Lessons for today

Logarithms (Y11) & Integration by Recognition (Y12)

Tue 02 June 2026  •  Cambridge Methods 1&2 §13E–13F  ·  Cambridge Methods 3&4 §11H

📚 What you're doing today

Three lessons across Year 11 and Year 12. Each one has worked examples (click Show solution), a video walkthrough, a quick auto-marked quiz, and a Cambridge working program at the bottom.

Bring your Cambridge textbook, your exercise book, and your calculator.

Year 11 Methods · Lessons for today

§13E · Start here

Logarithms

Definition  ·  converting between exponential and log form  ·  the seven log laws

  • What $\log_a(x)$ means and how to read it
  • Converting between $a^y=x$ and $\log_a(x)=y$
  • The product, quotient, power, and change-of-base laws
  • Two video walkthroughs  ·  5-question quiz  ·  Ex 13E working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions
§13F · Then this

Using Logarithms to Solve Exponentials

Take a log of both sides  ·  exact vs decimal answers  ·  inequality direction

  • Solving $a^x=b$ when the bases can't be matched
  • Exact answers using $\log_a$ and 2 d.p. decimals
  • Inequalities — when to flip the inequality sign
  • Finishing the $x$-intercept work for exponential graphs
  • Two video walkthroughs  ·  5-question quiz  ·  Ex 13F working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions

Year 12 Methods · Lesson for today

§11H

Integration by Recognition

Differentiate a given function and read off an antiderivative — the "hence find" pattern

  • The recognition idea: $\dfrac{d}{dx}[F(x)] = f(x) \Rightarrow \int f(x)\,dx = F(x)+c$
  • Chain-rule recognition (e.g. with logarithms)
  • Product-rule recognition with a definite integral
  • Three video walkthroughs  ·  5-question quiz  ·  Ex 11H working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions