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

M6 Calculus: Application of Integrals

This unit carries about 4 marks in the paper. We split it into 14 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 11 of them. 3 were never asked. The top 5 topics make 71% of all the times this unit was asked. Last asked: Specimen 2027.

11asked by the board at least once

3in the syllabus, never asked

21times a topic of this unit was asked

3.8hours for one attempt at every topic

What the papers ask most

  • Area between a parabola and a line5 times, last Specimen 2027
  • Sketch simple curves and find their intersection points5 times, last 2025
  • Area of a parabola cut off by line x=k2 times, last 2024
  • Area between two parabolas2 times, last 2024
  • Choose the integral that gives a shaded area (MCQ)once, last Specimen 2027
  • Case study: find the curve first, then the areaonce, last Specimen 2027
  • Area of a circle, ellipse or part by integrationonce, last 2026
  • Area under a curve between the x-axis and two ordinatesonce, last 2025
  • Area between a curve and the y-axis, integrating in yonce, last 2025 improvement
  • Word problem: area of a field bounded by three linesonce, last 2025

In the syllabus, never asked (3)

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

  • Area under an exponential or logarithmic curveSum
  • Area when the curve crosses the x-axis: split and addSum
  • Area between circle or ellipse and line or parabolaSum

All the topics in Mathematics: Calculus: Application of Integrals →

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