IB Mathematics AI

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IB 數學 AI 主題：格線資料板上放著散點與趨勢桿、常態分佈鐘形實體、四根柱狀圖，以及一張節點網絡圖。

Improve modelling, statistics and GDC judgement for AI papers and the exploration.

  • Translate real contexts into models with explicit variables, assumptions and limitations
  • Use the GDC only after predicting the behaviour and choosing the mathematical method
  • Interpret distributions, regression and statistical evidence beyond reporting calculator output
  • Improve modelling communication and reflection across papers and the exploration
課程重點收起課程重點

課程重點

Translate real contexts into defensible models Identify variables, assumptions and constraints before selecting a function, statistical or discrete model.
Define the system
State what is measured, controlled, omitted and assumed.
Compare models
Judge fit, interpretability and limitations rather than choosing by appearance alone.
Return to context
Explain what parameters and predictions mean in the original situation.
 Use the GDC with mathematical judgement Technology should execute and display a method that the student has already selected and can interpret.
Predict first
Estimate scale, shape and direction before pressing calculate.
Control the workflow
Manage data entry, window, regression, distribution and numerical settings.
Verify output
Use alternative representations, residuals, units and context.
 Interpret statistics and data as evidence Move beyond reporting a coefficient or p-value to judging what the data supports.
Read distributions
Connect centre, spread, shape and unusual values.
Separate association and causation
State confounding, sampling and model limitations.
Communicate uncertainty
Match the strength of the conclusion to the quality of evidence.
 Improve modelling communication across papers and exploration Use feedback to strengthen method choice, interpretation and reflection rather than rehearsing button sequences.
Diagnose the failure
Separate model choice, technology, calculation and interpretation errors.
Rewrite conclusions
Connect numerical output to the question with units and limitations.
Support the exploration responsibly
Develop data, models and reflection while preserving student decisions and authorship.
課程內容收起課程內容

課程內容

Number and algebra
Numerical representation, algebra, sequences, exponentials, logarithms and related reasoning.
  • Approximation and financial mathematics
  • Sequences and growth models
  • Algebraic methods required for modelling
Functions
Representations, features, transformations, equations and modelling.
  • Function interpretation
  • Linear, exponential, logarithmic and sinusoidal models
  • Regression and model comparison
Geometry and trigonometry
Geometry, trigonometry, vectors and spatial relationships.
  • Measurement and trigonometry
  • Coordinate and vector methods at the required level
  • Applications to spatial contexts
Statistics and probability
Data, distributions, probability, correlation and statistical inference.
  • Data description and visualisation
  • Probability and distributions
  • Correlation and regression
  • Statistical inference at the required level
Calculus
Limits, differentiation, integration, rates of change and accumulation.
  • Rates of change
  • Differentiation and optimisation
  • Integration and accumulation
  • Numerical and technological approaches
Assessment
SL: Paper 1, Paper 2 and exploration; HL: also Paper 3.
  • SL: Paper 1 and Paper 2
  • HL: Paper 1, Paper 2 and Paper 3
  • Internally assessed mathematics exploration
The exact duration and weighting depend on subject and SL or HL. Teaching follows the current IB Diploma Programme guide and the student’s registered level.

課程收費

每月 4 堂 每堂 90 分鐘

按年級收費

所有級別
HK$2,000／4堂
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