The aims and objectives of this qualification are to enable students to , understand mathematics and mathematical processes in a way that promotes confidence, fosters enjoyment and provides a strong foundation for progress to further study , extend their range of mathematical skills and techniques , understand coherence and progression in mathematics and how different areas of mathematics are connected , apply mathematics in other fields of study and be aware of the relevance of mathematics to the world of work and to situations in society in general , use their mathematical knowledge to make logical and reasoned decisions in solving problems both within pure mathematics and in a variety of contexts, and communicate the mathematical rationale for these decisions clearly , reason logically and recognise incorrect reasoning , generalise mathematically , construct mathematical proofs , use their mathematical skills and techniques to solve challenging problems that require them to decide on the solution strategy , recognise when mathematics can be used to analyse and solve a problem in context , represent situations mathematically and understand the relationship between problems in context and mathematical models that may be applied to solve them , draw diagrams and sketch graphs to help explore mathematical situations and interpret solutions , make deductions and inferences and draw conclusions by using mathematical reasoning , interpret solutions and communicate their interpretation effectively in the context of the problem , read and comprehend mathematical arguments, including justifications of methods and formulae, and communicate their understanding , read and comprehend articles concerning applications of mathematics and communicate their understanding , use technology such as calculators and computers effectively and recognise when their use may be inappropriate , take increasing responsibility for their own learning and the evaluation of their own mathematical development