NCEA Level 3

MapWorksheetExtension

Maths89 lessons

Complex numbers · AS 91577

Complex arithmetic, conjugates and equating partsVideoPolar form by hand: modulus, argument and quadrantsVideoDe Moivre's theorem: powers and roots of complex numbersVideoComplex roots of polynomials: factor theorem and conjugatesVideoAlgebra with k: quadratics, discriminants and surd equationsVideoComplex loci, purely real conditions and proofsVideoComplex arithmetic: 7 exam questions solved step by stepVideoPolar form: 7 exam questions solved step by stepVideoDe Moivre's theorem: 7 exam questions solved step by stepVideoComplex polynomials: 7 exam questions solved step by stepVideoAlgebra with constants: 7 exam questions solved step by stepVideoComplex loci and proof: 7 exam questions solved step by stepVideo

Differentiation · AS 91578

The derivative toolkit: chain, product and quotient rulesVideoStationary points, concavity and points of inflectionVideoTangents and normals: from gradient to finished equationVideoParametric differentiation, and the second derivativeVideoRelated rates of change: spheres, cones and the chain ruleVideoOptimisation: building the model and finding the max or minVideoLimits, continuity and differentiability from a graphVideoDerivative toolkit: 7 exam questions solved step by stepVideoStationary points: 7 exam questions solved step by stepVideoTangents and normals: 7 exam questions solved step by stepVideoParametric curves: 7 exam questions solved step by stepVideoRelated rates of change: 7 exam questions solved step by stepVideoOptimisation: 7 exam questions solved step by stepVideoLimits and continuity: 7 exam questions solved step by stepVideo

Integration · AS 91579

The integration toolkit: surds, e, trig and the chain ruleVideoIntegrating fractions: when it is ln, and when it is notVideoThe constant of integration: find c, never assume itVideoDefinite integrals and area, including between two curvesVideoTrapezium and Simpson's rules: numerical areasVideoDifferential equations: growth, decay and Newton's coolingVideoIntegration toolkit: 7 exam questions solved step by stepVideoIntegrating fractions: 7 exam questions solved step by stepVideoConstant of integration: 7 exam questions solved step by stepVideoDefinite integrals: 7 exam questions solved step by stepVideoNumerical integration: 6 exam questions solved step by stepVideoDifferential equations: 6 exam questions solved step by stepVideo

Statistical reports · AS 91584

Margin of error: the three rules of thumbVideoConfidence intervals, claims, and why overlap failsVideoExperiments vs observational studies: what you can concludeVideoSurveys and bias: sampling frames, non-response and wordingVideoEvaluating a statistical report: the full answerVideoMargin of error: 7 exam questions solved step by stepVideoConfidence intervals: 7 exam questions solved step by stepVideoStudy design: 7 exam questions solved step by stepVideoSurveys and bias: 7 exam questions solved step by stepVideoEvaluating reports: 7 exam questions solved step by stepVideo

Probability · AS 91585

Tables, trees and Venn diagrams from written informationVideoConditional probability from tables, trees and Venn diagramsVideoIndependent or mutually exclusive? The two testsVideoRelative risk: times as likely, and when you need a ratioVideoTrue probability, model estimates and experimental estimatesVideoOrganising information: 7 exam questions solved step by stepVideoConditional probability: 7 exam questions solved step by stepVideoIndependent or exclusive: 7 exam questions solved step by stepVideoRelative risk: 7 exam questions solved step by stepVideoProbability estimates: 7 exam questions solved step by stepVideo

Probability distributions · AS 91586

Choosing a distribution, and naming it every timeVideoDiscrete random variables: mean and standard deviationVideoBinomial and Poisson: at least, at most, and the rateVideoThe normal distribution: forwards, backwards and conditionalVideoUniform and triangular distributions, and judging a modelVideoChoosing a distribution: 7 exam questions solved step by stepVideoDiscrete random variables: 7 exam questions solved step by stepVideoBinomial and Poisson: 7 exam questions solved step by stepVideoNormal distribution: 7 exam questions solved step by stepVideoUniform and triangular: 7 exam questions solved step by stepVideo

Trigonometry · AS 91575

Trig functions and radiansVideoTrig identities and proofsVideoCompound and double-angle formulaeVideoTrig equations and general solutionsVideoModelling periodic situationsVideo

Time series · AS 91580

Features of a time seriesVideoMoving averages and the trendVideoSeasonal effects and forecastingVideoReporting on a time seriesVideo

Bivariate data · AS 91581

Scatter plots and correlationVideoFitting a linear modelVideoPredicting and residualsVideoEvaluating a relationshipVideo

Formal inference · AS 91582

Sampling variability and bootstrappingVideoFormal confidence intervalsVideoComparing populationsVideoJustifying an inferenceVideo

Systems of equations · AS 91587

Solving three equationsVideoGaussian eliminationVideoUnique, infinite and no solutionsVideoModelling with three unknownsVideo

Science55 lessons

Biology · AS 91601

Biology investigation: temperature and Daphnia heart rate

Biology · AS 91602

A socio-scientific issue: aerial 1080 in Aotearoa

Biology · AS 91603

Orientation in space: tropisms, taxes, kineses and migrationBiological rhythms: clocks, zeitgebers and photoperiodismRelationships between species: competition, mutualism, exploitationRelationships within a species: territories, hierarchies, mating

Biology · AS 91604

Homeostasis: how animals keep their internal environment stable

Biology · AS 91605

Mutation, gene flow, natural selection and genetic driftSpeciation and reproductive isolating mechanismsPatterns of evolution: divergence, convergence and radiationThe evidence for evolution: fossils, anatomy, DNA and Gondwana

Biology · AS 91606

Trends in human biological evolutionTrends in human cultural evolutionHow hominins spread across the world

Biology · AS 91607

Human manipulation of genetic transfer

Chemistry · AS 91387

A quantitative chemistry investigation: titration analysis

Chemistry · AS 91388

Spectroscopic data: identifying organic compounds

Chemistry · AS 91389

Chemical processes in the world: from natural gas to urea

Chemistry · AS 91390

Electron configuration and periodic trendsShapes, polarity and intermolecular forcesMelting, boiling, solubility and spontaneityThermochemistry and Hess's law

Chemistry · AS 91391

Functional groups, naming and isomersSubstitution reactions: from haloalkanes to amidesOxidation, reduction and eliminationPolyesters, polyamides, proteins and fats

Chemistry · AS 91392

Solubility and KsWeak acids, bases, pH and buffersTitration curves and indicators

Chemistry · AS 91393

Oxidation-reduction: electrode potentials and cells

Earth and Space Science · AS 91410

Planning and running an independent ESS investigation

Earth and Space Science · AS 91411

Investigating an Earth and Space Science issue in Aotearoa

Earth and Space Science · AS 91412

Dating geological events

Earth and Space Science · AS 91413

Ocean composition, layers and circulationThe ocean carbon cycle and ocean acidificationOcean heat, tides, waves and El Niño

Earth and Space Science · AS 91414

Composition, layers and energy balance of the atmosphereAtmospheric circulation: cells, wind belts and the westerliesWater, carbon, volcanoes and climate trends

Earth and Space Science · AS 91415

Investigating an aspect of astronomy with real data

Physics · AS 91521

Testing a physics theory by experiment

Physics · AS 91522

Physics applied to a context: fibre-optic broadband

Physics · AS 91523

Interference, double slits and diffraction gratingsStanding waves, harmonics, resonance and beatsThe Doppler effect

Physics · AS 91524

Centre of mass and momentum in two dimensionsCircular motion and gravityRotational motionSimple harmonic motion

Physics · AS 91525

Modern physics: photons, energy levels and the nucleus

Physics · AS 91526

DC circuits, internal resistance and Kirchhoff's lawsCapacitorsInductors, Faraday's law and transformersAC circuits

Physics · AS 91527

A physics issue: how should New Zealand make its electricity?