IB Mathematics AA

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IB 數學 AA 主題：斜置繪圖板上畫著單位圓、中心角扇形、半徑與切線（附直角記號），正弦波由圓緣展開，板上放著圓規與三角板。

Rebuild algebra, functions and calculus, then strengthen proof, analytical reasoning and AA paper performance.

  • Repair prerequisite gaps in algebra, functions, trigonometry and calculus before they compound
  • Use definitions, symbolic structure, graphs and proof to develop analytical reasoning
  • Break unfamiliar multi-stage problems into useful subgoals instead of relying on templates
  • Integrate no-technology work, GDC checking and exploration feedback without replacing student thinking
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課程重點

Repair prerequisite gaps before they compound AA problems expose weak algebra, functions, trigonometry and calculus quickly, especially at HL.
Trace dependencies
Identify which earlier technique a failed derivation assumes.
Separate understanding from fluency
Distinguish conceptual gaps from slow or inaccurate symbolic work.
Rebuild at the required level
Return from a focused foundation task to an SL or HL problem.
 Develop analytical reasoning rather than formula recall Move between definitions, symbolic structure, graphs and proof to explain why a method works.
Choose representations
Use algebraic, graphical, geometric or numerical forms deliberately.
Construct justification
State conditions, intermediate claims and conclusions clearly.
Preserve exactness
Control notation, domains and exact forms throughout the argument.
 Control unfamiliar and multi-stage problems Break long questions into useful subgoals instead of waiting to recognise a rehearsed template.
Identify invariants
Find constraints, symmetries and quantities that remain connected.
Plan a route
Work backwards from the target and choose decisive intermediate results.
Evaluate the solution
Use alternative forms, limiting behaviour or technology to check.
 Integrate paper practice, technology and exploration feedback Use assessment evidence to strengthen mathematical communication without replacing student thinking.
Compare technology modes
Retain analytical methods and use the GDC for checking or exploration.
Track command and presentation errors
Separate mathematical, strategic, notation and communication issues.
Support the exploration responsibly
Refine questions, mathematics and reflection while preserving student authorship.
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課程內容

Number and algebra
Numerical representation, algebra, sequences, exponentials, logarithms and related reasoning.
  • Scientific notation and approximation
  • Sequences and series
  • Exponents and logarithms
  • Proof, algebraic structure and complex numbers at the required level
Functions
Representations, features, transformations, equations and modelling.
  • Function concepts and notation
  • Graph features and transformations
  • Equations and inequalities
  • Modelling with functions
Geometry and trigonometry
Geometry, trigonometry, vectors and spatial relationships.
  • Trigonometric relationships
  • Geometry and coordinate methods
  • Vectors at the required level
Statistics and probability
Data, distributions, probability, correlation and statistical inference.
  • Data representation and summary
  • Probability and distributions
  • Correlation, regression and inference at the required level
Calculus
Limits, differentiation, integration, rates of change and accumulation.
  • Limits and rates of change
  • Differentiation and applications
  • Integration and applications
  • Differential equations at the required level
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.

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每月 4 堂 每堂 90 分鐘

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HK$2,000／4堂
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