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.

Pick a unit

M8 Vector Algebra

This unit carries about 5 marks in the paper. We split it into 24 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 20 of them. 4 were never asked. The top 5 topics make 45% of all the times this unit was asked. Last asked: Specimen 2027.

The syllabus says: Proofs of geometrical theorems by using vector algebra are excluded. Scalar triple product is not listed in this document.

20asked by the board at least once

4in the syllabus, never asked

38times a topic of this unit was asked

3.2hours for one attempt at every topic

What the papers ask most

  • Scalar and vector projection of one vector on another6 times, last Specimen 2027
  • Magnitudes from expanded dot products, e.g. |a + b|4 times, last 2026
  • Unit vector, or vector of given magnitude, along a direction3 times, last 2024
  • Compute a x b by the determinant and use it2 times, last Specimen 2027
  • Unit vector perpendicular to two vectors or to a plane2 times, last Specimen 2027
  • Area of a parallelogram from adjacent sides or diagonals2 times, last 2026
  • Find the unknown that makes two vectors perpendicular2 times, last 2025 improvement
  • Area of a triangle by the cross product2 times, last 2025
  • Structured case question: vectors, projection and area from three points2 times, last 2025 improvement
  • Angle or magnitude from |a x b| and a.b2 times, last 2024

In the syllabus, never asked (4)

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

  • Vectors and scalars, types of vectors, standard termsStatement
  • Direction cosines and direction ratios of a vectorSum
  • Dot product and the angle between two vectorsSum
  • Cross product: definition, standard results and propertiesStatement

All the topics in Mathematics: Vector Algebra →

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