LEARN · EXPLAIN · REVISE
Prepare by examination skill
Read the idea, work independently, then explain what changed.
Use the syllabus for your examination year. A school’s arts/science stream does not determine a paper code.
- Read a worked example and explain its conditions.
- Complete standard and transfer exercises without hints.
- Use a chapter mixed assessment to choose methods independently.
- Attempt the original paper, then compare every step and revise.
2027 JM01 · Syllabus and lesson mapping
Percentages and finance
Direct, inverse, joint and partial variation
Polynomials and rational fractions
Quadratic equations and functions
Indices and surds
Algebraic and absolute inequalities; linear programming
Exponential and logarithmic functions and equations
Rational and irrational equations
Permutations, combinations and binomial theorem
Sequences and infinite geometric series
Rectilinear figures and circles
Trigonometry and triangle solving
Lines, circles, conics and linear systems
- Inclination and slope of a line
- Equations of a line
- Intersections and distance formulas
- Equations of a circle
- Relations between lines and circles
- Ellipse
- Hyperbola
- Parabola
- Matrices, determinants and linear systems · Linear systems only; matrices and determinants belong to JM02
Function graphs and transformations
Probability and descriptive statistics
2027 JM02 · Syllabus and lesson mapping
JM02 includes the complete JM01 syllabus, together with these nine additional areas.
Functions, domains, ranges and inverses
Simple solids
Linear systems, matrices and determinants
Tangents, normals and polar coordinates
Trigonometric equations and general solutions
Polynomial calculus, extrema, inflection and areas
- Derivative: concept and meaning
- Derivative operations · Syllabus: sums, differences, products and quotients of polynomials; exponential, logarithmic and trigonometric derivatives are curriculum extensions
- Applications of derivatives
- Integration, area and school extensions
Curve sketching using symmetry, periodicity and derivatives
Plane vectors and scalar products
Complex numbers, polar form, powers and roots
Sets and commonly used logic
Lessons and 15-question mixed assessment
Quadratic functions, equations and inequalities
Lessons and 15-question mixed assessment
Functions: concept and properties
Lessons and 15-question mixed assessment
Exponential and logarithmic functions
Lessons and 15-question mixed assessment
Trigonometric functions
Lessons and 15-question mixed assessment
Plane vectors and applications
Lessons and 15-question mixed assessment
Complex numbers
Lessons and 15-question mixed assessment
Introduction to solid geometry
Lessons and 15-question mixed assessment
Statistics
Lessons and 15-question mixed assessment
Probability
Lessons and 15-question mixed assessment
Space vectors and solid geometry
Lessons and 15-question mixed assessment
Equations of lines and circles
Lessons and 15-question mixed assessment
Conic sections
Lessons and 15-question mixed assessment
Sequences
Lessons and 15-question mixed assessment
Derivatives and their applications
Lessons and 15-question mixed assessment
Counting principles
Lessons and 15-question mixed assessment
Random variables and distributions
Lessons and 15-question mixed assessment
Statistical analysis of paired data
Lessons and 15-question mixed assessment
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.