Ontario, Canada · Curriculum spine
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)
The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007 · 17 concepts
Strand A4
Exponential and Logarithmic Functions
Logarithms, their laws, and solving exponential and logarithmic equations.
- A1.1Coming soonLogarithm as inverse of exponentDefine a logarithm, convert between exponential and logarithmic form, and evaluate logarithms.
- A1.2Coming soonLaws of logarithmsUse the product, quotient and power laws to simplify and evaluate.
- A2.1Coming soonGraphs of log functionsSketch logarithmic functions and their transformations, and describe domain, range and asymptotes.
- A3.1Coming soonSolving exponential and log equationsSolve equations algebraically and graphically, including applications like half-life and pH.
Strand B5
Trigonometric Functions
Radians, identities, and trigonometric equations.
- B1.1Coming soonRadian measureConvert between degrees and radians and find exact values at special angles.
- B1.2Coming soonGraphs of trig functions in radiansSketch sine, cosine and tangent and their transformations, including reciprocal functions.
- B2.1Coming soonCompound angle formulasDerive and apply compound angle and double angle formulas.
- B2.2Coming soonProving identitiesProve trigonometric identities using known identities and algebra.
- B3.1Coming soonSolving trig equationsSolve linear and quadratic trigonometric equations over a domain, in radians.
Strand C5
Polynomial and Rational Functions
Polynomial behaviour, factoring, rational functions, equations and inequalities.
- C1.1Coming soonPolynomial functions and their graphsConnect degree, leading coefficient and zeros to the shape and end behaviour of a graph.
- C1.2Coming soonRemainder and factor theoremsDivide polynomials and use the remainder and factor theorems to factor.
- C2.1Coming soonRational functionsSketch rational functions and identify asymptotes, holes and intercepts.
- C3.1Coming soonPolynomial and rational equationsSolve polynomial and rational equations algebraically and interpret the solutions.
- C4.1Coming soonInequalitiesSolve polynomial and rational inequalities graphically and algebraically.
Strand D3
Characteristics of Functions
Rates of change, combining functions, and function behaviour.
- D1.1Coming soonAverage and instantaneous rate of changeEstimate rates of change from graphs and tables and connect them to slope.
- D2.1Coming soonCombining functionsAdd, subtract, multiply, divide and compose functions and describe the results.
- D3.1Coming soonChoosing a modelSelect and justify a function model for a real situation and solve problems with it.
Calculus and Vectors (MCV4U)
The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007 · 13 concepts
Strand A4
Rate of Change
Limits, the derivative and its rules.
- A1.1Coming soonLimits and continuityEvaluate limits numerically, graphically and algebraically, and describe continuity.
- A1.2Coming soonThe derivative from first principlesDefine the derivative as a limit of difference quotients and find it for simple functions.
- A2.1Coming soonDerivative rulesApply power, sum, product, quotient and chain rules.
- A3.1Coming soonDerivatives of exponential and trig functionsDifferentiate exponential, sine and cosine functions and their compositions.
Strand B3
Derivatives and Their Applications
Curve sketching and optimization.
- B1.1Coming soonCurve sketchingUse first and second derivatives to find extrema, intervals of increase and concavity, and sketch.
- B2.1Coming soonOptimizationModel a situation and use derivatives to find maximum or minimum values.
- B2.2Coming soonRelated rates and motionSolve related-rates problems and interpret velocity and acceleration as derivatives.
Strand C6
Geometry and Algebra of Vectors
Vectors in 2D and 3D, lines and planes.
- C1.1Coming soonVectors and operationsRepresent vectors geometrically and algebraically, and add, subtract and scale them.
- C1.2Coming soonDot and cross productsCompute dot and cross products and use them for angles, projections and areas.
- C2.1Coming soonApplications of vectorsSolve force and velocity problems with vectors.
- C3.1Coming soonLines in 2D and 3DWrite vector, parametric and scalar equations of lines.
- C3.2Coming soonPlanesWrite equations of planes and find intersections of lines and planes.
- C4.1Coming soonSystems of equationsSolve systems of linear equations and interpret them geometrically.
Mathematics of Data Management (MDM4U)
The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007 · 12 concepts
Strand A3
Counting and Probability
Permutations, combinations and probability.
- A1.1Coming soonCounting principlesUse the additive and multiplicative counting principles and Venn diagrams.
- A1.2Coming soonPermutations and combinationsCount arrangements and selections and use Pascal's triangle.
- A2.1Coming soonProbabilityCompute theoretical and experimental probabilities, including with counting techniques.
Strand B2
Probability Distributions
Discrete and continuous distributions.
- B1.1Coming soonDiscrete distributionsDescribe uniform, binomial and hypergeometric distributions and their expected values.
- B2.1Coming soonThe normal distributionUse the normal distribution and z-scores to solve problems.
Strand C2
Organization of Data for Analysis
Data types, sampling and bias.
- C1.1Coming soonKinds of data and variablesDistinguish data types and variables and choose appropriate representations.
- C2.1Coming soonSampling and biasDesign surveys, choose sampling methods and identify sources of bias.
Strand D3
Statistical Analysis
One- and two-variable statistics and validity.
- D1.1Coming soonOne-variable statisticsCompute and interpret measures of central tendency and spread.
- D2.1Coming soonTwo-variable statisticsAnalyse correlation, regression and causation.
- D3.1Coming soonEvaluating statistical claimsJudge the validity of statistical conclusions in the media.
Strand E2
Culminating Data Management Investigation
A full investigation from question to report.
- E1.1Coming soonDesigning the investigationPose a significant question and plan the data collection and analysis.
- E1.2Coming soonPresenting the investigationAnalyse the data, draw conclusions and present the findings.
English (ENG4U)
The Ontario Curriculum, Grades 11 and 12: English, 2007 · 13 concepts
Strand A2
Oral Communication (1)
Listening, speaking and reflecting.
- A1.1Coming soonListening to understandListen to complex texts and identify purpose, point of view and rhetorical techniques.
- A2.1Coming soonSpeaking to communicateDeliver presentations and lead discussions with a clear purpose and appropriate strategies.
Strand B4
Reading and Literature Studies (2)
Comprehension, analysis and understanding of form and style.
- B1.1Coming soonReading for meaningRead a range of challenging literary and informational texts and analyse ideas and themes.
- B2.1Coming soonForm and styleAnalyse how form, style and literary devices create meaning and effect.
- B2.2Coming soonCritical literacyEvaluate perspectives, ideology and bias in texts.
- B3.1Coming soonReading strategies and vocabularyUse strategies and word-solving skills with sophisticated texts.
Strand C4
Writing (3)
Developing ideas, form and style, conventions.
- C1.1Coming soonDeveloping and organizing contentGenerate, research and organize ideas for a variety of purposes and audiences.
- C2.1Coming soonForm and style in writingWrite in a range of forms with a controlled voice and effective structure.
- C2.2Coming soonThe literary essayWrite an analytical essay with a thesis, evidence and integrated quotations.
- C3.1Coming soonConventions and publishingEdit for grammar, usage and citation conventions and publish polished work.
Strand D3
Media Studies (4)
Understanding and creating media texts.
- D1.1Coming soonUnderstanding media textsAnalyse how media texts construct meaning and target audiences.
- D2.1Coming soonMedia forms and conventionsExplain how conventions and techniques of media forms create effect.
- D3.1Coming soonCreating media textsCreate media texts for a purpose and audience using appropriate conventions.
Physics (SPH4U)
The Ontario Curriculum, Grades 11 and 12: Science, 2008 (Revised), SPH4U pp. 193–206; unit order from the Bishop Ryan CSS course outline (2025) · 65 concepts
Chapter 16
Chapter 1 · Moving in two directions
Unit 1 · Dynamics. Arrows for motion, things that fly, and who is really moving.
- 1.1Free to tryPosition, velocity and acceleration are three different questions. Warm-up: everything Grade 11 needed, rebuilt.
- 1.2Lesson readyA vector is an arrow with a length and a direction. Add two arrows tip to tail.
- 1.3Lesson readyAny arrow is an across part plus an up part: components, with sin and cos.
- 1.4Lesson readyThe sideways motion and the falling are two separate stories that share a clock.
- 1.5Lesson readyRange, height and time of flight come from splitting the launch arrow.
- 1.6Lesson readyRelative velocity: walking on a train, a boat crossing a river.
Chapter 26
Chapter 2 · Forces make it happen
Unit 1 · Dynamics. Every push and pull, drawn and added.
- 2.1Coming soonNewton's three laws, one sittingThings keep doing what they are doing unless pushed; F = ma; pushes come in pairs. Warm-up.
- 2.2Coming soonDraw every push and pullThe free-body diagram: gravity, normal, applied, tension, friction.
- 2.3Coming soonFriction: grip vs slideStatic and kinetic friction, the coefficient, and why grip beats slide.
- 2.4Coming soonThe tilted worldOn an incline gravity splits into into-the-slope and down-the-slope.
- 2.5Coming soonTwo things tied togetherPulleys and connected masses: one system, one acceleration.
- 2.6Coming soonThe elevator and the truckApparent weight; inertial and non-inertial frames of reference.
Chapter 37
Chapter 3 · Going in circles
Unit 1 · Dynamics. Turning is accelerating.
- 3.1Coming soonTurning is acceleratingCentripetal acceleration points at the centre: a = v²/r.
- 3.2Coming soonRound and round: period and frequencyT and f, and a = 4π²r/T² derived in words.
- 3.3Coming soonFlat circlesA car on a curve, a banked turn, the spin cycle, a tether ball.
- 3.4Coming soonLoops and bucketsVertical circles: the roller-coaster loop and the bucket of water that does not spill.
- 3.5Coming soonThe force that isn't thereCentrifugal force is your frame moving, not a real push.
- 3.6Coming soonPhysics you can measureVideo analysis of a ride or a tether ball: measure T and r, find the force.
- 3.7Coming soonDynamics changed the worldTrebuchets, race cars, centrifuges, satellites, wind turbines: the good and the bad.
Chapter 47
Chapter 4 · Work and energy
Unit 2 · Energy and Momentum. Energy moves around but never disappears.
- 4.1Coming soonWork is a push that moves somethingW = Fd cos θ; carrying a bag on the flat is zero work. Warm-up.
- 4.2Coming soonEnergy of motionKinetic energy and the work–energy theorem.
- 4.3Coming soonEnergy stored in heightGravitational potential energy; conservation on a roller coaster.
- 4.4Coming soonWhere the energy hidesFriction turns motion into heat; efficiency.
- 4.5Coming soonSprings rememberHooke's law and elastic potential energy.
- 4.6Coming soonBack and forth foreverSimple harmonic motion: spring, pendulum, and the link to circular motion.
- 4.7Coming soonBungee, bouncing ballEnergy in two dimensions and in a simulated lab: test conservation.
Chapter 56
Chapter 5 · Momentum
Unit 2 · Energy and Momentum. Mass in motion, and why airbags work.
- 5.1Coming soonMass in motionMomentum p = mv and impulse FΔt = Δp; why airbags and crumple zones work.
- 5.2Coming soonWhat goes out must equal what came inConservation of momentum in one dimension: collisions, explosions, recoil.
- 5.3Coming soonBouncy or stickyElastic and inelastic collisions: where the energy went.
- 5.4Coming soonOff-centre hitsCollisions in two dimensions: the pool table and the air table.
- 5.5Coming soonThe rules nobody can breakNo perpetual motion; damping; how conservation predicted the neutrino.
- 5.6Coming soonDesign something saferHelmets, car seats, crash-test dummies, fireworks, demolition.
Chapter 64
Chapter 6 · Gravity
Unit 3 · Fields. A pull with no touching.
- 6.1Coming soonA push with no touchingWhat a field is; field lines; g near Earth and far away.
- 6.2Coming soonEverything pulls everythingNewton's law of universal gravitation and the inverse square.
- 6.3Coming soonFalling foreverOrbits and satellites: v = √(GM/r), geostationary.
- 6.4Coming soonEscape, black holes, dark matterGravitational potential energy far from Earth; escape speed; what orbits tell us.
Chapter 74
Chapter 7 · Electric fields
Unit 3 · Fields. Charges push and pull like gravity, only stronger.
- 7.1Coming soonCharge and CoulombCoulomb's law and how it mirrors gravity.
- 7.2Coming soonMapping the invisibleElectric field strength; field diagrams for point charges and parallel plates.
- 7.3Coming soonVoltage is height for chargesElectric potential energy and potential; the uniform field between plates.
- 7.4Coming soonWeighing an electronMillikan's oil drop and Rutherford's scattering, as simulated inquiries.
Chapter 85
Chapter 8 · Magnetic fields
Unit 3 · Fields. Moving charges make and feel magnetism.
- 8.1Coming soonWhere magnetism comes fromFields around magnets, straight wires and solenoids; the right-hand rules.
- 8.2Coming soonCharges that curveForce on a moving charge F = qvB; circles; the aurora and the mass spectrometer.
- 8.3Coming soonWires that jumpForce on a current-carrying wire F = BIL; motors.
- 8.4Coming soonThree fields side by sideCompare gravity, electric and magnetic fields; the fundamental forces.
- 8.5Coming soonFields at workMRI, particle accelerators, credit-card strips, RFID, satellites.
Chapter 99
Chapter 9 · The wave nature of light
Unit 4 · Light behaves like ripples on a pond.
- 9.1Coming soonWaves in one pictureWavelength, frequency, amplitude, phase, oscillate. Warm-up.
- 9.2Coming soonRipples that crossDiffraction and two-source interference in water; nodal lines.
- 9.3Coming soonLight is a wave: Young's slitsThe double-slit pattern; Δx = λL/d in words.
- 9.4Coming soonOne slit, many slitsSingle-slit diffraction, gratings, and why telescopes blur.
- 9.5Coming soonBending and splittingRefraction, dispersion, prisms, rainbows, mirages.
- 9.6Coming soonColours on a soap bubbleThin-film interference: bubbles, oil slicks, CDs.
- 9.7Coming soonSunglasses that pick a directionPolarization: filters, reflection, LCD screens, stressed plastic.
- 9.8Coming soonMaking lightElectromagnetic radiation from a shaking charge: radio to X-ray.
- 9.9Coming soonLight we live onFibre optics, holograms on money, GPS, lasers, polarized lenses.
Chapter 106
Chapter 10 · Quantum
Unit 5 · Light comes in packets and particles wave.
- 10.1Coming soonThe day light broke the rulesThe glow of hot objects and Planck's energy packets.
- 10.2Coming soonLight knocks electrons outThe photoelectric effect: E = hf, work function, KEmax.
- 10.3Coming soonPhotons bounce like ballsThe Compton effect and photon momentum.
- 10.4Coming soonParticles that waveDe Broglie wavelength and electron diffraction.
- 10.5Coming soonFingerprints of atomsEmission spectra and energy levels, as a simulated inquiry.
- 10.6Coming soonWhat everything is made ofThe standard model: quarks, hadrons, leptons, field particles.
Chapter 115
Chapter 11 · Relativity
Unit 5 · Fast things see time and space differently.
- 11.1Coming soonEinstein's two promisesThe same laws for everyone; the same light speed for everyone.
- 11.2Coming soonMoving clocks run slowTime dilation from the light clock; muons that reach the ground.
- 11.3Coming soonMoving rulers shrinkLength contraction; relativistic momentum and mass.
- 11.4Coming soonMass is frozen energyE = mc²; nuclear power; protons in the LHC.
- 11.5Coming soonTwo revolutions, one centuryHow new theories changed thought and gave us MRI, PET, lasers and quantum computers.
Chemistry (SCH4U)
The Ontario Curriculum, Grades 11 and 12: Science, 2008 · 14 concepts
Strand A1
Scientific Investigation Skills and Career Exploration
Investigation skills and careers.
- A1.1Coming soonInvestigation and analysisPlan and carry out investigations safely and analyse results quantitatively.
Strand B3
Organic Chemistry
Functional groups, reactions and polymers.
- B1.1Coming soonHydrocarbons and functional groupsName and draw alkanes, alkenes, alkynes, alcohols, aldehydes, ketones, acids, esters, amines, amides.
- B1.2Coming soonOrganic reactionsPredict products of addition, substitution, elimination, esterification and combustion.
- B1.3Coming soonPolymersDescribe addition and condensation polymers and their uses.
Strand C3
Structure and Properties of Matter
Atomic structure, bonding and intermolecular forces.
- C1.1Coming soonQuantum atomic modelDescribe orbitals and electron configurations and connect them to the periodic table.
- C1.2Coming soonBonding and molecular shapeUse Lewis structures and VSEPR to predict shapes and polarity.
- C1.3Coming soonIntermolecular forcesRelate physical properties to forces between molecules.
Strand D2
Energy Changes and Rates of Reaction
Thermochemistry and kinetics.
- D1.1Coming soonEnthalpy and calorimetryCalculate energy changes using calorimetry, Hess's law and enthalpies of formation.
- D1.2Coming soonRates of reactionAnalyse factors affecting rate, rate laws and reaction mechanisms.
Strand E3
Chemical Systems and Equilibrium
Equilibrium, acids and bases, solubility.
- E1.1Coming soonDynamic equilibrium and KExplain equilibrium, calculate K and apply Le Chatelier's principle.
- E1.2Coming soonAcids, bases and pHAnalyse strong and weak acids and bases, Ka, Kb, pH and buffers.
- E1.3Coming soonSolubility equilibriaUse Ksp to predict precipitation.
Strand F2
Electrochemistry
Redox, cells and applications.
- F1.1Coming soonOxidation and reductionAssign oxidation numbers and balance redox equations.
- F1.2Coming soonGalvanic and electrolytic cellsAnalyse cell potentials, electrolysis and their applications.
Biology (SBI4U)
The Ontario Curriculum, Grades 11 and 12: Science, 2008 · 14 concepts
Strand A1
Scientific Investigation Skills and Career Exploration
Investigation skills and careers.
- A1.1Coming soonInvestigation and analysisPlan investigations, use lab techniques and analyse biological data.
Strand B3
Biochemistry
Biological molecules, enzymes and membranes.
- B1.1Coming soonBiological macromoleculesDescribe the structure and function of carbohydrates, lipids, proteins and nucleic acids.
- B1.2Coming soonEnzymesExplain enzyme action and the factors that affect it.
- B1.3Coming soonMembranes and transportDescribe membrane structure and passive and active transport.
Strand C2
Metabolic Processes
Cellular respiration and photosynthesis.
- C1.1Coming soonCellular respirationDescribe glycolysis, the Krebs cycle and the electron transport chain, and ATP yield.
- C1.2Coming soonPhotosynthesisDescribe the light reactions and the Calvin cycle and factors that affect the rate.
Strand D3
Molecular Genetics
DNA, protein synthesis and biotechnology.
- D1.1Coming soonDNA structure and replicationExplain DNA structure and how it is replicated.
- D1.2Coming soonProtein synthesisDescribe transcription, translation and mutations.
- D1.3Coming soonBiotechnologyExplain recombinant DNA, PCR and gel electrophoresis and evaluate their uses.
Strand E3
Homeostasis
Nervous, endocrine and excretory systems.
- E1.1Coming soonFeedback and the nervous systemDescribe homeostasis, neurons and the nervous system.
- E1.2Coming soonEndocrine systemExplain hormonal regulation, including blood sugar and stress responses.
- E1.3Coming soonExcretion and water balanceDescribe kidney function and regulation of water and solutes.
Strand F2
Population Dynamics
Population growth and human impact.
- F1.1Coming soonPopulation growth modelsAnalyse exponential and logistic growth and carrying capacity.
- F1.2Coming soonHuman population and sustainabilityEvaluate the effects of human population growth on ecosystems.
Church and Culture (HRE4M)
Catholic boards · Ontario Catholic Secondary Curriculum Policy Document: Religious Education, Grades 9-12 (Institute for Catholic Education, 2016) · 11 concepts
Strand A2
Scripture (SC)
Scripture as a source for engaging culture.
- A1.1Coming soonReading Scripture criticallyInterpret biblical texts using literary and historical context.
- A1.2Coming soonScripture and social questionsApply Scripture to contemporary questions of justice and culture.
Strand B2
Profession of Faith (PF)
Faith and reason, Church and world.
- B1.1Coming soonFaith and reasonExplain the relationship between faith, reason and science in Catholic thought.
- B1.2Coming soonThe Church in the modern worldDescribe the Church's understanding of its mission in society.
Strand C2
Christian Moral Development (CM)
Catholic social teaching and moral reasoning.
- C1.1Coming soonPrinciples of Catholic social teachingExplain dignity, common good, subsidiarity and solidarity and apply them to issues.
- C1.2Coming soonMoral reasoning in cultureAnalyse a contemporary moral issue using Catholic moral principles.
Strand D2
Prayer and Sacramental Life (PS)
Prayer, liturgy and living faith in culture.
- D1.1Coming soonPrayer traditionsCompare prayer traditions and their role in adult faith.
- D1.2Coming soonSacraments and vocationExplain the sacraments of vocation and their meaning for adult life.
Strand E2
Family Life (FL)
Relationships, marriage and family in Catholic teaching.
- E1.1Coming soonLove, commitment and marriageDescribe Catholic teaching on relationships, marriage and family.
- E1.2Coming soonEthics of lifeAnalyse life issues in light of Catholic teaching on human dignity.
Strand F1
Research and Inquiry Skills (RI)
Investigating faith and culture.
- F1.1Coming soonCulminating inquiryCarry out a research inquiry on a question of Church and culture and present it.