UCL Online STEP and AEA Preparation Sessions
Session 2: Using algebraic identities and solving equations
In this session, you’ll look at the importance of precision and care
in algebra, particularly when finding roots of equations. This will
include suggestions about how to set out working to minimise the
chance of mistakes. An example which illustrates this is the
following, without care it’s easy to miss some of the roots:
Describe fully the roots of sin2x = sinx
Particular care is needed when both sides of an equation are
squared in working. For example how might you solve this
equation?
3x +10 = 2 + x + 4
Advice will be provided about algebraic techniques including
spotting how to factorise expressions. Can you see how the
following factorises?
a2b + abc + a2c +ac2 + b2a +b2c + abc + bc2
Some standard but perhaps less well-known algebraic
relationships will be considered. The following identity, for
example, can be very useful:
a3 – b3 ≡ (a – b)(a2 + ab + b2)
The session will include discussion of associated examples from
STEP and AEA past papers.