LEARN · EXPLAIN · REVISE
Senior 2 · Science
Read the idea, work independently, then explain what changed.
T04高二理組數學思維本(2026).pdf · PDF pages count from the first PDF page · Semester boundary not specified
Inequalities with parameters
PDF 4 · LEARNING AND PRACTICE
Properties of equalities and inequalities
Build understanding of properties of equalities and inequalities through definitions, contrasting cases and justified applications.
Basic inequality: AM–GM
Build understanding of basic inequality: am–gm through definitions, contrasting cases and justified applications.
Quadratic functions, equations and inequalities
Build understanding of quadratic functions, equations and inequalities through definitions, contrasting cases and justified applications.
Lines, circles and loci
PDF 9 · LEARNING AND PRACTICE
Inclination and slope of a line
Connect slope, inclination and parallel/perpendicular directions, including vertical lines.
Equations of a line
Choose point-slope, two-point, intercept or general form without losing exceptional lines.
Intersections and distance formulas
Solve intersections and calculate point-line and parallel-line distances with geometric checks.
Equations of a circle
Construct circle equations from centers, radii, diameters and point constraints.
Relations between lines and circles
Classify intersection and tangency using distances, discriminants and common chords.
Linear programming and discrete feasibility
Draw a feasible region and optimise a linear objective, then check integer restrictions when required.
Conics, translation and parameterisation
PDF 15 · LEARNING AND PRACTICE
Ellipse
Use the focal definition, standard equation and geometric properties of an ellipse.
Hyperbola
Use the distance-difference definition, asymptotes and branch restrictions.
Parabola
Relate focus, directrix and vertex, and retain conditions in line-parabola intersections.
Parametric curves and preserved domains
Eliminate parameters while retaining ranges, missing points and the geometry of the locus.
Sequences and induction
PDF 29 · LEARNING AND PRACTICE
Concept of a sequence
Connect general terms, recurrence relations and partial sums.
Arithmetic sequences
Derive terms and sums and solve indexed arithmetic models.
Geometric sequences
Connect ratios, indexed powers and finite geometric sums.
Mathematical induction
Build proofs with a verified base, an explicit induction hypothesis and a valid step.
Infinite geometric series and error control
Check convergence before summing and interpret recurring decimals and truncation errors.
Counting, probability and expectation
PDF 36 · LEARNING AND PRACTICE
Addition and multiplication counting principles
Count disjoint alternatives and sequential choices without overlap or omission.
Permutations and combinations
Distinguish ordered selections, unordered sets and symmetry in arrangements.
Binomial theorem
Use the general term to locate coefficients, constants and coefficient sums.
Random events and probability
Build understanding of random events and probability through definitions, contrasting cases and justified applications.
Independence of events
Build understanding of independence of events through definitions, contrasting cases and justified applications.
Frequency and probability
Build understanding of frequency and probability through definitions, contrasting cases and justified applications.
Conditional and total probability
Use conditional denominators, disjoint partitions and Bayes inversion.
Discrete random variables and distributions
Construct a distribution and compute event probabilities from its support.
Numerical characteristics of random variables
Compute expectation and variance and distinguish transformation from random independence.
Binomial and hypergeometric distributions
Choose the correct model for repeated independent trials or sampling without replacement.