A-Level Further Maths Past Paper Solutions
High-definition video walkthroughs and formal mathematical derivations for every single question on the Edexcel GCE Further Maths May 2025 examination, led by specialist Tutor Sheefa.
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3x3 Matrices, Determinants, Inverses & Transformations
Master 3x3 matrix multiplication, determinants, singular matrix conditions, inverse matrix calculati...
Complex Numbers: Argand Loci, Cubic Roots & De Moivre's Proofs
Comprehensive guide to complex numbers in A-Level Further Maths: Euler's formula, modulus-argument a...
First & Second Order Differential Equations & Physical Modelling
Master analytical methods for solving 1st order differential equations using integrating factors, an...
Hyperbolic Functions, Maclaurin Series & Inverse Trigonometry
Comprehensive breakdown of hyperbolic functions $(\sinh, \cosh, \tanh)$, logarithmic forms of invers...
Polar Coordinates: Curves, Tangents & Area Integration
Understand polar curve sketching ($r = f(\theta)$ like cardioids, limaçons, and lemniscates), vertic...
Summation of Series, Method of Differences & Vectors in 3D
Techniques for evaluating finite series using standard summation formulas $\sum r, \sum r^2, \sum r^...
Edexcel May 2025 CP1 Core Pure Mathematics 1 (9FM0/01)
Matrices (Singular & Inverse Matrix)
Step-by-step worked solution for Edexcel Further Maths CP1 May 2025 Q1. Learn how to find when a 3x3 matrix is singular ...
Hyperbolic Functions (Exact Values)
Worked solution for Edexcel Further Maths CP1 May 2025 Question 2 on hyperbolic functions. Tutor Sheefa explains exact v...
Complex Numbers (Purely Imaginary Proof)
Edexcel CP1 May 2025 Question 3 full walkthrough: proving an expression is purely imaginary using complex conjugates and...
Second Order Differential Equations
Edexcel Further Maths May 2025 CP1 Question 4 worked solution. Learn how to solve non-homogeneous 2nd order differential...
Method of Differences (Summation Proof)
May 2025 CP1 Q5 step-by-step solution: Method of Differences summation proof. Watch Tutor Sheefa show how to telescope t...
Complex Numbers (Cubic Roots & Argand Diagrams)
Edexcel CP1 May 2025 Question 6 worked solution on cubic roots of polynomials with complex conjugates and Argand plane p...
Partial Fractions (Improper Fractions)
Edexcel CP1 May 2025 Q7(a) solution. How to handle improper rational expressions with algebraic division before partial ...
Definite Integration & Natural Logs
Edexcel CP1 May 2025 Q7(b) solution: Definite integration leading to exact natural logarithms. Step-by-step walkthrough ...
Differential Equations (Modelling & Integrating Factor)
Edexcel CP1 May 2025 Question 8 worked solution: First order linear differential equations with integrating factor and p...
Hyperbolic Functions & Integration
Full walkthrough of Edexcel CP1 May 2025 Question 9 on integrating powers of hyperbolic functions and hyperbolic substit...
Volumes of Revolution (Trigonometric Identities)
Edexcel CP1 May 2025 Question 10 worked solution: Calculating exact volumes of revolution rotated $2\pi$ radians around ...
Edexcel May 2025 CP2 Core Pure Mathematics 2 (9FM0/02)
Complex Numbers (Modulus & Argument Properties)
Edexcel CP2 May 2025 Question 1 worked solution: Modulus and argument properties of complex numbers explained step-by-st...
3D Vectors (Lines and Planes)
Edexcel CP2 May 2025 Question 2 worked solution: Lines and planes in 3D, intersections, and shortest distance calculatio...
Mathematical Induction (Matrix Powers)
Edexcel CP2 May 2025 Q3(a) proof by mathematical induction for matrix powers $M^n$. Full step-by-step deduction by Tutor...
Matrix Transformations & Combined Geometry
Edexcel CP2 May 2025 Q3 parts b, c, d: Linear transformations in 2D, combined matrix multiplication order, and invariant...
Complex Numbers (Equations & Argand Loci)
Edexcel CP2 May 2025 Question 4 worked solution: Argand loci equations, intersecting geometric regions, and minimum dist...
Simultaneous Equations (Planes & Sheaf)
Edexcel CP2 May 2025 Question 5 worked solution: Solving systems of 3 planes, determinant conditions for consistency, an...
Roots of Polynomials (Quartic Equations)
Edexcel CP2 May 2025 Question 6 worked solution: Roots of quartic equations, Vieta's formulas, and polynomial transforma...
Polar Coordinates (Vertical Tangents)
Edexcel CP2 May 2025 Q7(a) solution: Finding vertical tangents perpendicular to the initial line on a polar curve $r = f...
Polar Area & Cosine Rule Applications
Edexcel CP2 May 2025 Q7(b,c) worked solution: Polar area integration and applying the cosine rule to find chord lengths ...
Maclaurin Series & Hyperbolic Differentiation
Edexcel CP2 May 2025 Question 8 worked solution: Deriving Maclaurin series using successive differentiation of hyperboli...
Differentiation of Inverse Sine Functions
Edexcel CP2 May 2025 Question 9 worked solution: Differentiating inverse trigonometric functions (arcsin) and Leibniz's ...