United Kingdom · National Curriculum Attainment Targets
Year 13 Mathematics
A comprehensive study of advanced calculus, complex structures, and statistical modeling. This course prepares students for university level mathematics by bridging the gap between procedural fluency and abstract theoretical proof.
Algebraic Structures and Proof
Deepening the understanding of mathematical rigor through formal proof and the manipulation of complex algebraic series.
Mastering the logic of mathematical induction to prove statements for all natural numbers.
Decomposing complex rational expressions to enable integration and power series expansion.
Exploring composite, inverse, and modulus functions within real world modeling contexts.
Trigonometric Identities and Applications
Extending trigonometric knowledge to compound angles and reciprocal functions for solving complex geometric problems.
Analyzing secant, cosecant, and cotangent alongside their inverse counterparts.
Deriving and applying identities for sums and differences of angles.
Using harmonic forms to model wave patterns and periodic motion.
Advanced Calculus Techniques
Exploring sophisticated methods of differentiation and integration, including chain rule applications and integration by parts.
Differentiating equations where variables are linked indirectly or cannot be isolated.
Developing strategies for integrating products and composite functions.
Solving first order differential equations with separable variables to model change.
Vectors and Three Dimensional Space
Applying vector algebra to solve problems in three dimensional geometry involving lines and intersections.
Extending 2D vector concepts into the third dimension using i, j, k notation.
Expressing lines in 3D using vector and parametric forms.
Calculating angles between lines and finding points of intersection.
Advanced Statistics and Probability
Analyzing correlation, conditional probability, and Normal distributions in the context of hypothesis testing.
Using tree diagrams and formulas to solve complex probability problems.
Modeling continuous data and using the standard normal distribution for probability calculations.
Testing the significance of the product moment correlation coefficient.
Mechanics: Dynamics and Statics
Applying Newton's laws to friction, projectiles, and rigid bodies in equilibrium.
Modeling the path of objects moving under gravity in two dimensions.
Analyzing forces on objects on rough surfaces and slopes.
Calculating the turning effect of forces and conditions for static equilibrium.