Grade 12
159 concepts across 8 subjects. Codes follow the ministry's own expectation numbers; where a course is broken into bites (chapter.bite), each bite names the expectations it covers.
Advanced Functions (MHF4U)
Exponential and Logarithmic Functions
Logarithms, their laws, and solving exponential and logarithmic equations.
- A1.1Coming to StudioLogarithm as inverse of exponentDefine a logarithm, convert between exponential and logarithmic form, and evaluate logarithms.
- A1.2Coming to StudioLaws of logarithmsUse the product, quotient and power laws to simplify and evaluate.
- A2.1Coming to StudioGraphs of log functionsSketch logarithmic functions and their transformations, and describe domain, range and asymptotes.
- A3.1Coming to StudioSolving exponential and log equationsSolve equations algebraically and graphically, including applications like half-life and pH.
Trigonometric Functions
Radians, identities, and trigonometric equations.
- B1.1Coming to StudioRadian measureConvert between degrees and radians and find exact values at special angles.
- B1.2Coming to StudioGraphs of trig functions in radiansSketch sine, cosine and tangent and their transformations, including reciprocal functions.
- B2.1Coming to StudioCompound angle formulasDerive and apply compound angle and double angle formulas.
- B2.2Coming to StudioProving identitiesProve trigonometric identities using known identities and algebra.
- B3.1Coming to StudioSolving trig equationsSolve linear and quadratic trigonometric equations over a domain, in radians.
Polynomial and Rational Functions
Polynomial behaviour, factoring, rational functions, equations and inequalities.
- C1.1Coming to StudioPolynomial functions and their graphsConnect degree, leading coefficient and zeros to the shape and end behaviour of a graph.
- C1.2Coming to StudioRemainder and factor theoremsDivide polynomials and use the remainder and factor theorems to factor.
- C2.1Coming to StudioRational functionsSketch rational functions and identify asymptotes, holes and intercepts.
- C3.1Coming to StudioPolynomial and rational equationsSolve polynomial and rational equations algebraically and interpret the solutions.
- C4.1Coming to StudioInequalitiesSolve polynomial and rational inequalities graphically and algebraically.
Characteristics of Functions
Rates of change, combining functions, and function behaviour.
- D1.1Coming to StudioAverage and instantaneous rate of changeEstimate rates of change from graphs and tables and connect them to slope.
- D2.1Coming to StudioCombining functionsAdd, subtract, multiply, divide and compose functions and describe the results.
- D3.1Coming to StudioChoosing a modelSelect and justify a function model for a real situation and solve problems with it.
Calculus and Vectors (MCV4U)
Rate of Change
Limits, the derivative and its rules.
- A1.1Coming to StudioLimits and continuityEvaluate limits numerically, graphically and algebraically, and describe continuity.
- A1.2Coming to StudioThe derivative from first principlesDefine the derivative as a limit of difference quotients and find it for simple functions.
- A2.1Coming to StudioDerivative rulesApply power, sum, product, quotient and chain rules.
- A3.1Coming to StudioDerivatives of exponential and trig functionsDifferentiate exponential, sine and cosine functions and their compositions.
Derivatives and Their Applications
Curve sketching and optimization.
- B1.1Coming to StudioCurve sketchingUse first and second derivatives to find extrema, intervals of increase and concavity, and sketch.
- B2.1Coming to StudioOptimizationModel a situation and use derivatives to find maximum or minimum values.
- B2.2Coming to StudioRelated rates and motionSolve related-rates problems and interpret velocity and acceleration as derivatives.
Geometry and Algebra of Vectors
Vectors in 2D and 3D, lines and planes.
- C1.1Coming to StudioVectors and operationsRepresent vectors geometrically and algebraically, and add, subtract and scale them.
- C1.2Coming to StudioDot and cross productsCompute dot and cross products and use them for angles, projections and areas.
- C2.1Coming to StudioApplications of vectorsSolve force and velocity problems with vectors.
- C3.1Coming to StudioLines in 2D and 3DWrite vector, parametric and scalar equations of lines.
- C3.2Coming to StudioPlanesWrite equations of planes and find intersections of lines and planes.
- C4.1Coming to StudioSystems of equationsSolve systems of linear equations and interpret them geometrically.
Mathematics of Data Management (MDM4U)
Counting and Probability
Permutations, combinations and probability.
- A1.1Coming to StudioCounting principlesUse the additive and multiplicative counting principles and Venn diagrams.
- A1.2Coming to StudioPermutations and combinationsCount arrangements and selections and use Pascal's triangle.
- A2.1Coming to StudioProbabilityCompute theoretical and experimental probabilities, including with counting techniques.
Probability Distributions
Discrete and continuous distributions.
- B1.1Coming to StudioDiscrete distributionsDescribe uniform, binomial and hypergeometric distributions and their expected values.
- B2.1Coming to StudioThe normal distributionUse the normal distribution and z-scores to solve problems.
Organization of Data for Analysis
Data types, sampling and bias.
- C1.1Coming to StudioKinds of data and variablesDistinguish data types and variables and choose appropriate representations.
- C2.1Coming to StudioSampling and biasDesign surveys, choose sampling methods and identify sources of bias.
Statistical Analysis
One- and two-variable statistics and validity.
- D1.1Coming to StudioOne-variable statisticsCompute and interpret measures of central tendency and spread.
- D2.1Coming to StudioTwo-variable statisticsAnalyse correlation, regression and causation.
- D3.1Coming to StudioEvaluating statistical claimsJudge the validity of statistical conclusions in the media.
Culminating Data Management Investigation
A full investigation from question to report.
- E1.1Coming to StudioDesigning the investigationPose a significant question and plan the data collection and analysis.
- E1.2Coming to StudioPresenting the investigationAnalyse the data, draw conclusions and present the findings.
English (ENG4U)
Oral Communication (1)
Listening, speaking and reflecting.
- A1.1Coming to StudioListening to understandListen to complex texts and identify purpose, point of view and rhetorical techniques.
- A2.1Coming to StudioSpeaking to communicateDeliver presentations and lead discussions with a clear purpose and appropriate strategies.
Reading and Literature Studies (2)
Comprehension, analysis and understanding of form and style.
- B1.1Coming to StudioReading for meaningRead a range of challenging literary and informational texts and analyse ideas and themes.
- B2.1Coming to StudioForm and styleAnalyse how form, style and literary devices create meaning and effect.
- B2.2Coming to StudioCritical literacyEvaluate perspectives, ideology and bias in texts.
- B3.1Coming to StudioReading strategies and vocabularyUse strategies and word-solving skills with sophisticated texts.
Writing (3)
Developing ideas, form and style, conventions.
- C1.1Coming to StudioDeveloping and organizing contentGenerate, research and organize ideas for a variety of purposes and audiences.
- C2.1Coming to StudioForm and style in writingWrite in a range of forms with a controlled voice and effective structure.
- C2.2Coming to StudioThe literary essayWrite an analytical essay with a thesis, evidence and integrated quotations.
- C3.1Coming to StudioConventions and publishingEdit for grammar, usage and citation conventions and publish polished work.
Media Studies (4)
Understanding and creating media texts.
- D1.1Coming to StudioUnderstanding media textsAnalyse how media texts construct meaning and target audiences.
- D2.1Coming to StudioMedia forms and conventionsExplain how conventions and techniques of media forms create effect.
- D3.1Coming to StudioCreating media textsCreate media texts for a purpose and audience using appropriate conventions.
Physics (SPH4U)
Chapter 1 · Moving in two directions
Unit 1 · Dynamics. Arrows for motion, things that fly, and who is really moving.
- 1.1Coming to StudioWhere is it, how fast, which wayPosition, velocity and acceleration are three different questions. Warm-up: everything Grade 11 needed, rebuilt.
- 1.2Coming to StudioArrows that addA vector is an arrow with a length and a direction. Add two arrows tip to tail.
- 1.3Coming to StudioSplitting an arrowAny arrow is an across part plus an up part: components, with sin and cos.
- 1.4Coming to StudioDrop it or throw it, same landing timeThe sideways motion and the falling are two separate stories that share a clock.
- 1.5Coming to StudioLaunch at an angleRange, height and time of flight come from splitting the launch arrow.
- 1.6Coming to StudioWho is moving?Relative velocity: walking on a train, a boat crossing a river.
Chapter 2 · Forces make it happen
Unit 1 · Dynamics. Every push and pull, drawn and added.
- 2.1Coming to StudioNewton's three laws, one sittingThings keep doing what they are doing unless pushed; F = ma; pushes come in pairs. Warm-up.
- 2.2Coming to StudioDraw every push and pullThe free-body diagram: gravity, normal, applied, tension, friction.
- 2.3Coming to StudioFriction: grip vs slideStatic and kinetic friction, the coefficient, and why grip beats slide.
- 2.4Coming to StudioThe tilted worldOn an incline gravity splits into into-the-slope and down-the-slope.
- 2.5Coming to StudioTwo things tied togetherPulleys and connected masses: one system, one acceleration.
- 2.6Coming to StudioThe elevator and the truckApparent weight; inertial and non-inertial frames of reference.
Chapter 3 · Going in circles
Unit 1 · Dynamics. Turning is accelerating.
- 3.1Coming to StudioTurning is acceleratingCentripetal acceleration points at the centre: a = v²/r.
- 3.2Coming to StudioRound and round: period and frequencyT and f, and a = 4π²r/T² derived in words.
- 3.3Coming to StudioFlat circlesA car on a curve, a banked turn, the spin cycle, a tether ball.
- 3.4Coming to StudioLoops and bucketsVertical circles: the roller-coaster loop and the bucket of water that does not spill.
- 3.5Coming to StudioThe force that isn't thereCentrifugal force is your frame moving, not a real push.
- 3.6Coming to StudioPhysics you can measureVideo analysis of a ride or a tether ball: measure T and r, find the force.
- 3.7Coming to StudioDynamics changed the worldTrebuchets, race cars, centrifuges, satellites, wind turbines: the good and the bad.
Chapter 4 · Work and energy
Unit 2 · Energy and Momentum. Energy moves around but never disappears.
- 4.1Coming to StudioWork is a push that moves somethingW = Fd cos θ; carrying a bag on the flat is zero work. Warm-up.
- 4.2Coming to StudioEnergy of motionKinetic energy and the work–energy theorem.
- 4.3Coming to StudioEnergy stored in heightGravitational potential energy; conservation on a roller coaster.
- 4.4Coming to StudioWhere the energy hidesFriction turns motion into heat; efficiency.
- 4.5Coming to StudioSprings rememberHooke's law and elastic potential energy.
- 4.6Coming to StudioBack and forth foreverSimple harmonic motion: spring, pendulum, and the link to circular motion.
- 4.7Coming to StudioBungee, bouncing ballEnergy in two dimensions and in a simulated lab: test conservation.
Chapter 5 · Momentum
Unit 2 · Energy and Momentum. Mass in motion, and why airbags work.
- 5.1Coming to StudioMass in motionMomentum p = mv and impulse FΔt = Δp; why airbags and crumple zones work.
- 5.2Coming to StudioWhat goes out must equal what came inConservation of momentum in one dimension: collisions, explosions, recoil.
- 5.3Coming to StudioBouncy or stickyElastic and inelastic collisions: where the energy went.
- 5.4Coming to StudioOff-centre hitsCollisions in two dimensions: the pool table and the air table.
- 5.5Coming to StudioThe rules nobody can breakNo perpetual motion; damping; how conservation predicted the neutrino.
- 5.6Coming to StudioDesign something saferHelmets, car seats, crash-test dummies, fireworks, demolition.
Chapter 6 · Gravity
Unit 3 · Fields. A pull with no touching.
- 6.1Coming to StudioA push with no touchingWhat a field is; field lines; g near Earth and far away.
- 6.2Coming to StudioEverything pulls everythingNewton's law of universal gravitation and the inverse square.
- 6.3Coming to StudioFalling foreverOrbits and satellites: v = √(GM/r), geostationary.
- 6.4Coming to StudioEscape, black holes, dark matterGravitational potential energy far from Earth; escape speed; what orbits tell us.
Chapter 7 · Electric fields
Unit 3 · Fields. Charges push and pull like gravity, only stronger.
- 7.1Coming to StudioCharge and CoulombCoulomb's law and how it mirrors gravity.
- 7.2Coming to StudioMapping the invisibleElectric field strength; field diagrams for point charges and parallel plates.
- 7.3Coming to StudioVoltage is height for chargesElectric potential energy and potential; the uniform field between plates.
- 7.4Coming to StudioWeighing an electronMillikan's oil drop and Rutherford's scattering, as simulated inquiries.
Chapter 8 · Magnetic fields
Unit 3 · Fields. Moving charges make and feel magnetism.
- 8.1Coming to StudioWhere magnetism comes fromFields around magnets, straight wires and solenoids; the right-hand rules.
- 8.2Coming to StudioCharges that curveForce on a moving charge F = qvB; circles; the aurora and the mass spectrometer.
- 8.3Coming to StudioWires that jumpForce on a current-carrying wire F = BIL; motors.
- 8.4Coming to StudioThree fields side by sideCompare gravity, electric and magnetic fields; the fundamental forces.
- 8.5Coming to StudioFields at workMRI, particle accelerators, credit-card strips, RFID, satellites.
Chapter 9 · The wave nature of light
Unit 4 · Light behaves like ripples on a pond.
- 9.1Coming to StudioWaves in one pictureWavelength, frequency, amplitude, phase, oscillate. Warm-up.
- 9.2Coming to StudioRipples that crossDiffraction and two-source interference in water; nodal lines.
- 9.3Coming to StudioLight is a wave: Young's slitsThe double-slit pattern; Δx = λL/d in words.
- 9.4Coming to StudioOne slit, many slitsSingle-slit diffraction, gratings, and why telescopes blur.
- 9.5Coming to StudioBending and splittingRefraction, dispersion, prisms, rainbows, mirages.
- 9.6Coming to StudioColours on a soap bubbleThin-film interference: bubbles, oil slicks, CDs.
- 9.7Coming to StudioSunglasses that pick a directionPolarization: filters, reflection, LCD screens, stressed plastic.
- 9.8Coming to StudioMaking lightElectromagnetic radiation from a shaking charge: radio to X-ray.
- 9.9Coming to StudioLight we live onFibre optics, holograms on money, GPS, lasers, polarized lenses.
Chapter 10 · Quantum
Unit 5 · Light comes in packets and particles wave.
- 10.1Coming to StudioThe day light broke the rulesThe glow of hot objects and Planck's energy packets.
- 10.2Coming to StudioLight knocks electrons outThe photoelectric effect: E = hf, work function, KEmax.
- 10.3Coming to StudioPhotons bounce like ballsThe Compton effect and photon momentum.
- 10.4Coming to StudioParticles that waveDe Broglie wavelength and electron diffraction.
- 10.5Coming to StudioFingerprints of atomsEmission spectra and energy levels, as a simulated inquiry.
- 10.6Coming to StudioWhat everything is made ofThe standard model: quarks, hadrons, leptons, field particles.
Chapter 11 · Relativity
Unit 5 · Fast things see time and space differently.
- 11.1Coming to StudioEinstein's two promisesThe same laws for everyone; the same light speed for everyone.
- 11.2Coming to StudioMoving clocks run slowTime dilation from the light clock; muons that reach the ground.
- 11.3Coming to StudioMoving rulers shrinkLength contraction; relativistic momentum and mass.
- 11.4Coming to StudioMass is frozen energyE = mc²; nuclear power; protons in the LHC.
- 11.5Coming to StudioTwo revolutions, one centuryHow new theories changed thought and gave us MRI, PET, lasers and quantum computers.
Chemistry (SCH4U)
Scientific Investigation Skills and Career Exploration
Investigation skills and careers.
- A1.1Coming to StudioInvestigation and analysisPlan and carry out investigations safely and analyse results quantitatively.
Organic Chemistry
Functional groups, reactions and polymers.
- B1.1Coming to StudioHydrocarbons and functional groupsName and draw alkanes, alkenes, alkynes, alcohols, aldehydes, ketones, acids, esters, amines, amides.
- B1.2Coming to StudioOrganic reactionsPredict products of addition, substitution, elimination, esterification and combustion.
- B1.3Coming to StudioPolymersDescribe addition and condensation polymers and their uses.
Structure and Properties of Matter
Atomic structure, bonding and intermolecular forces.
- C1.1Coming to StudioQuantum atomic modelDescribe orbitals and electron configurations and connect them to the periodic table.
- C1.2Coming to StudioBonding and molecular shapeUse Lewis structures and VSEPR to predict shapes and polarity.
- C1.3Coming to StudioIntermolecular forcesRelate physical properties to forces between molecules.
Energy Changes and Rates of Reaction
Thermochemistry and kinetics.
- D1.1Coming to StudioEnthalpy and calorimetryCalculate energy changes using calorimetry, Hess's law and enthalpies of formation.
- D1.2Coming to StudioRates of reactionAnalyse factors affecting rate, rate laws and reaction mechanisms.
Chemical Systems and Equilibrium
Equilibrium, acids and bases, solubility.
- E1.1Coming to StudioDynamic equilibrium and KExplain equilibrium, calculate K and apply Le Chatelier's principle.
- E1.2Coming to StudioAcids, bases and pHAnalyse strong and weak acids and bases, Ka, Kb, pH and buffers.
- E1.3Coming to StudioSolubility equilibriaUse Ksp to predict precipitation.
Electrochemistry
Redox, cells and applications.
- F1.1Coming to StudioOxidation and reductionAssign oxidation numbers and balance redox equations.
- F1.2Coming to StudioGalvanic and electrolytic cellsAnalyse cell potentials, electrolysis and their applications.
Biology (SBI4U)
Scientific Investigation Skills and Career Exploration
Investigation skills and careers.
- A1.1Coming to StudioInvestigation and analysisPlan investigations, use lab techniques and analyse biological data.
Biochemistry
Biological molecules, enzymes and membranes.
- B1.1Coming to StudioBiological macromoleculesDescribe the structure and function of carbohydrates, lipids, proteins and nucleic acids.
- B1.2Coming to StudioEnzymesExplain enzyme action and the factors that affect it.
- B1.3Coming to StudioMembranes and transportDescribe membrane structure and passive and active transport.
Metabolic Processes
Cellular respiration and photosynthesis.
- C1.1Coming to StudioCellular respirationDescribe glycolysis, the Krebs cycle and the electron transport chain, and ATP yield.
- C1.2Coming to StudioPhotosynthesisDescribe the light reactions and the Calvin cycle and factors that affect the rate.
Molecular Genetics
DNA, protein synthesis and biotechnology.
- D1.1Coming to StudioDNA structure and replicationExplain DNA structure and how it is replicated.
- D1.2Coming to StudioProtein synthesisDescribe transcription, translation and mutations.
- D1.3Coming to StudioBiotechnologyExplain recombinant DNA, PCR and gel electrophoresis and evaluate their uses.
Homeostasis
Nervous, endocrine and excretory systems.
- E1.1Coming to StudioFeedback and the nervous systemDescribe homeostasis, neurons and the nervous system.
- E1.2Coming to StudioEndocrine systemExplain hormonal regulation, including blood sugar and stress responses.
- E1.3Coming to StudioExcretion and water balanceDescribe kidney function and regulation of water and solutes.
Population Dynamics
Population growth and human impact.
- F1.1Coming to StudioPopulation growth modelsAnalyse exponential and logistic growth and carrying capacity.
- F1.2Coming to StudioHuman population and sustainabilityEvaluate the effects of human population growth on ecosystems.
Church and Culture (HRE4M)
Scripture (SC)
Scripture as a source for engaging culture.
- A1.1Coming to StudioReading Scripture criticallyInterpret biblical texts using literary and historical context.
- A1.2Coming to StudioScripture and social questionsApply Scripture to contemporary questions of justice and culture.
Profession of Faith (PF)
Faith and reason, Church and world.
- B1.1Coming to StudioFaith and reasonExplain the relationship between faith, reason and science in Catholic thought.
- B1.2Coming to StudioThe Church in the modern worldDescribe the Church's understanding of its mission in society.
Christian Moral Development (CM)
Catholic social teaching and moral reasoning.
- C1.1Coming to StudioPrinciples of Catholic social teachingExplain dignity, common good, subsidiarity and solidarity and apply them to issues.
- C1.2Coming to StudioMoral reasoning in cultureAnalyse a contemporary moral issue using Catholic moral principles.
Prayer and Sacramental Life (PS)
Prayer, liturgy and living faith in culture.
- D1.1Coming to StudioPrayer traditionsCompare prayer traditions and their role in adult faith.
- D1.2Coming to StudioSacraments and vocationExplain the sacraments of vocation and their meaning for adult life.
Family Life (FL)
Relationships, marriage and family in Catholic teaching.
- E1.1Coming to StudioLove, commitment and marriageDescribe Catholic teaching on relationships, marriage and family.
- E1.2Coming to StudioEthics of lifeAnalyse life issues in light of Catholic teaching on human dignity.
Research and Inquiry Skills (RI)
Investigating faith and culture.
- F1.1Coming to StudioCulminating inquiryCarry out a research inquiry on a question of Church and culture and present it.