Lessons for today

Trig Applications (Y10), Log Graphs (Y11) & Average Value (Y12)

Wed 03 June 2026  •  Cambridge Ch 6 §6C  ·  Cambridge Methods 1&2 §13G  ·  Cambridge Methods 3&4 §11J

📚 What you're doing today

Three lessons across all year groups. Each 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 — Y10 in degree mode, Y12 CAS in radian mode.

Year 10 Core · Lesson for today

Ex 6C

Applications in Two Dimensions

Angles of elevation and depression  ·  choosing the right ratio for the problem

  • Reading a worded problem and drawing the right-triangle diagram
  • Helicopter elevation — finding the horizontal distance
  • Two-elevation building height (top of building from two points)
  • Lighthouse depression with an extension on ramps
  • Two video walkthroughs  ·  5-question quiz  ·  Ex 6C working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions

Year 11 Methods · Lesson for today

§13G

Graphs of Logarithmic Functions

Reflection of the exponential in $y=x$  ·  translations  ·  finding inverses

  • Sketching $y=\log_a(x)$ as the reflection of $y=a^x$
  • Applying translations and reflections to log graphs
  • Finding the inverse of an exponential or a logarithmic function
  • Vertical asymptotes, domain, and range
  • Video walkthrough  ·  5-question quiz  ·  Ex 13G working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions

Year 12 Methods · Lesson for today

§11J

Average Value of a Function

Average value as the height of the balancing rectangle  ·  calculus + graphical shortcuts

  • The definition $\bar{f} = \dfrac{1}{b-a}\int_a^b f(x)\,dx$
  • Worked example with $\sqrt{x}$ on a closed interval
  • The "full-period mean = 0" shortcut for sine and cosine
  • A kinematics application (mean velocity from a velocity-time curve)
  • Three video walkthroughs  ·  5-question quiz  ·  Ex 11J working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions