LEARN · EXPLAIN · REVISE
Senior 3 · Science
Read the idea, work independently, then explain what changed.
T06高三理組數學思維本(2026).pdf · PDF pages count from the first PDF page · Semester boundary not specified
Differentiation and integration
PDF 4 · LEARNING AND PRACTICE
Derivative: concept and meaning
Distinguish average and instantaneous rates and derive tangents from a limit.
Derivative operations
Apply power, product, quotient and chain rules with elementary derivatives.
Applications of derivatives
Use derivative signs, boundary values and models to justify extrema and optimization.
Integration, area and school extensions
Find antiderivatives, evaluate definite integrals and distinguish signed accumulation from geometric area.
Space vectors and analytic geometry
PDF 10 · LEARNING AND PRACTICE
Space vectors and their operations
Add, scale and multiply space vectors; distinguish scalar and vector results.
The fundamental theorem of space vectors
Recognise a basis and use unique vector coordinates and affine combinations.
Coordinate representation of space vectors
Calculate spatial lengths, angles, projections and perpendicular directions from coordinates.
Applications of space vectors
Use direction and normal vectors to establish angles, distances and spatial relations.
Spatial lines, planes, spheres and cross products
Construct spatial equations and use normals, cross products and direction tests.
Whole-course review
PDF 18 · REVISION
Concept of a set
Build understanding of concept of a set through definitions, contrasting cases and justified applications.
Basic relations between sets
Build understanding of basic relations between sets through definitions, contrasting cases and justified applications.
Basic operations on sets
Build understanding of basic operations on sets through definitions, contrasting cases and justified applications.
Sufficient and necessary conditions
Build understanding of sufficient and necessary conditions through definitions, contrasting cases and justified applications.
Universal and existential quantifiers
Build understanding of universal and existential quantifiers through definitions, contrasting cases and justified applications.
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.
Function concept and representations
Build understanding of function concept and representations through definitions, contrasting cases and justified applications.
Basic properties of functions
Build understanding of basic properties of functions through definitions, contrasting cases and justified applications.
Power functions
Build understanding of power functions through definitions, contrasting cases and justified applications.
Applications of functions I
Build understanding of applications of functions i through definitions, contrasting cases and justified applications.
Exponents
Build understanding of exponents through definitions, contrasting cases and justified applications.
Exponential functions
Build understanding of exponential functions through definitions, contrasting cases and justified applications.
Logarithms
Build understanding of logarithms through definitions, contrasting cases and justified applications.
Logarithmic functions
Build understanding of logarithmic functions through definitions, contrasting cases and justified applications.
Applications of functions II
Build understanding of applications of functions ii through definitions, contrasting cases and justified applications.
General angles and radian measure
Build understanding of general angles and radian measure through definitions, contrasting cases and justified applications.
Concept of trigonometric functions
Build understanding of concept of trigonometric functions through definitions, contrasting cases and justified applications.
Reduction formulas
Build understanding of reduction formulas through definitions, contrasting cases and justified applications.
Graphs and properties of trigonometric functions
Build understanding of graphs and properties of trigonometric functions through definitions, contrasting cases and justified applications.
Trigonometric identities and transformations
Build understanding of trigonometric identities and transformations through definitions, contrasting cases and justified applications.
The function y=A sin(ωx+φ)
Build understanding of the function y=a sin(ωx+φ) through definitions, contrasting cases and justified applications.
Applications of trigonometric functions
Build understanding of applications of trigonometric functions through definitions, contrasting cases and justified applications.
Concept of plane vectors
Build understanding of concept of plane vectors through definitions, contrasting cases and justified applications.
Operations on plane vectors
Build understanding of operations on plane vectors through definitions, contrasting cases and justified applications.
Basis theorem and coordinate representation
Build understanding of basis theorem and coordinate representation through definitions, contrasting cases and justified applications.
Applications of plane vectors
Build understanding of applications of plane vectors through definitions, contrasting cases and justified applications.
Concept of complex numbers
Build understanding of concept of complex numbers through definitions, contrasting cases and justified applications.
Arithmetic of complex numbers
Build understanding of arithmetic of complex numbers through definitions, contrasting cases and justified applications.
Trigonometric representation of complex numbers (starred)
Build understanding of trigonometric representation of complex numbers (starred) through definitions, contrasting cases and justified applications.
Basic solid figures
Build understanding of basic solid figures through definitions, contrasting cases and justified applications.
Oblique drawings of solids
Build understanding of oblique drawings of solids through definitions, contrasting cases and justified applications.
Surface areas and volumes of simple solids
Build understanding of surface areas and volumes of simple solids through definitions, contrasting cases and justified applications.
Positions of points, lines and planes in space
Build understanding of positions of points, lines and planes in space through definitions, contrasting cases and justified applications.
Parallel lines and planes in space
Build understanding of parallel lines and planes in space through definitions, contrasting cases and justified applications.
Perpendicular lines and planes in space
Build understanding of perpendicular lines and planes in space through definitions, contrasting cases and justified applications.
Random sampling
Build understanding of random sampling through definitions, contrasting cases and justified applications.
Estimating a population from a sample
Build understanding of estimating a population from a sample through definitions, contrasting cases and justified applications.
Statistical case study
Build understanding of statistical case study through definitions, contrasting cases and justified applications.
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.
Space vectors and their operations
Add, scale and multiply space vectors; distinguish scalar and vector results.
The fundamental theorem of space vectors
Recognise a basis and use unique vector coordinates and affine combinations.
Coordinate representation of space vectors
Calculate spatial lengths, angles, projections and perpendicular directions from coordinates.
Applications of space vectors
Use direction and normal vectors to establish angles, distances and spatial relations.
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.
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.
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.
Derivative: concept and meaning
Distinguish average and instantaneous rates and derive tangents from a limit.
Derivative operations
Apply power, product, quotient and chain rules with elementary derivatives.
Applications of derivatives
Use derivative signs, boundary values and models to justify extrema and optimization.
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.
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.
Normal distribution
Standardise a normal variable and interpret supplied table probabilities and symmetry.
Correlation of paired data
Interpret scatter patterns and compute a correlation from centered paired summaries.
Linear regression and applications
Fit a least-squares line and distinguish prediction, residual and extrapolation.
Contingency tables and independence tests
Compute expected counts and a chi-square statistic and state a bounded conclusion.
Polynomial division and partial fractions
Divide polynomials and choose decomposition numerators matched to each denominator factor.
Variation and financial models
Identify direct, inverse, joint and partial variation and apply stated interest or depreciation models.
Euclidean figures and circle theorems
Use similarity, angle and circle theorems with labeled points and compatible arcs.
Linear programming and discrete feasibility
Draw a feasible region and optimise a linear objective, then check integer restrictions when required.
Matrices, determinants and linear systems
Add and multiply matrices, use determinants and solve systems without assuming invertibility.
Polar coordinates
Convert representations and eliminate polar variables without losing the geometric range.
Integration, area and school extensions
Find antiderivatives, evaluate definite integrals and distinguish signed accumulation from geometric area.
Spatial lines, planes, spheres and cross products
Construct spatial equations and use normals, cross products and direction tests.
Parametric curves and preserved domains
Eliminate parameters while retaining ranges, missing points and the geometry of the locus.
Infinite geometric series and error control
Check convergence before summing and interpret recurring decimals and truncation errors.
Radicals, rational equations and simultaneous equations
Build understanding of radicals, rational equations and simultaneous equations through definitions, contrasting cases and justified applications.
Absolute values and solution sets
Build understanding of absolute values and solution sets through definitions, contrasting cases and justified applications.
Inverse functions and domain restrictions
Build understanding of inverse functions and domain restrictions through definitions, contrasting cases and justified applications.
Exponential and logarithmic equations
Build understanding of exponential and logarithmic equations through definitions, contrasting cases and justified applications.