Download - Techniques for Step

8/10/2019 Techniques for Step

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Techniques

In this section I will write comprehensive guides for both defensive and offensive exam

strategies. My guides have been written through my own practice of STEP questions and

through reading examiners reports. Ive used quotes from examiners reports where

possible to back up my findings.

This section has been published on the Stepping Stones Facebook Page for students to

download and so its been written in an informal manner for the target audience. A

candidate should refer back to this section for each solution because I have included much

detail about how to first attack a solution and make good use of first impressions to avoid

overlap in my written solutions.

Defensive Exam Strategy

Before you start working towards a STEP exam you need to realise that STEP questions are

very different to the questions youve experienced in A-level exams. STEP examiners

compare the way that the A-level system rewards even the most modestly able with high

grades to a manner reminiscent of a dentist giving lollipops to kids who have done little

more than been brave and seen the course through. Whilst A-level questions require a

modest subject knowledge and reward candidates more for memorising methods, STEP isdesigned to really test the mathematical ability of the candidate and requires a certain

amount of mathematical intuition.

In the exam you are given 13 questions and your best 6 answers will be used. Cambridge

once reported that a candidate who answers 4 questions well (15/20) can expect to receive

a grade 1 however this is obviously no longer the case. The grade boundaries for the 2010

STEP exams were:

Max Mark S 1 2 3 U

120 103 84 70 47 0120 105 79 64 40 0

120 78 56 46 29 0

Cleary answering 4 questions well scoring 15/20 each would gain the candidate 60/120

marks in total and they wouldnt even gain a grade 2 in either STEP I or STEP II. The

standard has changed over the years and now youre expected to answer all 6 questions to a

high standard. I suggest that you take 10 minutes at the start of the exam to give your first

impressions on every question and decide the best 6 to answer. You are given 3 hours to

finish the exam so if you take 10 minutes to go over the paper at the beginning you have

about 28 minutes to answer each question.


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You need to have your techniques nailed down to save you those precious minutes in the

exam. Refer back to this section when reading through my solutions because I have

included much detail about how to first attack a solution and make good use of first

impressions to avoid overlap in my written solutions.

Question Picking

Examiners advice on the front of the STEP exam papers is that students should concentrate

on no more than 6 questions but last year (2010) examiners reported that a sizeable

number of candidates ignored the advice and attempted more than six question. They

suggest that question-picking is an important skill to develop during STEP preparation.

When you get the paper, have a flick through it and try to get a feel for what each question

would involve. Write down your first impressions for each question as I have done below.This should help you to evaluate whether or not this question is a good one to choose to

answer. Make a list of 7 to 8 questions which you could answer well, this should only take

you about 10 minutes and will give you a real plan of attack for the paper.

Start answering the question you think you can smash out the park and work towards your

sixth most answerable question. If you get completely stuck on a question go on to your

next choice in the list and aim to have fully answered 6 questions by the end of the exam.

Misread the Question!

Youve been told it over and over again but every now and then youll still lose simple marks

just because you havent read the question properly. Heres an example:

Read the following passage:

FINISHED FILES ARE THE RE-

SULT OF YEARS OF SCIENTIF-

IC STUDY COMBINED WITH

THE EXPERIENCE OF YEARS

Now go back and count the number of Fs out loud. Do it once only.

Most people only count 3 Fs rather than the 6 that are actually there. Your brain doesnt

need to see every word to make sense of a passage but you do need to read everything in a

STEP question to get full marks!

Take your time to reread the question and understand what it is asking you. If you get stuck

half way through a solution then go back to the question and remind yourself what youre


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being asked to do. Its something youve been told over and over again but you can never

be reminded too many times to read the question properly.

Persistence Pays OffNotice that for some questions its possible to answer a later part of a question without

answering the earlier parts. Realising this when youre stuck on a part of a question can

help you get back on track and answer the later parts whilst you mull over the earlier part in

your head. Examiners reported in the 2010 exam that an awareness of this could have

helped some of the weaker students to gain vital marks when they were stuck; it is generally

better to do more of one question than to start another question.

Calm and Calculated

Examiners mark students for progress towards a complete solution so you should clearly lay

out all your working along the way. Even if you make a mistake on the answer you could

still get good marks for your method. You should also know that if you present the correct

answer to a question you will get full marks regardless of how you ended up there.

Whilst examiners arent marking you for neatness, your work needs to be clear and logical.

Make sure you can read your own writing. It might seem obvious but in the 2010 STEP I

exam examiners reported that many candidates at some point in the paper lost marks

through misreading their own writing. Take a step back from what youre writing and look

at things from the examiners point of view; can they see how each step follows on from the

other? Help the examiner out! If youre using integration by parts then tell them thats

what youre doing. Examiners advise that it is very good practice to explain why you are

doing the calculation you are, and to write sentences in English to achieve this, they go on

to explain that it also forces one to focus on the purpose of the calculations, and may help

avoid some dead ends.

What to learn

The STEP syllabus is very broad and considering you only need to answer 6 questions on the

STEP paper you shouldnt try to learn everything. Cambridge themselves say that depth

rather than breadth is what matters in terms of subject knowledge. Pick out your strongest

topics from the syllabus document

(http://www.admissionstests.cambridgeassessment.org.uk/adt/digitalAssets/121337_Specif

ication.pdf) and focus on these. If pure mathematics is your thing then theres no reason

not to put all your eggs in one basket and only revise topics from the pure syllabus. In my

opinion this is a better idea because with 8 pure questions youre more likely to landquestions on your best topics.


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Finishing touches

Make it clear to an examiner when youve finished a question. Not only does it help keep

your solutions organised and logical but it makes it look like you know what youre doing!

As you will see, I choose to write as required when Ive finished to signal the end of my

solution. Its up to you what you writeto end your solutions but keep it consistent and

clear.

Dont rest on your laurels

Expect STEP exams to get harder every year and dont relax just because you managed to

blast through the previous years paper. Examiners reported that many of the pure maths

STEP II 2010 questions were a little too accessible and lacked a sufficiently tough difficultygradient after scores were higher than expected. Grade boundaries reflected this oversight

and examiners suggested that next years questions may be expected to be a little bit more

demanding, but only in the sense that the final 5 or 6 marks on each question should have

rather more bite to them. Make sure youve revised enough that youconsistently perform

well.

Offensive Exam Strategy

An offensive exam strategy complements the defensive exam strategy and focuses on

examining the building blocks of a STEP question. To tackle the more difficult questions you

will need to really understand how a STEP question works.

Youll find that the questions in each level of STEP paper are very different but you might

actually discover that you prefer the questions in STEP III to those in STEP I. STEP I seems to

be much more numerical than the other papers and often involves some tedious and even

A-level like exercises. STEP III is much more demanding in terms of mathematical intuition

and requires a great level of insight to find each step in your solution. Its easier to make a

small error in your working and mess up your whole solution in STEP I than it is when it all

clicks in your head and find your result in STEP III. For this reason some candidates find

STEP III questions more logical and even more enjoyable.

Step by Step

STEP questions come in many different forms but a typically STEP question will be split into

parts with the latter part requiring you to use your previous results. In this way STEP


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questions really do work step by step. This type of question is most prominent in STEP III

and understanding how its put together can shrink the last hurdle of the question to a

manageable hop.

Look out for keywords such as Hence, Show further,and Show also. These words

should prompt you to look to use answers from a previous question to find a solution. It

might seem obvious but noticing this under exam conditions can prompt you to follow the

right path to the solution. If you get stuck on a later part, re-read the question and then go

back through your earlier solutions noting down expressions which may be useful. The last

questions might seem daunting but usually most of your method is already there in your

earlier solutions and so re-reading what youve written can sometimes ignite the spark that

you need. This is one of the most useful techniques you can employ in a STEP exam.

Also look out for when the examiner gives you the option of Hence, or otherwise show.

The method for using Hence will usually be the easiest but you do have the option of

using any method you want. On the flip-side note that when an examiner only writes

Hence you need to use your previous results to gain full marks

Practice makes perfect well almost

Youve heard it time and time again but there really is no substitute for practicing STEP

questions. Whilst working through past papers wont make you perfect it will certainly help

you to understand what is required of you in a STEP exam. Reading through my techniques

should give you an idea of what to expect but until you do it yourself you wont fully

appreciate how STEP differs from A-Level exams.


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