UPDATE: From 2024, OCR will be replacing CAAT as the official testing body for STEP. The STEP 2 and 3 test papers will not be changing dramatically. For more information on scoring and important dates, please see the OCR website.
The STEP 2 syllabus is based on all of A-level Maths and AS-level Further Maths. Common topics in STEP 2 include:
- Polynomials
- Elementary number theory
- Vieta’s Formulas and equating coefficients
- Complex numbers
- Proof by induction
- Euclidean Geometry
- Coordinate Geometry
- Sequences defined iteratively
- Integration by parts and by substitution
- Differential equations
- Function composition
- Curve sketching
- Trigonometry
- Complex numbers
- Inequality manipulation
- Vector geometry and matrices in 2D
- Projectile motion
- Pulleys
- Collisions
- Equilibrium and friction
- Elementary probability
Five top tips for STEP 2
Study the problem progression
There’s no multiple choice in STEP. Furthermore, all the problems consist of multiple parts, often related. Results and techniques are usually developed throughout the question, and a key skill for both STEP papers is reflecting on the methods you’ve used and identifying how you can adapt them to solve later parts. Here’s a STEP 2 example question from last year:
The first part introduces a technique: evaluating an indefinite integral by integrating one of the terms by parts. What then happens is a convenient cancellation where the other term disappears. For the second part you should consider this technique and how it could be applied here. We would like there to be two terms, one of which we will integrate by parts. The most natural way to do this is to expand the brackets. Then we have to pick which term will be integrated by parts. This term will have to integrate to cancel out the other one. One way to do this is to integrate the term twice which will yield a
term which will cancel as desired.
Take time to reflect after you solve a problem
Finally, the most important part of the problem-solving process which students often miss out on is reflection on the problem once it’s solved. Here are some key questions you should ask yourself:
- What are the question components and their corresponding solution components?
- What new techniques are developed throughout the question?
- How are earlier parts connected to later parts?
- What existing methods that I already knew about were used in unconventional ways?
- Can I apply one of these techniques to a slight variation of the problem?
- Is this question similar to other questions (possibly non-STEP) that I’ve seen before?
- Are there alternative solution methods? (You may want to check the mark schemes for this)
- Are there parts of the STEP 2 syllabus that I should look over again to ensure I understand them fully?
Work through lots of past papers to figure out what questions you are best at
You get free choice of the 6 questions you want to answer. You can choose to do more than 6 but it’s highly recommended that you focus on just 6 questions and do those as best as you can. Another STEP 2 tip is working through lots of STEP past papers; you’ll get a feel for what your strengths and weaknesses are. For example, if you’re good with vector geometry questions, which tend to come up on Q7 or Q8, then you can plan to do that question first if it comes up.
Alternatively, perhaps you find that you’re struggling with Statistics and Mechanics a lot more than with Pure Maths questions. Then you might want to consider focusing solely on Pure Maths questions and doing 6 of those in the exam. Firstly, at the start of the exam, take a look through the paper and pick out some preferred questions that look like they’re more in your comfort zone. This will then allow you to secure some easier marks towards the start.
STEP 2 timing tips and how to get ‘unstuck’
You have 3 hours to do 6 questions, which means on average you should be spending 30 minutes per question. Moreover, you may even want to spend around 25 minutes per question to give yourself time at the end to go over your work and reattempt any tricky parts.
What’s even more important is how not to lose excessive amounts of time on difficult question parts. When working on a hard problem it can be easy to think yourself into a rut. If you notice that you’re going in circles or not really getting anywhere, try to remind yourself of the different methods that are on the table, e.g. algebraic, geometric, calculus, as well as results and techniques that have been developed in earlier parts. Think about what those techniques and results are really saying and what they can enable you to do. Sometimes a small shift in perspective is all that’s needed to find a path to a solution.
If you’re still struggling to come up with ideas then don’t dwell on the question for too long. Move to the next part and give your subconscious mathematician some time to process the problem. Then later when you revisit the problem you’ll be able to see it with fresh eyes, which will often help you find a new approach.
Use available STEP resources
There are lots of great resources for STEP 2 preparation that can help you if you’re stuck. These include worked solutions on the STEP and MEI websites and a guide dedicated to STEP preparation. Read our article ‘What are the best STEP resources‘ to boost your STEP preparation. You can also read our article on ‘STEP 3 Top Tips‘.
Still got a question? Leave a comment