Essential Mathematical Skills and Techniques Spring Semester 4, Exams of Mathematics

The document is an exam paper for MAS152: Essential Mathematical Skills and Techniques, offered during the Spring Semester at the University of Sheffield, School of Mathematics and Statistics. The exam is 3 hours long and is divided into two sections: Section A with 12 questions worth 3 marks each, and Section B with 8 questions worth 8 marks each. The paper covers a wide range of topics, including functions, inverse functions, logarithms, matrices, integration, partial differentiation, differential equations, and Laplace transforms. A formula sheet is provided, containing essential trigonometric identities, hyperbolic functions, series expansions, differentiation rules, and integration techniques. The exam requires students to justify their solutions fully and limits calculator use to basic arithmetic. The paper is comprehensive, testing both foundational and advanced mathematical skills.