Pure Mathematics 2 and 3 — A Level Mathematics 9709

Pure Mathematics 2 and 3 — A Level Mathematics 9709: 9 chapters and 635 lesson cards — AI teacher explanations, worked examples, diagrams, common mistakes and exam-style questions, aligned to the Cambridge A Level Mathematics 9709 syllabus.

Topics

  1. 2.1 / 3.1 Algebra — Introduction · Key ideas — The modulus function (P2, P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Polynomial division (P2, P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — The remainder and factor theorems (P2, P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Partial fractions (P3 only) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Binomial expansion for any rational n (P3 only) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples — Example 1: modulus equation and inequality · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 2: unknown coefficients · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 3: dividing by a quadratic · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 4: partial fractions (P3) · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 5: binomial series (P3) · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  2. 2.2 / 3.2 Logarithmic and Exponential Functions — Introduction · Key ideas — Logarithms and indices · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — e and the natural logarithm · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Solving equations with the unknown in a power · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Inequalities · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Reducing a law to a straight line · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  3. 2.3 / 3.3 Trigonometry — Introduction · Key ideas — Reciprocal functions · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Pythagorean identities · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Compound-angle formulae · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Double-angle formulae · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — The R form · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples — Example 1: a quadratic in tan · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 2: using a double angle · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 3: a compound angle · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 4: the R form · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  4. 2.4 / 3.4 Differentiation — Introduction · Key ideas — Standard derivatives (P2, P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Product rule (P2, P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Quotient rule (P2, P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Parametric differentiation (P2, P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Implicit differentiation (P2, P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples — Example 1: product with a composite · 🔍 Worked example — Easy · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 2: quotient · ⚠️ Common errors · Worked examples — Example 3: parametric tangent · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 4: implicit gradient · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 5: inverse tangent (P3) · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  5. 2.5 / 3.5 Integration — Introduction · Key ideas — Standard integrals (P2, P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Using trigonometric identities (P2, P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — The trapezium rule (P2) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Integrals of the form kf′(x)/f(x) (P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Partial fractions (P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Integration by parts (P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Substitution (P3) · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples — Example 1: double angle and sec² · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 2: trapezium rule (P2) · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 3: partial fractions (P3) · 🔍 Worked example — Easy · 🔍 Worked example — Standard · ⚠️ Common errors · Worked examples — Example 4: by parts (P3) · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 5: a given substitution (P3) · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  6. 2.6 / 3.6 Numerical Solution of Equations — Introduction · Key ideas — Locating a root by a change of sign · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Sequences that converge · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Where an iterative formula comes from · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Using the iteration to a given accuracy · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — When iteration fails · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  7. 3.7 Vectors — Introduction · Key ideas — Notation and basic operations · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Magnitude and unit vectors · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — The scalar product · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Vector equation of a line · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Two lines: parallel, intersecting or skew · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Foot of the perpendicular · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples — Example 1: line through two points · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 2: intersecting lines and the angle between them · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 3: skew lines · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 4: foot of the perpendicular · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  8. 3.8 Differential Equations — Introduction · Key ideas — Formulating a differential equation · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Separating the variables · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Particular solutions · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Interpreting the solution · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples — Example 1: a basic separable equation · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 2: Newton's law of cooling · 🔍 Worked example — Easy · 🔍 Worked example — Standard · ⚠️ Common errors · Worked examples — Example 3: using partial fractions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  9. 3.9 Complex Numbers — Introduction · Key ideas — The language of complex numbers · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Arithmetic in Cartesian form · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Conjugate pairs of roots · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — The Argand diagram · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Polar and exponential forms · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Square roots · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Loci · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples — Example 1: modulus and argument · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 2: a cubic with a given complex root · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 3: polar form · 🔍 Worked example — Easy · 🔍 Worked example — Standard · ⚠️ Common errors · Worked examples — Example 4: a locus and a greatest value · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice