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Teacher resources
Read the idea, work independently, then explain what changed.
Choose a lesson to use its question sequence, board plan, anticipated answers and reasoning rubric. Classroom mode shows one question at a time; print student or teacher versions from the lesson tools.
Concept of a set
What must be true before using the main rule for concept of a set?
Basic relations between sets
What must be true before using the main rule for basic relations between sets?
Basic operations on sets
What must be true before using the main rule for basic operations on sets?
Sufficient and necessary conditions
What must be true before using the main rule for sufficient and necessary conditions?
Universal and existential quantifiers
What must be true before using the main rule for universal and existential quantifiers?
Properties of equalities and inequalities
What must be true before using the main rule for properties of equalities and inequalities?
Basic inequality: AM–GM
What must be true before using the main rule for basic inequality: am–gm?
Quadratic functions, equations and inequalities
What must be true before using the main rule for quadratic functions, equations and inequalities?
Function concept and representations
What must be true before using the main rule for function concept and representations?
Basic properties of functions
What must be true before using the main rule for basic properties of functions?
Power functions
What must be true before using the main rule for power functions?
Applications of functions I
What must be true before using the main rule for applications of functions i?
Exponents
What must be true before using the main rule for exponents?
Exponential functions
What must be true before using the main rule for exponential functions?
Logarithms
What must be true before using the main rule for logarithms?
Logarithmic functions
What must be true before using the main rule for logarithmic functions?
Applications of functions II
What must be true before using the main rule for applications of functions ii?
General angles and radian measure
What must be true before using the main rule for general angles and radian measure?
Concept of trigonometric functions
What must be true before using the main rule for concept of trigonometric functions?
Reduction formulas
What must be true before using the main rule for reduction formulas?
Graphs and properties of trigonometric functions
What must be true before using the main rule for graphs and properties of trigonometric functions?
Trigonometric identities and transformations
What must be true before using the main rule for trigonometric identities and transformations?
The function y=A sin(ωx+φ)
What must be true before using the main rule for the function y=a sin(ωx+φ)?
Applications of trigonometric functions
What must be true before using the main rule for applications of trigonometric functions?
Concept of plane vectors
What must be true before using the main rule for concept of plane vectors?
Operations on plane vectors
What must be true before using the main rule for operations on plane vectors?
Basis theorem and coordinate representation
What must be true before using the main rule for basis theorem and coordinate representation?
Applications of plane vectors
What must be true before using the main rule for applications of plane vectors?
Concept of complex numbers
What must be true before using the main rule for concept of complex numbers?
Arithmetic of complex numbers
What must be true before using the main rule for arithmetic of complex numbers?
Trigonometric representation of complex numbers (starred)
What must be true before using the main rule for trigonometric representation of complex numbers (starred)?
Basic solid figures
What must be true before using the main rule for basic solid figures?
Oblique drawings of solids
What must be true before using the main rule for oblique drawings of solids?
Surface areas and volumes of simple solids
What must be true before using the main rule for surface areas and volumes of simple solids?
Positions of points, lines and planes in space
What must be true before using the main rule for positions of points, lines and planes in space?
Parallel lines and planes in space
What must be true before using the main rule for parallel lines and planes in space?
Perpendicular lines and planes in space
What must be true before using the main rule for perpendicular lines and planes in space?
Random sampling
What must be true before using the main rule for random sampling?
Estimating a population from a sample
What must be true before using the main rule for estimating a population from a sample?
Statistical case study
What must be true before using the main rule for statistical case study?
Random events and probability
What must be true before using the main rule for random events and probability?
Independence of events
What must be true before using the main rule for independence of events?
Frequency and probability
What must be true before using the main rule for frequency and probability?
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
What must be true before using the main rule for radicals, rational equations and simultaneous equations?
Absolute values and solution sets
What must be true before using the main rule for absolute values and solution sets?
Inverse functions and domain restrictions
What must be true before using the main rule for inverse functions and domain restrictions?
Exponential and logarithmic equations
What must be true before using the main rule for exponential and logarithmic equations?