1. **Problem 1: Differentiation from First Principles** State the problem: Find the derivative of the function $f(x) = x^2 + 3x$ using first principles. 2. **Problem 2: Integration by Substitution** State the problem: Evaluate the integral $$\int (2x+1)^5 \, dx$$ using substitution. 3. **Problem 3: Solving Quadratic Inequalities** State the problem: Solve the inequality $$x^2 - 5x + 6 < 0$$ and express the solution set. 4. **Problem 4: Binomial Expansion** State the problem: Expand $$(1 + 2x)^4$$ using the binomial theorem. 5. **Problem 5: Parametric Equations** State the problem: Given the parametric equations $$x = t^2 + 1$$ and $$y = 2t - 3$$, find $$\frac{dy}{dx}$$ in terms of $t$. 6. **Problem 6: Arithmetic Series** State the problem: Find the sum of the first 20 terms of the arithmetic series where the first term is 3 and the common difference is 5. 7. **Problem 7: Trigonometric Identities** State the problem: Prove the identity $$1 + \tan^2 x = \sec^2 x$$. 8. **Problem 8: Vectors** State the problem: Find the magnitude and direction of the vector $$\mathbf{v} = 3\mathbf{i} - 4\mathbf{j}$$. Each problem covers key topics from AS Level Edexcel Pure Maths chapters 12 to 14, including differentiation, integration, inequalities, binomial expansion, parametrics, sequences and series, trigonometry, and vectors.