Lesson library
One page to find any lesson, worksheet or solutions sheet from the term. Grouped by year level and Cambridge chapter, with the date each section was taught.
Rational vs irrational, simplifying with the largest perfect-square factor, combining like surds.
Product and quotient rules, squares of surds, the distributive law on brackets containing surds.
Multiply top and bottom by the surd in the denominator. Bonus binomial-numerator section.
Labelling opposite, adjacent and hypotenuse; SOHCAHTOA; solving for an unknown side length.
Inverse trig functions to find an angle from two sides. Short worded applications.
Angles of elevation and depression, choosing the right ratio, ramps and buildings.
Cardinal compass points, true bearings (clockwise from N), multi-leg journeys, final position.
Cube diagonals, masts with cables, square pyramids, rectangular boxes — the two-triangle method.
Fractional powers, evaluating roots, negative exponents, combining all index laws in one expression.
Shape of $y=a^x$, dilations, translations and reflections, asymptote, y-intercept and range.
Same-base method, quadratic-in-disguise via substitution, exponential inequalities, CAS for awkward bases.
Definition, converting between exponential and log form, the seven log laws (product, quotient, power, change-of-base).
Take a log of both sides for awkward bases, exact vs decimal answers, inequality-direction with bases less than 1.
Reflection of $y=a^x$ in $y=x$, translations on log graphs, finding the inverse of an exponential or a log function.
Derive Newton's formula from a tangent, iterate bisection on $x^3+3x+1=0$, learn the three classic failure modes.
Exponential antiderivatives with initial conditions, trig antiderivatives, and the stationary-point method.
The Fundamental Theorem of Calculus, the five properties of the definite integral, signed vs total area, and a VCAA-style application.
The "top minus bottom" rule, the 4-step recipe, intersections as limits, and splitting at curve cross-overs.
Differentiate a given function and read off the antiderivative — the "hence find" pattern with chain-rule and product-rule examples.
Average value as the height of the balancing rectangle, with calculus examples, the full-period shortcut for sin/cos, and a kinematics application.
"Which technique?" decision tree plus mixed worked examples spanning §11E/F/G, §11I, §11H and §11J.