Exam season is over, and most of us are winding down to enjoy the summer break. I have a few slots left for new starters in September so please get in touch if you're local and looking for Maths tuition! One of my main tasks over the summer is going to be getting fully up to speed on the new A level specification, which is prescribed by Ofqual and so is the same across all exam boards, although of course there will be small differences. The bulk of it is similar to the old one and there isn't supposed to be any increase in difficulty but, as with the new GCSE, there's more emphasis on problem solving and proof - and also on mathematical modelling. Decision Maths is completely disappearing (though it will still feature in some Further Maths specifications) and the applied maths element - still a third of the overall total - will consist only of Statistics and Mechanics. The big change in Statistics is the use of "large data sets" which vary depending on which exam board you're with. The student is expected to be familiar with the data for their particular board, and a variety of ways of analysing it. The grade scale will be unchanged, with the lowest pass grade being an E and the highest at A*. There will still be an AS level available, but many schools/colleges are not entering their students for it, because it costs money and doesn't count towards the A level result. An AS level is now worth 40% of an A level in terms of UCAS points. (There will no longer be any such thing as an A2 level.) If you want to keep your Maths skills ticking over during the summer, regardless of whether you're just finishing Year 9 or about to go on to A-level, take a look at Corbettmaths 5-a-day. Each day, answer the questions for the grade level that you're working at - or try the next level up - and then check your answers against the worked solutions. This is a great resource to keep you up to speed on a wide range of topics throughout the year, even though your lessons at school are likely to be focusing on a particular topic for a week or two at a time.
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Well, GCSE Paper 1 is out of the way, and there are a couple of weeks until Paper 2, with Paper 3 just a few days after that. Although nobody can predict with any certainty what will be on the remaining papers, it makes sense to focus on the topics and skills that haven't already been tested, and of course these will vary from one board to another and between the Foundation and Higher Tiers.
Starting with the Edexcel GCSE, the amazing people at JustMaths have put together sets of practice papers, complete with examiner reports and mark schemes, covering the stuff that wasn't in the first paper. You can find them at http://justmaths.co.uk/2017/05/26/best-guess-papers-yeah-right/ This post on Twitter by the equally amazing Corbettmaths lists the topics not yet tested by AQA; the videos referred to can be found at https://corbettmaths.com/ and the promised papers are now online at https://corbettmaths.com/2017/05/28/aqa-papers-2-3-predictions-2017/. The Edexcel IGCSE is a little easier to predict as it's an older spec and there are only two papers. Key topics that have been predicted for Higher Paper 2 are: - Circle theorems
- Histograms
- nth term of a sequence
- Inequalities
- Differentiation (calculus)
Thanks go to the folks on the Facebook "Maths Tutors UK" group for the info in this post! As most of my tutees are acutely aware, the exams are now almost upon us. Here are a few tips to help you get maximum marks in whatever Maths exams you may be sitting. My marking experience is mostly on the AQA A-level so that's the basis of my advice, but it holds true for most Maths exams.
- Look at how many marks are available and divide your time accordingly. For example, an AQA A-level module paper has 75 marks available and 90 minutes allowed, so 1 mark per minute is a good rate to aim for, leaving you with a bit of time to go back and check your answers, or wrestle with the tricky bits, at the end.
- You can answer the questions in any order you like, so start with the ones that you feel most confident about.
- Make sure you read each question carefully and answer it - don't just assume that it's asking you to do exactly what you've practised doing in the past!
- Make sure you answer each question in the correct space - if you have lots of extra space on the pages for Q5 but need more space for Q4 then ask for more paper, DON'T write your Q4 answer on the Q5 pages!
- If a question has several parts then number each part clearly.
- If you can't do the first part of a question then don't be afraid to try the rest of it; the first part will often be a "Show that" which provides you with an answer that you wil use later in the question, and sometimes the question parts are completely independent of each other.
- Write down ALL your working, explaining what you are doing so that it's easy for the examiner to follow and give you marks. This is especially important on "Show that" questions!
- A sketch diagram can often help you to visualise what's going on and see what needs to be done.
- Give final answers to a sensible degree of accuracy, but use extra significant figures throughout your working. 3 s.f. is usually a safe bet for your final answer, though if the original information you were given was only to 1 s.f. then your answer can only really be accurate to 1 s.f. too. If the question asks for an exact value then give your answer as a fraction or a surd or in terms of pi - a decimal is only OK if it's exact.
- If the question says "Show that..." or "Verify that..." then you should always finish your answer with a statement that you have shown what you were asked to show. If the question says "Show that x+2 is a factor of f(x)" then you should end your answer with "so x+2 is a factor of f(x)".
- "Show that..." means you should work out the answer for yourself and end up with the answer given. You won't normally get full marks if you try to do it by working backwards from the answer. With "Verify that..." questions, on the other hand, it's fine to just plug in the value given and show that it works. Don't forget to finish with a statement! (If you're doing AQA C2 then you might find it helpful to have a look at the "June '11 Show Thats" document in my Resource Bank - see link on home page. That particular paper had lots of this type of question on it and this document shows you how carefully you have to present your answers to get full marks on them.)
- Don't cross anything out unless you DEFINITELY don't want the examiner to look at it. If you think you've messed up an attempt at a question then box it off and make another attempt before you cross out the first one. Even if you do cross something out, just put a line through it - don't obliterate it so that it's illegible, as occasionally you may still get a mark or two if you've done something correctly and haven't got those particular marks for your (otherwise largely correct) replacement attempt.
- Exam boards vary on how they mark multiple attempts at the same question; at AQA A-level the current policy is to mark every attempt and give credit for the best one, so it's best to leave all your answers un-crossed out. Until about four years ago, though, the policy was to average the marks and round down to the nearest whole number - so if one attempt got 2 out of 4 and another got 3 then they'd average it to 2.5 and round down to 2.
- Above all, don't panic! If anxiety starts to get on top of you then see if you can calm yourself down by slowing down your breathing or concentrating on counting backwards in 3s from 300. You can find more tips on dealing with exam stress here. If you don't do as well as you hoped in the exam then it's not the end of the world; true, you may end up having to adjust your life plan, but in the long run that may well turn out to have been a good thing.
I've had the responses in from my existing tutees and am now able to offer the following sessions to anyone else who would like to take advantage of them:
Wed 12th April 10.00-11.30 Trigonometry (Geometry) - 2 places leftSOHCAHTOA, sine rule, cosine rule, triangle area, trig graphs, arcs and sectors Fri 14th April (Good Friday) 10.00-11.30 Grouped data (Statistics) - 2 places leftEstimating averages & spread, cumulative frequency curves & box plots, histograms Fri 21st April 10.00-11.30 Probability (Statistics) - 1 place leftProbability basics, Venn diagrams and set notation, listing strategies, 2-way tables, tree diagrams, conditional probability, independent events The cost is £20 per student per session (maximum of 4 in a group). If you'd like to join any of these sessions then please use the contact form on this website to get in touch. I will need the following information: - Student name, school, exam board and target grade
- Which session(s) the student would like to attend (it would also be helpful if you could tell me which particular aspects of the topic he/she is most concerned about)
- Parent/guardian name, address, email and phone number (preferably mobile).
During the Easter holidays, I will be offering a series of small group sessions, each lasting 1½ hours and targeting a particular area of the Higher GCSE specification. Maximum class size in each case will be 4 and the fee will be £20 per student.
The sessions will cover the following areas (or as much of them as we have time for): Wed 12th April 10.00-11.30 Trigonometry (Geometry)SOHCAHTOA, sine rule, cosine rule, triangle area, trig graphs, arcs and sectors Fri 14th April (Good Friday) 10.00-11.30 Grouped data (Statistics)Estimating averages & spread, cumulative frequency curves & box plots, histograms Wed 19th April 10.00-11.30 Vectors (Geometry)Vector terminology, adding/subtracting vectors, multiplying by a scalar, using vectors in geometric arguments and proofs Fri 21st April 10.00-11.30 Probability (Statistics)Probability basics, Venn diagrams and set notation, listing strategies, 2-way tables, tree diagrams, conditional probability, independent events Each session will run subject to a minimum of 2 students signing up; if I only get a single taker for a session then I’ll offer the option of a normal 1-to-1 session at £30 for an hour instead. Existing Year 11 tutees (including those on my waiting list) will be given priority, but if anyone else would like to come along then they’ll be welcome to do so if there are still spaces available once existing tutees have had an opportunity to claim their places. If you would like to join one or more of these sessions then please send me an email, or use the contact form on this website, to let me know which ones you’d like to sign up for. For newcomers, I will also need the following information: - Student name, school, exam board and target grade
- Parent/guardian name, address, email and phone number (preferably mobile)
For a good few years I've been a member of the TES website, a fantastic source of teaching materials, very many of them shared for free despite the site's increasingly strong encouragement to its contributors to charge for their resources. I've shared a number of my own resources on there; one that has proved particularly popular, with over 20,000 downloads to date, is this PowerPoint on transformations for GCSE (opens in a new window). I'm also starting to build up a resource bank accessible from my own website, primarily for my tutees' reference, but open to anyone. You can find it using the button below. There's not a huge amount on there at the moment, but it's a start. Where I've used others' resources, I've tried to give credit - for example there's a set of GCSE exam revision booklets with new-style exam questions grouped by topic, created by Pixi of PixiMaths fame, which I've been using extensively as homework for my Year 11 tutees. I've made a few minor tweaks but they're basically her work. In other news, I'm now up to 14 regular tutees and not taking on any more for the time being. Half them are doing GCSE exams this summer, and most of the others are doing A-level (either AS or A2) - but I have one who's doing an American qualification called the GRE which appears at first glance to be pretty straightforward but actually serves as a hurdle to entry to a number of very prestigious universities in various parts of the world and involves some very challenging questions under extremely tight time constraints.
Rehearsals for Pirates are going well (tickets available from www.stamps-solihull.co.uk, £14 including a fish-and-ship supper, and selling quickly!) and from initially being cast as a pirate and policeman, I've now been promoted to pirate and maiden (despite being a little long in the tooth for such a role - but since the entire plot requires considerable suspension of disbelief, that's not too major an issue), which means a lot more choreography to remember. All good fun! Well, things have really taken off: from just starting to advertise over the Christmas holidays, I've now got nine regular tutees signed up and another four or five possibles in the pipeline. I never thought I'd be deactivating my ads before the end of January, but that's what I've just done. On top of that I've joined a musical theatre society (going to be in a production of The Pirates of Penzance at the end of March, just as a chorus member) and spent most of the last two weeks doing full-time cover work at my old college, so it's been a busy time!
My nine students, who are studying at eight different schools/colleges, range from struggling Year 10s to Year 13 students aiming for a high grade at A2 level, with a roughly even split between GCSE and A-level, and I've also been in discussions about taking on a couple of adult learners who are studying for Level 2 Maths qualifications. Some tutees are doing term-time only; others also want to continue through the school holidays. All so far have been looking for 1-to-1 tuition, which of course means they get a much more personalised approach than they'll get at a tuition centre. Of course, this is the busiest time of year for tuition enquiries - when students in Years 11, 12, and 13 have just got their mock results back and a family decision has been made that they could benefit from a bit of extra support to help boost their grades in the exams in May and June. Once those exams are over, I expect demand to slow down significantly, which will free up time for my exam marking and other activities. But at the same time, I hope, word of mouth will bring in a few enquiries for next academic year. When I am approached by a new student who is working towards their GCSE in Maths, the first thing I ask them to do is to try a “skills check” sheet of questions. The purpose of this exercise is for me to establish how good a grasp they have of the basic skills that they should have covered before the end of Key Stage 3, so that I know what level we are starting from and can plan accordingly.
I don’t want them to see it as a test and feel under pressure. Calculators aren’t allowed, but I don’t mind if they need to look a few things up to remind themselves of how to do them; I’m more interested in their understanding of the underlying concepts, and the way they apply this understanding. Maths should make sense; not only is it a lot more enjoyable if you understand it, but if the basics don’t make sense to the learner then what hope do they have of getting to grips with the harder material needed for the exam? Skills that I ask them to demonstrate are: - Addition, subtraction, multiplication and division, including long multiplication and long division
- Sorting positive and negative numbers into order using place value
- Rounding to a given degree of accuracy (nearest hundred, nearest tenth, 1 decimal place, 3 significant figures)
- Using order of operations (BIDMAS) to find the value of an expression
- Fractions: finding a fraction of an amount, identifying equivalent fractions, arithmetic with fractions
- Finding simple percentages of amounts
- Multiplying and dividing with decimals
- Solving linear equations
Some may question when they would ever use these skills in the real world, and sometimes that’s hard to answer. However, every one of these skills is still examined at GCSE, and some of the techniques – such as arithmetic with fractions – will be needed if the student goes on to study Maths at a higher level. It always surprises me how many students starting A-level Maths can’t remember how to divide by a fraction! At the student’s initial consultation we’ll run through the exercise – which ideally they’ll already have worked through beforehand – and identify the gaps in their knowledge, addressing some of them there and then. The rest – as well as revisiting those newly addressed – can be worked into the first few lessons. We’ll also discuss any areas of the GCSE course that they feel need special attention; perhaps they have struggled with the material in a particular topic or maybe they have missed out on teaching due to illness or a change of teaching set. We will of course aim to cover all the topics in the relevant exam specification (provided that there is enough time left before the exams), but this initial discussion allows me to plan for that particular student’s immediate needs. Think of a number,
multiply it by 2 and take away 6.Now halve your answer and add 3. You should end up back at the number you first thought of.Can you use algebra to explain why this happens? Hint: start by using a letter for the number that you first thought of. Try it before you read on... ... ... ... ... ... Okay, so let's call the number that you started with " n".We're going to start by "dressing it up" to make an algebraic expression. "Think of a number, multiply it by 2 and take away 6."If you multiply n by 2 then you get 2n.Now take away 6 and you have 2 n - 6.Now we're going to "undress" it again to get the n on its own... but by a slightly different route!"Now halve your answer and add 3."How can we halve it? Well, 2 n - 6 is the same as 2 lots of n and one lot of -6...... and -6 is the same as 2 lots of -3 ... so if you halve 2 n - 6 then you get half of 2n and half of -6, giving n - 3.The last step is easy: we now have n - 3, i.e. 3 less than n. If we add 3 to that then the -3 and the +3 cancel outand we're left with just n, the number we started with!How about this one?Think of a number, add 4 and treble it (i.e. multiply it by 3). Take away 12. Tell me what you got and I'll tell you what number you started with. How do I do it? Think it through and see if you can work it out yourself first. Of course, I could do the whole calculation backwards (add 12, divide the answer by 3 and then take away 4) but the numbers are carefully chosen to make it much easier than that. In fact, all I have to do is to divide by 3. It's a bit like going through a labyrinth of side streets and eventually finding yourself just a few steps away from where you started! Here's why: If you start with n and add 4 then you have n + 4. Treble it then you get 3 lots of n + 4, i.e. 3(n + 4).This is the same as 3 lots of n and 3 lots of 4, which we can write as 3n + 12 (this is called multiplying out the bracket).When you take away the 12 you're left with just 3 n...... so to get back to n I just have to divide by 3.What we're doing here - in a mathematical sense - is building up equations and then solving them. In the first example, you found the value of 2 n - 6 and then "undressed the n" to get back to its original value.In the second one you found the value of 3( n + 4), multiplied out the bracket and again "undressed the n" to find its value.Here's a slightly harder one for you to mull over:Think of a number. Double it, add 2 and multiply your answer by 3. Take away 6 from your answer. Now take away the number you first thought of. If you were to tell me the number you'd ended up with, how could I work out the number you started with? Can you make up some more of your own? Actually, "first-time blogger" isn't really accurate; in fact, quite a while before blogging was a "thing", I published what today would be described as a blog. When I lived in Japan, 1999-2001, I kept an online diary of my time there. It was all done in basic HTML - if such things as blogging platforms existed back then then I wasn't aware of them - and can still be found at www.tanuki.org.uk, although not all of the photos are still there.
Anyway, life has moved on since the last update on that site (published in 2009). Still happily married to Craig but we now have Xander (7) as well as Freya. Still living in Hall Green but now in a different house. Still teaching Maths but now striking out on my own rather than being employed by a school or college. It will be nice to be able to focus on the teaching and not worry about crowd control! I'm carrying on a family tradition really; my mum did maths tuition at home for many years. I remember, as a small child, frequently being urged to be quiet because Mummy was "chootering"! I'm not expecting to be a frequent blogger but I'll post occasional updates, mostly Maths-related. |
## AuthorB28 Maths Tutor Lynne Davis at www.b28mathstutor.co.uk - offering private tuition in the Hall Green area of Birmingham, UK ## Archives
May 2017
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