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Mathematics in Education and Industry

Mathematics in Education and Industry. Warm Up…. 2. x - 4. (X-5) = 1. Warm Up…. Find all 4 real values of x that satisfy. AEA Session 1: Constructing a beautiful, clear, concise argument: the proper use of notation. how to write mathematics in “good style”

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Mathematics in Education and Industry

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  1. Mathematics in Education and Industry

  2. Warm Up…

  3. 2 x - 4 (X-5) = 1 Warm Up… Find all 4 real values of x that satisfy

  4. AEA Session 1: Constructing a beautiful, clear, concise argument: the proper use of notation • how to write mathematics in “good style” • understanding key symbols and using them correctly • ‘exact’ values • reasoning, conciseness and clarity

  5. Warm Up

  6. Common symbols with which you should be familiar: “implies”, “means that” – very useful for linking statements together and can help avoid the tendency to overuse the “equals” sign “not equal to” – hardly ever used by students but surprisingly useful “identically equal to” – so signifies an identity, something which is true for all values, as opposed to an equation “approximately equal to” “because” “therefore” “the SUM of” (“sigma”) – eg: equivalent statements for “inverse sine”, ie: “the angle whose sine is …”

  7. Exact values: Fill in the table!

  8. Exact values: Learn these (or know how to quickly derive them)

  9. AEA Specimen Paper Q4 8 Marks The notation in the printed answer looks daunting – it is meant to be! But this question relies only on standard co-ordinate geometry techniques.

  10. AEA June 2004 Q2 2 Marks 2 Marks This question makes use of the “sigma” notation and requires a fairly standard application of the binomial theorem

  11. AEA June 2007 Q3 (a) Solve, for 0 ≤ x < 2π, 5 Marks (b) Find the exact value of x, x ≥ 0, for which 6 Marks This question uses the “arc” notation, meaning “inverse cos” or “the angle whose cosine is ..” (alternative symbol cos -1 x); you should aim to answer the first part as concisely as possible whilst still maintaining clarity and reason. The second part is a bit more of a challenge …

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