Quadratic formula
x = (−b ± √(b² − 4ac)) / (2a) Pearson Edexcel Level 2 Award 8360
🔢 Pearson Edexcel Level 2 Further Mathematics Formula Sheet 2026
Consolidate the pure skills assessed in Edexcel’s Level 2 Further Mathematics award: proof-style algebra, rich coordinate geometry, matrices, and introductory calculus.
Level 2 Award Pearson Edexcel UK schools
Our formula sheets are free to download — save this one as PDF for offline revision.
Aligned with the latest 2026 syllabus and board specifications. This sheet is prepared to match your exam board’s official specifications for the 2026 exam series.
Confident Further Maths at GCSE Stage
Whether you sit the award alongside GCSE 1MA1 or as enrichment, this reference keeps key relationships visible so you can focus on problem structure and communication.
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Algebra, proof & number
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Geometry, trig & circles
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Matrices & linear systems
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Calculus & series
Algebra & functions
Quadratics, inequalities, simultaneous equations, and function ideas.
Discriminant
Δ = b² − 4ac Completing the square
x² + px = (x + p/2)² − (p/2)² Simultaneous (linear–quadratic)
Substitute; or eliminate; check solutions in context.
Composite function
(f ∘ g)(x) = f(g(x)) Inverse (simple cases)
Swap x and y; rearrange; state domain restrictions.
Topic Focus
Accuracy
- Show factorisation or formula clearly before decimal answers.
- Reject extraneous roots from squaring.
Coordinate geometry & circles
Lines, distances, midpoints, and circle equations.
Distance
√((x₂ − x₁)² + (y₂ − y₁)²) Midpoint
((x₁ + x₂)/2 , (y₁ + y₂)/2) Gradient
m = (y₂ − y₁)/(x₂ − x₁) Perpendicular lines
m₁ m₂ = −1 Circle
(x − a)² + (y − b)² = r² Tangent condition
Distance from centre to line equals radius.
Topic Focus
Sketching
- Mark centre and radius before algebraic work.
- Tangents from external point: equal lengths or right angle at point of contact.
Trigonometry
Identities, equations, sine/cosine rules, and area.
Pythagorean identity
sin² θ + cos² θ = 1 tan
tan θ = sin θ / cos θ Sine rule
a / sin A = b / sin B = c / sin C Cosine rule
a² = b² + c² − 2bc cos A cos A = (b² + c² − a²)/(2bc) Area
½ ab sin C Simple equations
Use identities; find all solutions in given interval.
Topic Focus
Ambiguous case
- Sine rule can yield two triangles — check with diagram.
- Use degrees or radians consistently.
Matrices
Addition, multiplication, determinants, and inverses (typically 2×2).
Matrix product
Row × column; check dimensions (m×n)(n×p) = (m×p).
Determinant
det [[a,b],[c,d]] = ad − bc Inverse
A⁻¹ = (1/det A) [[d, −b], [−c, a]] Linear systems
AX = B ⇒ X = A⁻¹B Topic Focus
Non-invertible
- det A = 0: no unique solution to AX = B in general.
- Show matrix multiplication is not commutative.
Differentiation
Gradients, tangents, and turning points.
Power rule
d/dx (x^n) = n x^{n−1} Constant multiple & sum
d/dx (k f + g) = k f′ + g′ Chain rule
dy/dx = dy/du · du/dx Stationary points
f′(x) = 0 Second derivative test
f″ > 0 minimum; f″ < 0 maximum (simple cases).
Topic Focus
Interpretation
- Gradient of tangent; rate of change with correct units.
- Sketch curve using turning points and intercepts.
Integration
Antiderivatives and definite integrals for area.
Antiderivative
∫ x^n dx = x^{n+1}/(n+1) + C (n ≠ −1) Definite integral
∫_a^b f(x) dx = F(b) − F(a) Area under curve
∫_a^b y dx Constant of integration
+C for indefinite integrals.
Topic Focus
Signed area
- Negative region below x-axis; split at roots if needed.
- Verify limits match the shaded region in the diagram.
Sequences & series
Arithmetic and geometric progressions.
Arithmetic nth term
a + (n − 1)d Arithmetic sum
S_n = n/2 (2a + (n − 1)d) Geometric nth term
ar^{n−1} Geometric sum
S_n = a(1 − r^n)/(1 − r), r ≠ 1 Infinite sum
S_∞ = a/(1 − r) for |r| < 1 Topic Focus
Modelling
- Identify first term and common difference/ratio.
- Check whether n is the number of terms or index of last term.
Number & proof
Indices, surds, and simple deductive reasoning.
Index laws
a^m × a^n = a^{m+n} (a^m)^n = a^{mn} Rationalising
Multiply numerator and denominator by conjugate surd.
Contradiction (structure)
Assume opposite; deduce impossible conclusion ⇒ original true.
Topic Focus
Presentation
- Each step should follow logically with reasons.
- State ‘assume …’ clearly in proof by contradiction.
How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Follow the SAMs
Use Pearson specimen and past papers to see how topics combine — Edexcel often rewards sustained reasoning across parts.
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Matrix habits
Always check dimensions before multiplying; verify inverses with A A⁻¹ = I on a calculator when allowed.
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Calculus meaning
Link derivatives to gradients and integrals to area — examiners like short interpretations after calculations.
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Core GCSE
Keep higher-tier GCSE fluency warm; further maths adds depth, not a separate basic toolkit.
Formula sheet FAQ
Quick answers about this free PDF, how to use it for exam revision, and how it relates to your official syllabus.
Is the Pearson Edexcel Level 2 Further Mathematics Formula Sheet 2026 free to download as a PDF?
Yes. This Tutopiya formula sheet is free to use and you can download it as a PDF from this page for offline revision. There is no payment or account required for the PDF download.
What Mathematics topics and equations does this formula sheet cover?
This page groups key Mathematics formulas in one place for revision. Pearson Edexcel Level 2 Award in Further Mathematics (8360) formula sheet for 2026: algebra, geometry, trigonometry, matrices, differentiation, integration, and series. Always cross-check with your official syllabus and past papers for your exam session.
Can I use this instead of the official exam formula booklet in the exam?
No. In the exam you must follow only what your exam board allows in the hall—usually the official formula booklet or data sheet where provided. This page is a revision and teaching aid, not a replacement for board-issued materials.
Who is this formula sheet for (Secondary)?
It is written for students preparing for assessments at Secondary in Mathematics, including classroom revision, homework support, and independent study. Teachers and tutors can also share it as a quick reference.
How should I revise with this formula sheet?
Work through past paper questions, quote the correct formula before substituting values, and check units and notation every time. Pair this sheet with timed practice and mark schemes so you see how examiners expect working to be set out.
Where can I get more help with Mathematics revision?
Explore Tutopiya’s study tools, past paper finder, and revision checklists linked from our tools hub, or book a trial lesson with a subject specialist for personalised support alongside this formula reference.
Strengthen Level 2 Further Maths
Tutors can align practice to Edexcel’s 8360 style: structured working, efficient methods, and exam timing.
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Aligned with common themes in the Pearson Edexcel Level 2 Award in Further Mathematics (8360); confirm final topic lists against the live specification.
Not a substitute for the official formula booklet or any materials issued in your examination.