Mathematics Unit P1

Course Overview

This unit lays the foundation for advanced mathematical study by introducing essential algebraic, trigonometric, and calculus concepts. Students develop fluency in manipulating algebraic expressions, solving equations, and interpreting graphs.

The course builds problem-solving skills through applications in coordinate geometry, sequences, and series. Trigonometric identities and equations are introduced alongside exponential and logarithmic functions, preparing students for calculus.

Differentiation and integration are covered at an introductory level, with emphasis on understanding their geometric and physical interpretations. By the end, students will be able to model and solve problems in a variety of contexts, using precise mathematical reasoning.

Key Topics:

• Algebra: polynomials, factor theorem, remainder theorem, inequalities
• Functions: domain, range, transformations, composite and inverse functions
• Coordinate geometry: straight lines, gradients, midpoints, distance formula
• Sequences and series: arithmetic and geometric progressions, sum formulae
• Trigonometry: sine, cosine, tangent graphs; basic identities; solving equations
• Exponentials and logarithms: laws of logs, natural logarithm, solving equations
• Differentiation: gradient functions, tangents, normals, stationary points
• Integration: indefinite and definite integrals, area under curves