This book has two aims. The general aim is to help bridge the gap between school and university mathematics. You might wonder why such a gap exists. The reason is that mathematics is taught at school for various purposes: to improve numeracy; to hone problem-solving skills; as a service for students going on to study subjects that require some mathematical skills (economics, biology, engineering, chemistry—the list is long); and, finally, to provide a foundation for the small number of students who will continue to a specialist mathematics degree. It is a very rare school that can achieve all this, and almost inevitably the course is least successful for its smallest constituency, the real mathematicians. The more specific aim is to help you to prepare for STEP or other examinations required for uni- versity entrance in mathematics. To find out more about STEP, read the next section
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