Mathematics in Education and Industry

Warm Up…

Find all 4 real values of x that satisfy x - 4 (X-5) = 1 2

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

Warm Up

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” “therefore” “because” “the SUM of” (“sigma”) – eg: equivalent statements for “inverse sine”, ie: “the angle whose sine is …”

Exact values: Fill in the table! sincostan 0

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

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.

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

AEA June 2007 Q3 (a) Solve, for 0 ≤ x < 2π, (b) Find the exact value of x, x ≥ 0, for which 5 Marks 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 …