counting possible matrices2 times, last 2026

In the syllabus, never asked (10)

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

  • Equality of matrices: find unknown entriesSum
  • Addition, subtraction and scalar multiple; solve matrix equationsSum
  • Non-zero matrices whose product is the zero matrixSum
  • Proof that the inverse of a matrix is uniqueProof
  • Minors and cofactors of elements of a determinantSum
  • Collinearity of three points; line through two pointsSum
  • Adjoint and inverse of a 2x2 matrixSum
  • Verify A(adj A) = |A|I or (AB)^-1 = B^-1A^-1Proof
  • Inverse from a matrix equation like A^2-kA+I=OSum
  • Solve 2 linear equations in 2 unknowns by matrix methodSum

All the topics in Mathematics: Algebra: Matrices and Determinants →

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