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Advanced Level (A-Level) Mathematics is a qualification of further education taken in the United Kingdom (and occasionally other countries as well). In the UK, A-Level exams are traditionally taken by 17-18 year-olds after a two-year course at a sixth form or college.
Further Mathematics, as studied within the International Baccalaureate Diploma Programme, was a Higher Level (HL) course that could be taken in conjunction with Mathematics HL or on its own. It consisted of studying all four of the options in Mathematics HL, plus two additional topics. Topics studied in Further Mathematics included: [9]
A 2007 report by Robert Coe compared students' scores in the ALIS ability test with equivalent grades achieved in A-level exams over a period of approximately 20 years; he found that students of similar ability were achieving on average about 2 grades higher than in the past. In the case of maths it was nearer to 3.5 grades higher. [42]
To compute the integral, we set n to its value and use the reduction formula to express it in terms of the (n – 1) or (n – 2) integral. The lower index integral can be used to calculate the higher index ones; the process is continued repeatedly until we reach a point where the function to be integrated can be computed, usually when its index is 0 or 1.
Edexcel (also known since 2013 as Pearson Edexcel) [2] is a British multinational education and examination body formed in 1996 and wholly owned by Pearson plc since 2005. It is the only privately owned examination board in the United Kingdom. [3] Its name is a portmanteau term combining the words education and excellence.
More compact collections can be found in e.g. Brychkov, Marichev, Prudnikov's Tables of Indefinite Integrals, or as chapters in Zwillinger's CRC Standard Mathematical Tables and Formulae or Bronshtein and Semendyayev's Guide Book to Mathematics, Handbook of Mathematics or Users' Guide to Mathematics, and other mathematical handbooks.
Vieta's formulas can equivalently be written as < < < (=) = for k = 1, 2, ..., n (the indices i k are sorted in increasing order to ensure each product of k roots is used exactly once). The left-hand sides of Vieta's formulas are the elementary symmetric polynomials of the roots.
Spaces within a formula must be directly managed (for example by including explicit hair or thin spaces). Variable names must be italicized explicitly, and superscripts and subscripts must use an explicit tag or template. Except for short formulas, the source of a formula typically has more markup overhead and can be difficult to read.