Complex numbers, matrices and series
Write your reasoning, then compare it with the indicative marking points. Check your own exam-board specification for required coverage.
- Complex numbers
- Matrices
- Series
Practice betaUsable beta practice. Treat marking points as a helpful practice guide, not a certified answer key.
AS/A Level · Learning hub
Further Mathematics
About this subject
Original concept practice. Limited preview, not a complete syllabus or official past-paper collection.
Topics & subtopics
Proof and linear algebra
Original application practice with worked explanations and indicative self-marking points. Not an official exam paper or a board-specific assessment.
- Mathematical proof
- Matrix operations
- Linear systems
Complex geometry and roots
Original practice: Argand loci; De Moivre's theorem; Polynomial roots. Not board-specific or independently reviewed.
- Argand loci
- De Moivre's theorem
- Polynomial roots
Matrix transformations and eigenvectors
Original practice: Composition; Invariant directions; Diagonalisation. Not board-specific or independently reviewed.
- Composition
- Invariant directions
- Diagonalisation
Induction and series
Original practice: Finite sums; Divisibility proofs; Recurrences. Not board-specific or independently reviewed.
- Finite sums
- Divisibility proofs
- Recurrences
Hyperbolic functions and inverses
Original practice: Exponential definitions; Inverse domains; Hyperbolic calculus. Not board-specific or independently reviewed.
- Exponential definitions
- Inverse domains
- Hyperbolic calculus
Advanced integration and improper integrals
Original practice: Integration by parts; Reduction formulae; Convergence. Not board-specific or independently reviewed.
- Integration by parts
- Reduction formulae
- Convergence
Second-order differential equations
Original practice: Characteristic roots; Resonant forcing; Initial conditions. Not board-specific or independently reviewed.
- Characteristic roots
- Resonant forcing
- Initial conditions
Three-dimensional vector geometry
Original practice: Lines and planes; Cross products; Shortest distances. Not board-specific or independently reviewed.
- Lines and planes
- Cross products
- Shortest distances
Polar curves and area
Original practice: Coordinate conversion; Polar tangents; Loop area. Not board-specific or independently reviewed.
- Coordinate conversion
- Polar tangents
- Loop area
Structured progression
Revision Ladder
Start with foundations, then move through application and challenge. Stages use activity marks and complexity.
Stage 1
Start stage Foundation
Recall core ideas and establish reliable methods.
18 questions available0/18 completedStage 2
Start stage Apply
Connect concepts and apply them in exam-style contexts.
19 questions available0/19 completedStage 3
Start stage Challenge
Tackle advanced reasoning and multi-step questions.
17 questions available0/17 completedProgress dashboard
Topic practice
Recommended next: Complex numbers, matrices and series
01
Complex numbers, matrices and series
Not startedWrite your reasoning, then compare it with the indicative marking points. Check your own exam-board specification for required coverage.
0%0/3 complete
02Proof and linear algebra
Not startedOriginal application practice with worked explanations and indicative self-marking points. Not an official exam paper or a board-specific assessment.
0%0/3 complete
03Complex geometry and roots
Not startedOriginal practice: Argand loci; De Moivre's theorem; Polynomial roots. Not board-specific or independently reviewed.
0%0/6 complete
04Matrix transformations and eigenvectors
Not startedOriginal practice: Composition; Invariant directions; Diagonalisation. Not board-specific or independently reviewed.
0%0/6 complete
05Induction and series
Not startedOriginal practice: Finite sums; Divisibility proofs; Recurrences. Not board-specific or independently reviewed.
0%0/6 complete
06Hyperbolic functions and inverses
Not startedOriginal practice: Exponential definitions; Inverse domains; Hyperbolic calculus. Not board-specific or independently reviewed.
0%0/6 complete
07Advanced integration and improper integrals
Not startedOriginal practice: Integration by parts; Reduction formulae; Convergence. Not board-specific or independently reviewed.
0%0/6 complete
08Second-order differential equations
Not startedOriginal practice: Characteristic roots; Resonant forcing; Initial conditions. Not board-specific or independently reviewed.
0%0/6 complete
09Three-dimensional vector geometry
Not startedOriginal practice: Lines and planes; Cross products; Shortest distances. Not board-specific or independently reviewed.
0%0/6 complete
10Polar curves and area
Not startedOriginal practice: Coordinate conversion; Polar tangents; Loop area. Not board-specific or independently reviewed.
0%0/6 complete
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