1. Linear Algebra & Systems of Equations | Unique Solutions & Geometric Interpretation – Finding values of \\\\( k \\\\) ensuring a unique solution and interpreting it geometrically.

2. Differential Equations & Parametric Curves | Second Derivative Calculation – Deriving and expressing the second derivative of a parametric function.

3. Surface Area of Revolution & Hyperbolic Substitutions | Evaluating Integrals – Using substitutions to compute the surface area integral of a given curve.

4. Eigenvalues, Eigenvectors & Matrix Inversion | Characteristic Equation & Inverse Calculation – Determining eigenvalues, eigenvectors, and calculating the inverse matrix.

5. Numerical Integration & Approximation | Error Bounds for Definite Integrals – Applying upper and lower sum methods to approximate an integral with error estimation.

6. Complex Numbers & Recurrence Relations | Trigonometric Identities & Integral Reduction – Expanding powers using De Moivre’s theorem and deriving recurrence relations for definite integrals.