Further Maths: Core Pure 1
9
specification units
42
named subtopics
Year 12
year groups
Pearson Edexcel AS Level Further Maths: Core Pure 1 (Further) is organised here into 9 specification units covering 42 named subtopics, studied across Year 12. The units are Complex Numbers, Argand Diagrams, Series, Roots of Polynomials, Volumes of Revolution, Matrices, Linear Transformations, Proof by Induction and Vectors.
Each subtopic is tagged on the question bank, so you can practise one skill at a time, sit a full Edexcel AS past paper, or build a mixed worksheet from several units at once. Answers are checked against the Pearson Edexcel AS Level mark scheme, awarding method, accuracy and final-answer marks separately so you can see exactly where marks were lost.
Matrices is the widest unit on this specification with 6 subtopics, so it is usually the highest-value place to start revision.
How Pearson Edexcel AS Level Further Maths: Core Pure 1 is examined
Edexcel AS Further Maths Core Pure 1 introduces the content that defines Further Maths — complex numbers, matrices and proof by induction — and assumes total fluency with the AS Pure algebra running underneath it.
Assessment at a glance
- •A compulsory core module for AS Further Mathematics, taken alongside optional applied units.
- •Content is examined largely through structured multi-part questions built around one context.
- •Exact answers are expected throughout; the calculator supports arithmetic but not the argument.
Where marks are most often lost
- •Proof by induction where the inductive step is asserted rather than derived, or the conclusion is not stated formally.
- •Argand diagram work: modulus-argument form, loci and correctly identifying the region.
- •Matrix transformations where the order of multiplication is reversed.
- •Roots of polynomials — using the relationships between roots and coefficients rather than solving directly.
What to revise first: Complex numbers first, then matrices, then proof by induction. Volumes of revolution and series are faster to secure once those are in place.
Complex Numbers
- Imaginary and complex numbers
- Multiplying complex numbers
- Complex conjugation
- Roots of quadratic equations
- Solving cubic and quartic equations
Argand Diagrams
- Argand diagrams
- Modulus and argument
- Modulus-argument form of complex numbers
- Loci in the Argand diagram
- Regions in the Argand diagram
Roots of Polynomials
- Roots of a quadratic equation
- Roots of a cubic equation
- Roots of a quartic equation
- Expressions relating to the roots of a polynomial
- Linear transformations of roots
Volumes of Revolution
- Volumes of revolution around the x-axis
- Volumes of revolution around the y-axis
- Adding and subtracting volumes
- Modelling with volumes of revolution
Matrices
- Introduction to matrices
- Matrix multiplication
- Determinants
- Inverting a 2 x 2 matrix
- Inverting a 3 x 3 matrix
- Solving systems of equations using matrices
Linear Transformations
- Linear transformations in two dimensions
- Reflections and rotations
- Enlargements and stretches
- Successive transformations
- Linear transformations in three dimensions
- The inverse of a linear transformation
Proof by Induction
- Proof by mathematical induction
- Proving divisibility results
- Proving statements involving matrices
Vectors
- Equation of a line in three dimensions
- Equation of a plane in three dimensions
- Scalar product
- Calculating angles between lines and planes
- Points of intersection
- Finding perpendiculars
How to revise Edexcel AS Further Maths: Core Pure 1
- 1
Diagnose with one mixed set
Start with a mixed set drawn from all 9 units to find where Further Maths: Core Pure 1 marks are actually being lost, rather than revising what already feels comfortable.
- 2
Drill unit by unit
Work through the subtopics in order, from Complex Numbers to Vectors, doing short focused sets rather than long unfocused sessions.
- 3
Sit a full past paper under timing
Once two or three units are solid, sit a complete Edexcel AS Further Maths: Core Pure 1 paper to timing and mark it against the official mark scheme.
- 4
Re-practise only the dropped marks
Convert every dropped mark into a targeted set on that subtopic, then re-test it a week later to check the fix stuck.
Continue with Further Maths: Core Pure 1
Every board and level we cover for this subject
A Level MathematicsSearchable formula sheet with worked micro-examples
Predicted papersPractice papers built from the topics that recur most
Past paper practiceSit whole papers online with examiner-grade marking
Other specifications for this subject
Further Maths: Core Pure 1 — frequently asked questions
Everything students and parents ask about revising Edexcel AS Further Maths: Core Pure 1.
The fastest route is past-paper-first revision: practise exam-style questions by topic, mark every answer against the real Pearson Edexcel AS Level mark scheme, then drill the topics where you lose marks. On MathsGradeUp you can do all of this for Further Maths: Core Pure 1 in one place — topic practice, full past papers and instant examiner-grade feedback.
Pearson Edexcel AS Level Further Maths: Core Pure 1 is mapped to the official specification and covers 9 units, including Complex Numbers, Argand Diagrams, Series, Roots of Polynomials, Volumes of Revolution, Matrices and more. Every unit is broken down into subtopics so you can target exactly what you need to revise.
Yes. You can open full Edexcel AS Further Maths: Core Pure 1 past papers, write directly on them with pen and maths tools, save your work, export a PDF, and submit for examiner-grade marking against the mark scheme.
Yes — our predicted papers for Further Maths: Core Pure 1 are assembled from the topics that recur most in Pearson Edexcel AS Level exams and the topics you have practised least. They are a revision aid built from the specification, not leaked content.
Each answer is checked against the real Pearson Edexcel AS Level mark scheme, awarding method, accuracy and final-answer marks the way a real examiner would. You see exactly where marks were earned or dropped, with feedback you can act on.
Further Maths: Core Pure 1 on the Pearson Edexcel AS Level specification is aimed at Year 12. You can filter practice by year group and topic so the questions always match where you are in the course.
Yes. The Further Maths: Core Pure 1 content follows the current Pearson Edexcel AS Level specification, including all units and subtopics, so what you practise reflects what you will actually be examined on.
Yes — Further Maths: Core Pure 1 practice, past papers and marking are free during our early launch period. Subscription plans may be introduced later, but launch users get full access now.
You do not just get an answer to copy. Further Maths: Core Pure 1 marking guides you with hints, worked steps and mark-scheme-based feedback so you understand the method and pick up the marks yourself next time. Questions are tagged calculator and non-calculator so you can practise exactly the way each paper is sat.
Yes. Parents and tutors can see completed Further Maths: Core Pure 1 practice, accuracy, weak topics and overall exam readiness, making it easy to support revision and focus on the right areas.
Short, regular sessions beat occasional long ones. Aim for a few focused Further Maths: Core Pure 1 sessions a week, always finishing by marking your work so each session ends with clear next steps. The progress dashboard shows what to revise next.