Mathematics in Education and Industry

Warm Up…

Warm Up…

Find all 4 real values of x that satisfy

x - 4(X-5) = 12

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:

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 …”

Exact values:

Fill in the table!

sin cos tan

0

4

3

2

6

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

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

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,

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 …