DSE M2

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DSE M2: a clear acrylic polyhedron, a three-axis wireframe coordinate frame, vector arrows and a matrix grid on squared paper, with a compass and a pencil.

Connect functions, calculus, matrices and vectors through symbolic, geometric and deductive reasoning.

  • Build complete proof chains without skipping validity conditions or decisive steps
  • Choose differentiation, integration and trigonometric transformations from function structure
  • Use diagrams to connect matrices and vectors with geometric relationships
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Course highlights

Proof and deduction Build a complete chain from the given conditions Separate the target, intermediate results and conclusion to avoid circular reasoning, skipped steps or unused information.
Work backwards from the target
Identify the intermediate relationships required for the conclusion.
Justify each step
Name the theorem, identity or given result used and keep the direction clear.
Check validity
Review domains, ranges, non-zero conditions and signs.
 Advanced calculus Recognise structure before selecting a method Compare algebraic rearrangement, trigonometric identities, substitution and integration by parts and explain the choice.
Recognise function structure
Identify composition, products, powers and trigonometric relationships first.
Compare routes
Evaluate alternative methods by length, risk and ease of verification.
Verify results
Use differentiation, graphs, boundaries and dimensions to check integrals or extrema.
 Matrices and vectors Recover geometric meaning from algebraic operations Use diagrams to understand determinants, systems, dot products, cross products and projections.
Matrices and systems
Compare Cramer’s rule, inverse matrices and elimination by problem structure.
Visualise vectors
Interpret dot and cross products through direction, projection, angle and area.
Prevent sign errors
Set checkpoints for determinant expansion, vector order and signs.
 Integrated review Rebuild the decision path behind an error Find where the wrong formula, missed condition or lost direction occurred instead of changing the final answer only.
Locate the error
Separate conceptual, algebraic, method-selection and communication issues.
Redo a variation
Change conditions to test whether the method is genuinely understood.
Check completeness
Confirm that all solutions, ranges, units and task requirements are handled.
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Course content

Function foundations
Odd and even functions, the number e and the natural logarithm.
Induction and the binomial theorem
Proof by mathematical induction and general terms and coefficients in binomial expansions.
Trigonometric functions
Radians, trigonometric functions, compound and double angles, and product-to-sum formulas.
Differentiation
Limits, differentiation methods, tangents, extrema, rates of change and curve analysis.
Integration
Substitution, trigonometric substitution, integration by parts, plane areas and volumes of revolution.
Determinants and matrices
Determinants, matrices, inverses and systems of linear equations in two and three variables.
Vectors
Two- and three-dimensional vectors, dot and cross products, projections, angles and areas.

Course fees

4 lessons per month 90 minutes per lesson

Fees by level

S4
HK$1,380/ 4 lessons
S5-S6
HK$1,560/ 4 lessons
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