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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M4 Calculus: Applications of Derivatives

This unit carries about 7 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 27 of them. 6 were never asked. The top 5 topics make 30% of all the times this unit was asked. Last asked: Specimen 2027.

27asked by the board at least once

6in the syllabus, never asked

53times a topic of this unit was asked

7.4hours for one attempt at every topic

What the papers ask most

  • Related rates with one formula: cube, sphere, circle, cylinder4 times, last 2026
  • Intervals of increase and decrease of a polynomial3 times, last Specimen 2027
  • Equation of tangent and normal at a given point3 times, last Specimen 2027
  • Find critical, stationary or turning points of a function3 times, last Specimen 2027
  • Case study on a function model: values, turning points, meaning3 times, last Specimen 2027
  • Points where tangent is parallel or perpendicular to a line3 times, last 2025
  • Prove a solid of given volume or surface is optimal3 times, last 2023
  • Related rates word problem: cone, funnel or tank filling/draining2 times, last Specimen 2027
  • Related rates on a curve or implicit relation2 times, last Specimen 2027
  • Interpret the sign or zero of a derivative in context2 times, 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.

  • Velocity and acceleration of a particle from s = f(t)Sum
  • Intervals of increase/decrease for trig, log or exponential functionsSum
  • Find the parameter for which a function is monotonicSum
  • Tangent and normal to a curve in parametric formSum
  • Angle between two curves at their point of intersectionSum
  • Word problem: numbers with given sum, maximise productSum

All the topics in Mathematics: Calculus: Applications of Derivatives →

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