This document presents a comprehensive assignment solution for BTEC HND in Civil Engineering, focusing on analytical methods for engineers. The assignment covers a range of topics including solving simultaneous equations using the matrix method, sketching functions, and performing factorisation. It also delves into algebraic manipulations like partial fractions and algebraic division. The second task addresses practical applications, such as calculating forces in ropes, determining volumes, and finding room dimensions. Trigonometry, including sinusoidal waves and logarithmic relationships, is also explored. The third task involves calculus, focusing on finding gradients, optimisation problems related to poster design, and static force analysis. Finally, the assignment incorporates statistical concepts such as calculating mean and standard deviation, probability calculations involving different scenarios, and the application of probability to exam scenarios. The document includes an executive summary, table of contents, and references, providing a complete and detailed solution.