Mathematics — B-Level
Eleven advanced chapters — from polynomial theorems through differentiation.
Chapter 1
The Remainder Theorem and the Factor Theorem
Dividing polynomials by long division and synthetic division, and using the remainder and factor theorems to find and confirm roots without full division.
Chapter 2
The Binomial Theorem
Pascal's triangle and binomial coefficients, expanding small binomial powers, and the general binomial theorem for finding any term or coefficient directly.
Chapter 3
Elementary Functions and Transformations
The core family of functions — linear, cubic, reciprocal, square-root and exponential — and how they translate, reflect, stretch and compress.
Chapter 4
Sequences and Series
Sequences versus series, arithmetic progressions and series, geometric progressions and series, and the surprising finite sum of an infinite geometric series.
Chapter 5
Matrices
Matrix notation, addition, subtraction, scalar and matrix multiplication, determinants, and the inverse of a 2×2 matrix for solving simultaneous equations.
Chapter 6
Statistics
Measuring spread with range, IQR, variance and standard deviation; cumulative frequency tables and the ogive; and scatter diagrams and the correlation coefficient.
Chapter 7
Circles
Tangent-radius perpendicularity, the two-tangent theorem, the tangent-chord (alternate segment) theorem, and proving four points are concyclic.
Chapter 8
Areas of Similar Triangles
How the area of similar triangles scales with the square of the side ratio, and how that contrasts with the (linear) scaling of perimeter.
Chapter 9
Introduction to Vectors
Geometric vectors and the Triangle Law, using vectors to prove classic geometry results, position vectors, and two-dimensional (column) vector notation.
Chapter 10
Trigonometry
An advanced extension of Level A trigonometry — ratios of any angle, negative angles, the basic acute angle, further identities, the Law of Sines and Cosines, bearings, and triangle area using sine.
Chapter 11
Methods of Differentiation
Limits, the derivative as a rate of change and as the limit of the difference quotient, the core differentiation rules (power, sum/difference, product, quotient, chain), and implicit differentiation.