Further Mathematics (9231)

Cambridge International Examination (CIE) A-level

Further Mathematics (9231)

Further Pure Mathematics 1: (2023-2025 syllabus)

1.1 Roots of Polynomial equations
      Note (1.1). 

      Past Year Questions (1.1)

      Solved Questions (1.1)

      Video Lessons (1.1)

1.2 Rational functions and graphs

      Note (1.2). 

      Past Year Questions (1.2)

      Solved Questions (1.2)

      Video Lessons (1.2)

     

1.3 Summation of series
      Note (1.3). 

      Past Year Questions (1.3)

      Solved Questions (1.3)

      Video Lessons (1.3)

1.4 Matrices
       Note (1.4). 

       Past Year Question (1.4)

       Solved Questions (1.4)

       Video Lessons (1.4)

1.5 Polar Coordinates 

     Note (1.5)

     Past Year Questions (1.5)

     Solved Questions (1.5)

     Video Lessons (1.5)

1.6 Vectors
      Note (1.6). 

      Past Year Question (1.6)

      Solved Question (1.6)

      Video Lessons (1.6)

1.7 Proof by induction
      Note (1.7). 

      Past Year Question (1.7)

      Solved Questions (1.7)

      Video Lessons (1.7)

Exam Papers (these are designed based on 2023-2025 syllabus)
Model Test Paper 1 (Set 1)
Model Test Paper 1 (Set 2)
Mark Scheme and fully-worked solution (for the Model Test Papers above)

Further Pure Mathematics 2: (2023-2025 syllabus)

2.1 Hyperboc Functions
       Note (2.1). 

       Past Year Questions (2.1)

2.2 Matrices
       Note (2.2). 

       Past Year Questions (2.2)

2.3 Differentiation 
       Note (2.3) 

       Past Year Questions (2.3)

2.4 Integration
       Note (2.4) 

       Past Year Questions (2.4)

       Solved Questions (2.4)

2.5 Complex Numbers
      Note (2.5).

      Past Year Questions (2.5)

2.6 Differential Equations
       Note (2.6) 

       Past Year Question (2.6)

Further Mechanics: Notes: (2023-2025 syllabus)

3.1 Motion of a Projectile

      Note. 

      Past Year Questions (3.1)

3.2 Equilibrium of a Rigid Body

      Note. 

      Past Year Questions (3.2)

      Solved Questions (3.2)

3.3 Circular Motion

      Note 

      Past Year Questions (3.3)

      Solved Questions (3.3)

      Subtopic highlight: circular motion leading to projectile motion

3.4 Hooke’s Law

      Note. 

      Past Year Questions (3.4)

      Solved Questions (3.4)

3.5  Linear Motion Under a Variable Force

       Note. 

       Past Year Questions (3.5)

3.6 Momentum

      Note. 

      Past Year Question (3.6)

Further Statistics: (2023-2025 syllabus)

4.1 Continuous random variables
       Note (4.1). 

       Past Year Questions (4.1)

4.2 Inference using normal and t-distributions 
       Note (4.2). 

       Past Year Questions (4.2)

4.3 Chi-square Tests

       Note (4.3). 

       Past Year Questions (4.3)

4.4 Non-parametric Tests
       Note (4.4). 

       Past Year Questions (4.4)
4.5 Probability Generating Functions (notes). Past Year Questions (4.5)

Self-learning video lessons for all chapters are available here: Click here for video lessons

Fully explained past year questions (video) Click here

Full solution of past year questions (year by year): Click here

Further Pure: (2019 and previous syllabus)

a) Roots of Equations
b) Rational Functions