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

M5 Calculus: Integrals

This unit carries about 10 marks in the paper. We split it into 53 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 36 of them. 17 were never asked. The top 5 topics make 27% of all the times this unit was asked. Last asked: Specimen 2027.

The syllabus says: Fundamental Theorem of Calculus without proof.

36asked by the board at least once

17in the syllabus, never asked

70times a topic of this unit was asked

12.1hours for one attempt at every topic

What the papers ask most

  • Definite integral of a modulus function5 times, last 2026
  • Property f(a-x) or f(a+b-x): add the integral to itself5 times, last 2026
  • Substitution: f'(x)[f(x)]^n and f'(x) g(f(x))3 times, last Specimen 2027
  • By parts with a single log or inverse-trig function3 times, last Specimen 2027
  • Evaluate a definite integral with the fundamental theorem3 times, last Specimen 2027
  • Odd and even functions on -a to a3 times, last Specimen 2027
  • Substitution (e^x, sin x, cos x) then partial fractions3 times, last 2026
  • Substitution that reduces to a quadratic standard form3 times, last 2026
  • Trig integrand rewritten by identities into standard forms3 times, last 2025 improvement
  • x times f(trig): property removes x, then evaluate3 times, last 2025 improvement

In the syllabus, never asked (17)

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

  • Integrals of sin^2 x, cos^2 x, sin^4 x, cos^4 xSum
  • Integrals of sin^3 x and cos^3 xSum
  • Cyclic by parts: e^(ax) sin bx or e^(ax) cos bxSum
  • Partial fractions: repeated linear factorSum
  • Improper rational function: divide first, then partial fractionsSum
  • Integrals of 1/(ax^2+bx+c) by completing the squareSum
  • Integrals of sqrt(a^2-x^2), sqrt(x^2+a^2), sqrt(x^2-a^2)Sum
  • Integrals of sqrt(ax^2 + bx + c)Sum
  • Integrals of (px + q) sqrt(ax^2 + bx + c)Sum
  • Integrals of 1/(a cos x + b sin x)Sum
  • Integrals of 1/(a cos x+b sin x+c)Sum
  • Ratio (a cos x+b sin x)/(c cos x+d sin x)Sum
  • Integrals of (1 +- x^2)/(1 + x^4)Sum
  • Integrals of 1/(1 + x^4) and x^2/(1 + x^4)Sum
  • Integrals of sqrt(tan x) and sqrt(cot x)Sum
  • Definite integral by substitution or by parts, with limitsSum
  • Standard result: integral 0 to pi/2 of log sin xSum

All the topics in Mathematics: Calculus: 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