Mathematics in Education and Industry
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Transcript of Mathematics in Education and Industry
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Mathematics in Education and Industry
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Warm Up…
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Warm Up…
Find all 4 real values of x that satisfy
x - 4(X-5) = 12
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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
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Warm Up
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Common symbols with which you should be familiar:
1
n
nnx
“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:
xarcsinx1sin equivalent statements for “inverse sine”, ie: “the angle
whose sine is …”
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Exact values:
Fill in the table!
sin cos tan
0
4
3
2
6
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Exact values:
Learn these (or know how to quickly derive them)
sin cos tan
0 0 1 0
1
1 0
23
4
3
2
23
6
21
21
31
212
1
3
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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.
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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
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AEA June 2007 Q3
(a) Solve, for 0 ≤ x < 2π,
02coscos xx(b) Find the exact value of x, x ≥ 0, for which
22arccosarccos
xx
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 …