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

M3 Calculus: Continuity and Differentiation

This unit carries about 8 marks in the paper. We split it into 32 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 26 of them. 6 were never asked. The top 5 topics make 38% of all the times this unit was asked. Last asked: Specimen 2027.

The syllabus says: Successive differentiation up to second order.

26asked by the board at least once

6in the syllabus, never asked

39times a topic of this unit was asked

5.6hours for one attempt at every topic

What the papers ask most

  • Prove a second-order relation: clear the denominator, differentiate again4 times, last 2025
  • Prove a second-order relation by direct differentiation3 times, last 2026
  • Limits used in continuity checks: factorise, rationalise, standard limits3 times, last 2024
  • Find k so a function is continuous at a point3 times, last 2024
  • Removable discontinuity: identify it and redefine f(a)2 times, last Specimen 2027
  • Read discontinuities and non-differentiable points from a graph2 times, last Specimen 2027
  • Inverse trig derivative by substitution, e.g. x = tan t2 times, last Specimen 2027
  • Derivative of one function with respect to another2 times, last 2023
  • Find constants making a piecewise function differentiableonce, last Specimen 2027
  • Simplify logs or surds first, then differentiateonce, last Specimen 2027

In the syllabus, never asked (6)

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

  • Definition of continuity at a point; algebra of continuous functionsStatement
  • Find two constants for continuity of a three-piece functionSum
  • Exponential and logarithmic functions: laws, domain and rangeStatement
  • Implicit relation: make y explicit, then prove the given dy/dxProof
  • Logarithmic differentiation of a product or quotient of many factorsSum
  • Second derivative of an explicit function, value at a pointSum

All the topics in Mathematics: Calculus: Continuity and Differentiation →

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