DSE M1

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DSE M1: a curve with a stepped resin Riemann sum and a tangent bar on a metal coordinate frame, an amber normal distribution ribbon in front of a solid histogram, a 3D scatter plot with a trend rod, and a graphing calculator in the foreground.

Build calculus, probability and statistical estimation skills through modelling and data interpretation.

  • Check model conditions before choosing a calculus, probability or statistical method
  • Train notation, limits and working rigorously to reduce non-conceptual losses
  • Translate calculated values into statistically accurate contextual conclusions
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Course highlights

Method judgement Check conditions before applying a model Organise variables, assumptions and goals so that a formula is selected by conditions rather than keywords.
Model condition table
Compare the assumptions and limits of distributions, estimation and calculus methods.
Translate words into mathematics
Define variables, events and parameters before building a workable representation.
Return results to context
Check numerical range and state the conclusion in the language of the question.
 Calculus Protect method marks through disciplined notation Build traceable working from symbols and rules through the treatment of limits and bounds.
Symbols and brackets
Check functions, derivatives, integral signs, dx, constants and bracket placement.
Choose a method
Select differentiation, integration or numerical approximation from the function structure.
Interpret applications
Connect derivatives, areas and accumulated quantities to graphs and meaning.
 Probability and statistics Move from event relationships to statistical inference Understand what conditional probability, distributions and estimation results mean, not only how to calculate them.
Visualise event relationships
Use trees, tables and conditions to reduce confusion in conditional probability.
Choose a distribution
Use random-variable properties and question conditions to identify the appropriate model.
State statistical conclusions
Explain estimates, intervals and uncertainty accurately without overclaiming.
 Integrated problems Manage intermediate results in multi-step questions Divide a long task into verifiable stages and check notation, precision and plausibility at each one.
Route map
Mark required intermediate quantities and dependencies before calculating.
Manage precision
Avoid premature rounding and present the requested accuracy clearly.
Trace errors backwards
Use an implausible result to inspect the model, formula, substitution and calculator input.
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Course content

Expansions and functions
Binomial expansion and the graphs, relationships and applications of exponential and logarithmic functions.
Differentiation
Differentiation methods, tangents, rates of change, extrema and related applications.
Integration and numerical approximation
Indefinite and definite integrals, area applications and the trapezoidal rule.
Conditional probability
Conditional probability, Bayes' theorem and relationships between events.
Probability distributions
Discrete and continuous random variables, including binomial, Poisson and normal distributions.
Sampling and estimation
Sampling distributions, point estimates and confidence intervals for a population mean.

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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