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.
The Null Factor Law; common factor, monic and non-monic factorising, and difference of two squares.
Setting up and solving worded problems, and rejecting answers that don't make sense in context.
Solving quadratics by completing the square, including answers in exact surd form.
The quadratic formula, and using the discriminant to tell whether there are two, one or no solutions.
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.
Cheat sheet of every rule across both chapters, decision tree for picking the right technique, six mixed worked examples, four short walkthroughs, and a 10-question quiz with deep-dive links back to every sub-topic above. Mixed-practice worksheet covers surds and trig together.
Multi-step extension questions: conjugate rationalising, surd equations, two-observer elevation, perpendicular bearings legs, square-based pyramids, and surds meeting trig. Hints plus full worked solutions on the page, with a printable worksheet and answer key.
The basic parabola and its key features, plus the effect of dilations and reflections.
Sketching from turning-point form by shifting, stretching and reflecting the basic parabola.
Finding x-intercepts by factorising, then the axis of symmetry and the turning point.
Completing the square to find the turning point, then sketching with key features labelled.
Irrational x-intercepts from the quadratic formula, and the discriminant for the number of x-intercepts.
Maximum and minimum problems — projectile paths and areas — using the turning point and intercepts.
Solving a line and a parabola together, and the discriminant for whether they cross, touch or miss.
Add the choices for "this or that"; multiply them for "this and then that".
Factorials and the permutations rule for ordering, including arrangements with restrictions.
Choosing a group when order doesn't matter, team-selection problems, and selections of any size.
Using arrangements and selections to count outcomes and find probabilities.
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.
Cheat sheet of every rule, decision tree for picking the right technique, six mixed worked examples, 10-question quiz, and deep-dive links back to every sub-topic above. Mixed-practice worksheet covers all six sections.
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.
Play Rock–Paper–Scissors on the micro:bit, work out how its code makes a decision, then improve it. Answers save in the browser; the MakeCode editor is built in; download or print to hand in.
How micro:bits talk by radio, then design, build, test and share your own game. Carries on from Lesson 1 — answers are shared between the two.