Explicit Mathematics

OG AKINTUNDE, OS OGBEIDE

269 pages

Mathematics rewards understanding far more than memory. A candidate who knows why a method works can adapt it to any variation the examiner invents; a candidate who has only memorised a worked example is lost as soon as a number or a word changes. Explicit Mathematics was written to build that understanding, and then to convert it into speed and accuracy under examination conditions. It is designed primarily for candidates preparing for the Unified Tertiary Matriculation Examination (UTME) conducted by JAMB, and it also serves senior secondary school students preparing for WAEC and NECO, as well as teachers and tutors who need a rigorous, examination focused reference. The book follows the five sections of the current JAMB Mathematics syllabus, Number and Numeration, Algebra, Geometry and Trigonometry, Calculus, and Statistics, in thirty-three chapters. Every topic and objective in the syllabus is covered, and nothing outside it is allowed to crowd the pages. The syllabus coverage table that follows shows exactly where each item of the syllabus is taught. Each chapter opens with the syllabus objectives it serves, a JAMB Watch panel showing how often the topic appears and what is asked most, and a short Before You Start box recalling the earlier skills the chapter needs. The essential concepts are then developed concisely, with key results collected in formula boxes. The heart of every chapter is its Question Types: the handful of question patterns that JAMB repeats year after year, each with a "Recognise it" clue and a numbered recipe of steps. Every solved past question is set out in the same numbered steps, so that a student who finds mathematics difficult can follow the reasoning one line at a time and then copy the method. After each question type comes a Try These set of past questions of the same type, for the student to work alone. Each chapter closes with an Exam Focus panel, a list of Common Errors and JAMB traps, a set of revision questions and a chapter summary of formulae for quick recall. The past questions are drawn mainly from the UTME (including the former UME and the PCE paper), with WAEC and NECO questions added where they strengthen a topic and give variety. Nearly two thousand past questions appear in the book, many of them going back to 1978, because JAMB repeats its question patterns far more often than candidates realise. The year and question number are shown only where the source is reliable. Questions that were defective, ambiguous or obsolete have been corrected or excluded, and every answer has been independently recomputed. All equations are set as editable mathematics and all diagrams are drawn in clear black and white. To use the book effectively, study a section, read the question-type recipe, follow the solved questions step by step, and then attempt the Try These set before looking at the answers. Work the revision questions under time pressure (about one minute per question) and check them against the consolidated Answers and Explanations at the back of the book, where every Try These and revision question is fully explained. Use the explanations to diagnose errors, not merely to check letters: keep a list of the questions you miss, return to the relevant question type and try those questions again after a few days. Our hope is that Explicit Mathematics will raise examination scores and, more importantly, develop the clear and disciplined reasoning through which mathematics becomes a coherent and enjoyable subject.