Class 12 Maths common misconceptions

Common NCERT Class 12 Maths misconceptions across 13 chapters, from Relations and Functions to Probability: the tempting mistake, why it feels right, and a worked visual example.

How to teach Class 12 Maths · Class 12 Maths questions with answers

• Chapter 1: Relations and Functions

  Does every function have an inverse function? — Tempting mistake: “Squaring can be undone by square root for every real input.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 2: Inverse Trigonometric Functions

  Does inverse sine always recover the original angle? — Tempting mistake: “sin⁻¹(sin 150°) is 150°.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 3: Matrices

  Can you reverse a matrix product? — Tempting mistake: “If A and B are square, AB must equal BA.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 4: Determinants

  What happens to the determinant when every entry doubles? — Tempting mistake: “Doubling every entry doubles the determinant.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 5: Continuity and Differentiability

  Does a continuous curve always have a tangent slope? — Tempting mistake: “Every continuous function is differentiable.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 6: Application of Derivatives

  Does a zero derivative guarantee a maximum or minimum? — Tempting mistake: “Every point where f′(x) = 0 is a turning point.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 7: Integrals

  Does the power integration rule work for 1/x? — Tempting mistake: “Integrating x⁻¹ gives x⁰/0 by the usual power rule.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 8: Application of Integrals

  Can areas above and below the x-axis cancel? — Tempting mistake: “The area between y = x and the x-axis from −1 to 1 is zero.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 9: Differential Equations

  Does an initial value only check a solution? — Tempting mistake: “All curves y = Ceˣ solve y′ = y, so any one works when y(0) = 2.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 10: Vector Algebra

  Does a zero dot product mean a vector is zero? — Tempting mistake: “If two vectors have dot product 0, at least one has length 0.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 11: Three Dimensional Geometry

  Must nonparallel lines meet in space? — Tempting mistake: “Two nonparallel lines always intersect.”

  1 worked visual example · 8 “If your child says…” checks

• Chapter 12: Linear Programming

  Can you optimise using just one constraint at a time? — Tempting mistake: “A point is feasible if it satisfies at least one constraint.”

  1 worked visual example · 5 “If your child says…” checks

• Chapter 13: Probability

  Can you swap the event and the condition? — Tempting mistake: “The probability of a heart given red equals the probability of red given a heart.”

  1 worked visual example · 8 “If your child says…” checks