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Grade 12 · 48 knowledge points · 258 sub-skills · Browse every skill by grade and topic.

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SkillsMap

A. Patterns & Algebra

  1. 1Exponential Functions and Equations
    5 sub-skills
    1. 1aWhat makes a function exponential
    2. 1bGraphs of y = b^x: asymptote, domain and range
    3. 1cTransforming exponential graphs
    4. 1dSolving exponential equations with a common base
    5. 1eModelling growth and decay
  2. 2Geometric Sequences and Series
    5 sub-skills
    1. 2aRecognising a geometric sequence
    2. 2bThe general term t_n = t₁·r^(n−1)
    3. 2cSum of a finite geometric series
    4. 2dInfinite geometric series and convergence
    5. 2eApplications of geometric series
  3. 3Graphical Representations of Polynomial, Logarithmic, Exponential, and Sinusoidal Functions
    6 sub-skills
    1. 3aThe common language of graphs
    2. 3bPolynomial graphs
    3. 3cExponential graphs
    4. 3dLogarithmic graphs
    5. 3eSinusoidal graphs
    6. 3fChoosing the right family — and knowing when to stop
  4. 4Logarithms: Operations, Functions, and Equations
    6 sub-skills
    1. 4aA logarithm is an exponent
    2. 4bEvaluating logs and changing base
    3. 4cThe graph of y = log_b(x) and its transformations
    4. 4dLaws of logarithms
    5. 4eSolving logarithmic equations
    6. 4fUsing logs to solve exponential equations
  5. 5Polynomial Functions and Equations
    6 sub-skills
    1. 5aDegree, leading coefficient and end behaviour
    2. 5bPolynomial division and the remainder theorem
    3. 5cThe factor theorem and finding one root
    4. 5dFactoring a polynomial completely
    5. 5eSketching from factored form: zeros and multiplicity
    6. 5fSolving polynomial equations and inequalities
  6. 6Rational Functions
    5 sub-skills
    1. 6aThe reciprocal graph y = 1/f(x)
    2. 6bVertical asymptotes versus holes
    3. 6cHorizontal and oblique asymptotes
    4. 6dSketching a rational function
    5. 6eWriting the equation of a rational function
  7. 7Transformations of Graphs and Equations of Parent Functions and Relations
    6 sub-skills
    1. 7aParent functions and their graphs
    2. 7bTranslations: y = f(x − h) + k
    3. 7cStretches and reflections: y = a·f(bx)
    4. 7dCombined transformations and the mapping rule
    5. 7eInverse functions and relations
    6. 7fWriting the equation of a transformed graph

B. Geometry & Measurement

  1. 12D and 3D Shapes: Including Area, Surface Area, Volume, and Nets
    6 sub-skills
    1. 1aArea of composite shapes
    2. 1bSurface area and coverage rates
    3. 1cVolume of prisms and cylinders
    4. 1dVolume of cones, pyramids and spheres
    5. 1eNets and sheet-metal layout
    6. 1fEstimating materials, waste and cost
  2. 23D Objects and Their Views (Isometric Drawing, Orthographic Projection)
    5 sub-skills
    1. 2aFront, top and side views
    2. 2bIsometric drawing
    3. 2cBuilding the object from its views
    4. 2dHidden lines, centre lines and sections
    5. 2eReading a real shop drawing
  3. 3Circle Geometry
    6 sub-skills
    1. 3aCentral angle and inscribed angle
    2. 3bThe angle in a semicircle
    3. 3cChord properties
    4. 3dCyclic quadrilaterals
    5. 3eTangent-chord angle and segment lengths
    6. 3fCircle proofs, flawed arguments and counterexamples
  4. 4Circles as Tools in Constructions
    4 sub-skills
    1. 4aA circle is a set of equidistant points
    2. 4bEquidistance and centres of a triangle
    3. 4cLocating points with intersecting circles
    4. 4dCircumscribed and inscribed circles
  5. 5Constructing Tangents
    4 sub-skills
    1. 5aA tangent is perpendicular to the radius
    2. 5bConstructing the tangent at a point on the circle
    3. 5cConstructing tangents from an external point
    4. 5dEqual tangent lengths and common tangents
  6. 6Geometric Constructions
    5 sub-skills
    1. 6aWhat counts as a construction
    2. 6bThe basic constructions
    3. 6cProving that a construction works
    4. 6dConstructing polygons and dividing segments
    5. 6eFinding the flaw in a construction or argument
  7. 7Geometric Explorations
    6 sub-skills
    1. 7aFrom conjecture to proof
    2. 7bTransformations and symmetry
    3. 7cTessellations
    4. 7dThe golden ratio
    5. 7eFractals and self-similarity
    6. 7fPerspective and geometry on a sphere
  8. 8Measuring
    5 sub-skills
    1. 8aReading tapes, rules and calipers
    2. 8bAdding and subtracting fractional inches
    3. 8cConverting units on the job
    4. 8dTolerance and cumulative error
    5. 8eLinear material and cut lists
  9. 9Non-Euclidean Geometries
    5 sub-skills
    1. 9aAxioms and the parallel postulate
    2. 9bSpherical geometry
    3. 9cHyperbolic geometry
    4. 9dTesting a Euclidean statement in another geometry
    5. 9eWhere non-Euclidean geometry is the right model
  10. 10Parallel and Perpendicular Lines
    5 sub-skills
    1. 10aAngle pairs formed by a transversal
    2. 10bProving two lines are parallel
    3. 10cConstructing parallel and perpendicular lines
    4. 10dProving the triangle angle theorems
    5. 10eWriting a two-column proof
  11. 11Similar Triangles
    5 sub-skills
    1. 11aSpotting similar triangles
    2. 11bSolving for a missing side
    3. 11cIndirect measurement on site
    4. 11dSlope, grade and roof pitch
    5. 11eWorking from a scale drawing
  12. 12Transformations of 2D Shapes
    5 sub-skills
    1. 12aTranslations, rotations and reflections
    2. 12bComposing transformations
    3. 12cSymmetry of a figure
    4. 12dDilations and similarity
    5. 12eProving congruence and similarity by transformation
  13. 13Trigonometry: Functions, Equations, and Identities
    6 sub-skills
    1. 13aRadians and the unit circle
    2. 13bGraphing y = a·sin(b(x − c)) + d
    3. 13cGraphs of tangent and the reciprocal functions
    4. 13dModelling periodic situations
    5. 13eProving trigonometric identities
    6. 13fSolving trigonometric equations

C. Data & Probability

  1. 1Association Between Two Variables
    6 sub-skills
    1. 1aReading a scatterplot
    2. 1bThe correlation coefficient r
    3. 1cThe least-squares regression line
    4. 1dResiduals and r²
    5. 1eAssociation between two categorical variables
    6. 1fWhat association does not prove
  2. 2Combinatorics
    5 sub-skills
    1. 2aThe fundamental counting principle
    2. 2bPermutations
    3. 2cCombinations
    4. 2dPermutation or combination?
    5. 2ePathways and Pascal's triangle
  3. 3Common Graphical Representations of Variation
    5 sub-skills
    1. 3aTypes of variables
    2. 3bDotplots, stemplots, and histograms
    3. 3cDescribing a distribution
    4. 3dFive-number summary and boxplots
    5. 3eWhen a graph misleads
  4. 4Communication of Statistical Findings
    5 sub-skills
    1. 4aAnswering the question you actually asked
    2. 4bReporting uncertainty honestly
    3. 4cChoosing a display for your audience
    4. 4dCritiquing a statistical claim
    5. 4eStating your own limitations
  5. 5Intuition and Appreciation of Inferential Concepts, Such as Confidence Intervals and Hypothesis Tests
    6 sub-skills
    1. 5aSampling distributions
    2. 5bMargin of error
    3. 5cBuilding a confidence interval
    4. 5dWhat 95% confident actually means
    5. 5eThe logic of a hypothesis test
    6. 5fWhat a p-value is not
  6. 6Mathematics in the Workplace
    5 sub-skills
    1. 6aWork rates and productivity
    2. 6bWages, overtime and deductions
    3. 6cMixes, ratios and dilutions
    4. 6dCosting a job and writing a quote
    5. 6eUsing spec tables and charts
  7. 7Observational and Experimental Studies
    5 sub-skills
    1. 7aObservational study or experiment?
    2. 7bConfounding and lurking variables
    3. 7cDesigning an experiment
    4. 7dBlinding, placebo, and ethics
    5. 7eWhat you are allowed to conclude
  8. 8Odds, Probability, and Expected Value
    5 sub-skills
    1. 8aProbability: theoretical and experimental
    2. 8bOdds versus probability
    3. 8cMutually exclusive or independent?
    4. 8dConditional and dependent events
    5. 8eExpected value and fair decisions
  9. 9Probability Models for Variation
    6 sub-skills
    1. 9aRandomness and simulation
    2. 9bProbability rules
    3. 9cConditional probability
    4. 9dRandom variables and expected value
    5. 9eThe binomial model
    6. 9fThe normal model
  10. 10Regression Analysis
    5 sub-skills
    1. 10aScatterplots and correlation
    2. 10bThe line of best fit
    3. 10cInterpolation and extrapolation
    4. 10dQuadratic, exponential and sinusoidal regression
    5. 10eIs the model any good?
  11. 11Role of Statistical Thinking in Research and the Scientific Method
    5 sub-skills
    1. 11aVariation and statistical questions
    2. 11bPopulation, sample, parameter, statistic
    3. 11cSampling methods
    4. 11dBias: when a sample lies
    5. 11eThe statistical investigation cycle
  12. 12Use of Software and Technology to Enhance Statistical Ideas
    5 sub-skills
    1. 12aGetting data into a usable shape
    2. 12bSummaries and plots with technology
    3. 12cReading regression output
    4. 12dSimulating with technology
    5. 12eThe software always answers — should you believe it?
  13. 13Use of Summary Statistics to Describe Variation
    5 sub-skills
    1. 13aMean, median, and resistance
    2. 13bRange, IQR, and outliers
    3. 13cStandard deviation
    4. 13dz-scores and percentiles
    5. 13eChoosing — and misusing — summary statistics

D. Calculus

  1. 1Differentiation
    7 sub-skills
    1. 1aThe derivative as an instantaneous rate of change
    2. 1bPower, constant multiple and sum rules
    3. 1cProduct and quotient rules
    4. 1dChain rule and implicit differentiation
    5. 1eDerivatives of trigonometric, exponential and logarithmic functions
    6. 1fUsing f′ and f″ to describe a curve
    7. 1gOptimization and related rates
  2. 2Functions and Graphs
    5 sub-skills
    1. 2aDomain, range and why calculus asks first
    2. 2bComposing and decomposing functions
    3. 2cPiecewise and absolute value functions
    4. 2dInverses, even and odd symmetry
    5. 2eDescribing asymptotic behaviour in words
  3. 3Integration
    6 sub-skills
    1. 3aThe area problem and Riemann sums
    2. 3bAntiderivatives and the constant of integration
    3. 3cStandard indefinite integrals
    4. 3dIntegration by substitution
    5. 3eDefinite integrals and the Fundamental Theorem
    6. 3fArea between curves and net change
  4. 4Limits
    6 sub-skills
    1. 4aWhy we need limits at all
    2. 4bReading limits from graphs and tables
    3. 4cEvaluating limits algebraically
    4. 4dLimits at infinity and horizontal asymptotes
    5. 4eInfinite limits and vertical asymptotes
    6. 4fContinuity and types of discontinuity

E. Computer Science

  1. 1Access Variables in Memory
    5 sub-skills
    1. 1aA variable is a name for a location
    2. 1bValue vs reference
    3. 1cWhat a function can change about your data
    4. 1dAliasing, shallow copy, deep copy
    5. 1eStack, heap and lifetime
  2. 2Classical Algorithms, Including Sorting and Searching
    5 sub-skills
    1. 2aWhy binary search is correct
    2. 2bBubble, selection and insertion sort
    3. 2cMerge sort and divide and conquer
    4. 2dSort keys, comparators and stability
    5. 2eChoosing a sort for the situation
  3. 3Encapsulation of Data
    5 sub-skills
    1. 3aClasses and objects
    2. 3bState and methods
    3. 3cHiding data behind an interface
    4. 3dProtecting the object's invariants
    5. 3eDesigning with objects
  4. 4Persistent Memory
    5 sub-skills
    1. 4aRAM forgets, disk remembers
    2. 4bReading and writing text files
    3. 4cStructured formats: CSV and JSON
    4. 4dWhen files go wrong
    5. 4eFrom files to records and databases
  5. 5Recursive Problem Solving
    6 sub-skills
    1. 5aSpotting a self-similar problem
    2. 5bThe base case
    3. 5cThe recursive call must shrink the problem
    4. 5dTracing the call stack
    5. 5eRecursion or a loop?
    6. 5fRecursion on nested structures
  6. 6Use of Big-O Notation to Help Predict Run-time Performance
    6 sub-skills
    1. 6aWhy O(n²) breaks on big inputs
    2. 6bCounting operations in code
    3. 6cWriting it as Big-O
    4. 6dThe complexity classes you'll meet
    5. 6eWorst case, average case, and space
    6. 6fPredicting performance in practice
  7. 7Uses of Multidimensional Arrays
    5 sub-skills
    1. 7aRows, columns and a[r][c]
    2. 7bVisiting every cell
    3. 7cRow and column totals
    4. 7dNeighbours and staying in bounds
    5. 7eModelling with grids
  8. 8Ways in Which Data Structures Are Organized in Memory
    6 sub-skills
    1. 8aArrays are contiguous
    2. 8bLinked structures: nodes and pointers
    3. 8cStacks and queues
    4. 8dHash tables: keys to slots
    5. 8eTrees: hierarchy in memory
    6. 8fChoosing the right structure
  9. 9Ways to Model Mathematical Problems
    5 sub-skills
    1. 9aChoosing how to represent the math
    2. 9bPrecision limits in numeric models
    3. 9cConvergence and stopping rules
    4. 9dSimulation at scale
    5. 9eWill the model finish?

F. Financial Literacy

  1. 1Financial Literacy: Business Investments and Loans
    6 sub-skills
    1. 1aSimple and compound interest in business
    2. 1bFinancing a truck or a tool package
    3. 1cLease or buy the equipment?
    4. 1dLines of credit and cash flow
    5. 1eReturn on investment and payback
    6. 1fBreak-even and the rate you must charge
  2. 2Financial Planning
    6 sub-skills
    1. 2aHow compound interest actually works
    2. 2bInvesting over a lifetime
    3. 2cLoans, mortgages and amortization
    4. 2dCredit cards and consumer debt
    5. 2eRent, buy, or lease?
    6. 2fBudgets and net worth