Lessons for today

Trigonometry (Y10), Exp/Log (Y11) & Integration (Y12)

Mon 01 June 2026  •  Cambridge Ch 6, §6A–6B  ·  Cambridge Methods 1&2 §13C–13D  ·  Cambridge Methods 3&4 §11E/F/G & §11I

📚 What you're doing today

Six web lessons across three year groups. Each one has worked examples (click Show solution), a video walkthrough, a quick auto-marked quiz, and a Cambridge working program at the bottom.

You'll need your Cambridge textbook, your exercise book, and your calculator — Y10 in degree mode, Y11 either scientific or CAS, Y12 CAS in radian mode.

Year 10 Core · Lessons for today

Ex 6A · Start here

Trigonometric Ratios

SOHCAHTOA  ·  finding unknown sides  ·  right-angled triangles

  • Labelling sides: opposite, adjacent, hypotenuse
  • Solving for an unknown in the numerator (Example 1)
  • Solving for an unknown in the denominator (Example 2)
  • 2 video walkthroughs  ·  5-question quiz  ·  Cambridge 6A working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions
Ex 6B · Then this

Finding Unknown Angles

Inverse trig functions to find an angle given two sides

  • What the inverse trig functions do
  • Find an angle from two sides (Example 3)
  • A worded application — mine tunnel (Example 4)
  • 2 video walkthroughs  ·  5-question quiz  ·  Cambridge 6B working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions

Year 11 Methods · Lessons for today

§13C · Start here

Graphs of Exponential Functions

Shape of $y=a^x$  ·  dilations, translations, reflections  ·  asymptote, $y$-intercept, range

  • The basic growth/decay shapes and the common point $(0,1)$
  • Vertical shifts that move the asymptote (Example 1)
  • Combined dilation + translation (Example 2)
  • Reflection in the $x$-axis (Example 3)
  • 2 video walkthroughs  ·  5-question quiz  ·  Ex 13C working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions
§13D · Then this

Solving Exponential Equations & Inequalities

Same-base method  ·  quadratic in $a^x$  ·  inequalities  ·  CAS for awkward bases

  • Same-base method: rewrite both sides, equate indices (Examples 1–4)
  • Quadratic in disguise via $u=a^x$ (Examples 5–6)
  • CAS for $5^x=10$ (Example 7)
  • Exponential inequalities — direction depends on the base (Examples 8–10)
  • 2 video walkthroughs  ·  5-question quiz  ·  Ex 13D working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions

Year 12 Methods · Lessons for today

§11E/F/G · Start here

Area Under a Curve — the definite integral

Fundamental Theorem of Calculus  ·  properties of $\int$  ·  signed vs total area

  • The FTC: $\int_a^b f\,dx = G(b)-G(a)$
  • Properties (sum, swap, constant multiple, split)
  • Signed area vs total area; split at every $x$-intercept
  • VCAA-style application (find $a$ from an area)
  • 2 video walkthroughs  ·  5-question quiz  ·  11E/F/G working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions
§11I · Then this

Area Between Two Curves

"Top minus bottom"  ·  intersection points as limits  ·  cross-over handling

  • The "top minus bottom" rule and the 4-step recipe
  • Line vs parabola, two parabolas, curve vs line
  • Splitting when the upper curve swaps (cubic vs line)
  • Exponential vs line application
  • 2 video walkthroughs  ·  5-question quiz  ·  11I working program
Open online lesson
📄 Worksheet (2 pp A4) ✅ Solutions