- Algebra and Curves :
developing a deep understanding of polynomial factorization methods is essential.
Learning formulae without an understadning doesn’t work very well on STEP.
- Trigonometry and Functions :
Trigonometry is the number one topic that students are struggling with.
School maths doesn’t generally currently provide a good basis for trigonometry on STEP.
One things that makes Trig a harder topic for STEP is that it involves:
a lot of learning and procedures to follow, as well as difficult linking and problem solving.
Also, Trigonometry is a good way of starting to understand Function theory, which is being increased on STEP.
[sometimes it’s just a case of ‘knowing’ what you don’t know’ (not always obvious), rather than thinking you can’t do a question].
- Calculus :
Learning similar methods together and practicing mixed up integral questions is very useful
A thorough knowledge of all standard integration techniques is necessary for integration on STEP.
- Number theory :
Euclid’s simple proofs, and related methods are useful to learn for Number theory.
Learn, understand and extend Euclid’s proofs that ‘sqrt(2) is irrational’ and there are an ‘Infinity of Primes’.
‘Proof by contradiction’ is used a lot in Number theory, as well as ‘modulo’ and set-theoretic ideas.
It’s all about ‘Primes’.
Unique Prime Factorization in the Natural Number, as shown by Euclid
demonstrates contradictions in Logic when the Natural numbers are viewed as infinite.
- Logic and Function theroy :
Function theory is often an ‘unseen’ idea behind a question, or the ‘theme’ of a question.
Inequalities and application of non one-to-one functions, such as trigonometric functions, can test the logic of function theory.
- Sequences and Series :
Learning general sequence relationships, rather than just specfic is useful for STEP.
Get familiar with the ‘Fibonacci’ Series.
- Probability and Counting :
It is important to have an understanding of ‘Combinatorics’ and factorial algebra.
This comes up in pure maths, as well as probability.
STEP Vector questions are the only questions I have so far found that actually ensure you have a good understanding of vectors, as opposed to just learning methods, which are likey to get forgotten at Degree, whilst this is one of the most important pure topics to understand for a degree.
Vectors are also imporotant to understand for STEP III topics such as complex numbers.
One of the main issues in Vector questions is not understadning the scalar product, nor knowing the rules of it, and some issues in understanding vectors arise from lacking a proper grounding in coordinate geometry.
- Maclaurin and Taylor Series :
It’s useful to learn this topic as early as possible for STEP, as it links many important ideas.
Common differentiable and continuous fucntions that students need to sketch at this level are themselves Power series, and differentiation of simple continuous functions is actually based on differentiation of these powers of x,
( eg. ‘Sin x ‘, ‘Cos x’, ‘Exp x’).