Retired Teacher

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 Useful Background  By Chris Patterson, Head of Maths, Kainos International School Some useful ideas in the background while doing integration problems. Vocabulary Base: a factor in a multiplication. For {z\ =\ ax}^p\times\ {by}^q, x and y are bases. Power: the number of times the base is a factor in a multiplication calculation. For  {z\ =\ ax}^p\times\ {by}^q, p and q are powers of their respective bases. Instead of ‘power’ we can say ‘exponent’, ‘index’, or ‘logarithm’.  Coefficient: a constant multiplying a variable term. For  {z\ =\ ax}^p\times\ {by}^q, a and b are coefficients of their respective bases. Factoring and indices (or powers): 60\ =\ 15\ \times\ 4\  60\ =\ 5\ \ \times\ 3\times\ 2\ \times\ 2 60\ =\ \ 2^2\times\ 3^1\times\ 5^1\ \  The power counts the number of times the base is used as a factor. If a factor x is used once, its power is 1.  If a factor is not used, its power is 0.  For example, 11 is not a factor of 60.  T...