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German uses cases to convey information about the grammatical roles words play in a sentence. In English, this information is often conveyed using word order. The fact that German uses cases instead means th...

Photosynthesis is the process by which light energy and carbon dioxide are utilised by plants to produce sugars like glucose. Through two reaction cycles, the light-independent and light-dependent reactions....

Getting enough quotes memorised for the exam always seems like a huge task, but it's helpful to view quote-learning as similar to learning a language (but easier!): little and often is essentially the way fo...

f(-1) = (-1)^3 - (-1)*7 - 6 = -1 + 7 - 6 = 0 Hence f(x) = (x+1)(x^2 + ax - 6) Expand this out f(x) = x^3 + ax^2 - 6x + x^2 + ax - 6 = x^3 + (a+1)x^2 + (a-6)x -6 By comparing co-efficients a + 1 = 0 a - 6 = -...

Mathematical induction is a type of direct proof, where you can prove sequences or series. A good example of this is that we can prove 1 + 3 + 5 + .... + (2n-1) = n^2. There are 4 steps: 1. Prove the first c...