*Last Updated on 11 April 2021 *

Are you starting sixth form this year? Want to know how you can make a flying start to A-level Maths? Here’s some guidance to help you ease your path and make a success of your studies!

As anyone who’s done the A-level Maths course will tell you, it’s pretty intense right from Day 1.

If you can make sure that you’re fully up to speed on the aspects of GCSE Maths that the A-level builds on, then you’re going to find the course much easier going.

First of all, do give some consideration to whether A-level Maths is for you.

- Love algebra, trigonometry and problem solving? Then you’ll be in your element!
- Avoid algebra wherever possible but quite like the data handling stuff? Look at A-level Statistics instead, if it’s on offer at the sixth form you’re going to. Alternatively consider Biology, Psychology, Business, Economics, Core Maths… just bear in mind that if you don’t get on with algebra then you’ll find A-level Maths really hard going.

There’s a blog post here that goes into a lot more depth about the sixth form options and whether A-level Maths is likely to be a good choice for you.

Let’s assume that you’ve already given the matter due consideration and you’re ready to do what’s needed to make a flying start to A-level Maths!

Not everything in the GCSE features in the A-level, so – once your GCSE is out of the way – try to focus on only the topics that you’re actually going to need.

You’ve got to be comfortable with fraction arithmetic. That may seem pretty basic, but you’ll be doing a lot of work with algebraic fractions, and ordinary fractions work underpins that. It’s surprising how many new Year 12s can’t remember how to add two fractions with different denominators!

You need to be fluent with surds and indices, including negative and fractional indices, and converting between forms; for example you should know that .

You’ll need your knowledge of vectors, as they’re often used contextually in Mechanics questions. You do get the occasional pure vectors question too, but those are usually no harder than you get at the top end of GCSE.

Just about everything you’ve ever done in algebra and trigonometry will be needed, including all the graph work – algebra and graphs really are the backbone of A-level Maths, and trig is a big element too.

If you did the OCR/MEI GCSE then you may not have covered f(x) notation for functions, but Edexcel and AQA do include it, so if you’re going to a sixth form where most people did one of those exam boards then the teacher might assume that everyone is familiar with it.

That all comes under the banner of Pure Maths; then there’s the Applied Maths, which consists of Statistics and Mechanics.

Under Statistics, the work that you’ve done on populations, sampling, averages and spread will come into your A-level studies, as will histograms, cumulative frequency curves and box plots. (If you did Edexcel IGCSE then box plots aren’t on your spec, but if you’re going to a sixth form where much of the student intake comes from a GCSE background then you might find that they are assumed knowledge.)

Probability also comes under Statistics, and everything you did on that at GCSE is in the A-level too.

For Mechanics, you’ll need to call on your knowledge of travel graphs (distance-time and speed-time, or displacement-time and velocity-time), and the work you’ve done in Science on forces and Newton’s Laws of motion.

As I’m sure you’ve been told countless times, the most effective way to improve your maths skills is to DO lots of maths! Watching videos is all well and good, but what really makes the understanding stick is working through questions, comparing with the answers you *should *have got, and re-working any bits where there’s room for improvement.

It’s also really helpful to revisit each topic after a few days, and then again after about three weeks, in between studying other topics. That’s called interleaving, and it’s a very effective technique for embedding knowledge and understanding in your long-term memory.

You’re going to need these independent study skills for A-level – if you want to achieve your potential then you should be spending roughly the same amount of time on independent study for each topic as you spend in lessons – so you might as well get started now!

There are hundreds of sites out there offering free resources – this blog post lists a selection that you might find helpful – and between them, if you’re happy to do some digging, they’ll provide just about everything you could need.

But if you want a course that’s specifically designed to bridge the gap between GCSE and A-level, focusing purely on the topics that you’re going to need, then you might like to take a look at my Flying Start to A-level Maths course. For less than the cost of a single hour’s 1-to-1 tuition you get:

- over 10 hours of specially-prepared video lessons with lots of practice built in
- additional practice questions for every topic, with full worked solutions
- a free Facebook group for help with anything you’re still struggling with
- and even a certificate that you can download on completion!

… and since a lot of the content is the top-end GCSE material that schools often don’t have enough time to cover in depth, if you start early enough then it will *also *help you to hit those top grades at GCSE!

It’s very tempting, once your GCSEs are out of the way, to relax over the summer and not do any study at all. Some people can get away with doing that, but most, when the A-level course hits them in early September, will wish they’d put a bit more effort into preparing!

If you can put that effort in now then you won’t be playing catch-up when you start sixth form and find gaps in your knowledge that need to be filled in. A bit of effort over the spring/summer will make your life a lot easier in the autumn, and get you that flying start to A-level Maths!

*If you’re a student who’s about to go on to sixth form, what subjects are you planning to do and how are you preparing for them?*

*If you’re already an A-level student or beyond, what tips would you give someone who’s about to start their A-levels, especially Maths?*

*Last Updated on 14 March 2021 *

Once you’ve got to grips with the basic techniques involved in rounding numbers, as covered in my recent blog post, the next step is to deal with upper and lower bounds.

The section down to the embedded video is required for both Foundation and Higher GCSE, but the lower section is mainly just for Higher.

A number line can come in handy here. The key is to work out (a) what’s the *smallest *number that would be rounded *up *to the number we’re looking at, and (b) when you’d start to round up to the *next *mark on the scale. For the upper bound, you also need to consider whether the quantity you’re dealing with is discrete or continuous.

If there are 15000 people in a stadium, rounded to the nearest thousand, then you should picture, or sketch, a number line with divisions at intervals of 1000:

The cut-off at which we start to round up to 15000, rather than down to 14000, is half way in between the two values, at 14500, so **14500 **is the lower bound.

Similarly, at 15500, we stop rounding down to 15000 and start rounding up to 16000.

Now, since you can only have a whole number of people – it’s a discrete quantity – the maximum number of people that will round down to 15000 is *one less than* 15500, i.e. **15499**.

Therefore the upper bound is 15499.

So 15000 to the nearest thousand could be **any integer from 14500 up to and including 15499**.

What if the number were 15000 to the nearest *hundred*?

This time the divisions on the scale will only be at intervals of 100, so the next one down will be 14900 and the next one up will be 15100. What are the cutoffs this time? So what will the upper and lower bounds be?

The lower bound will be **14950 **and the upper bound will be one less than 15050, i.e. **15049**.

So 15000 to the nearest hundred could be **any integer from 14950 up to and including 15049**.

If you had a collection of 350 china elephants, rounded to the nearest 50, what would be the upper and lower bounds? *Answers at the bottom of the page.*

If the 15000 were a continuous quantity, for example a car had covered 15000 miles to the nearest thousand miles, then the lower bound would still be the same, but you’d round 15499.99… miles down to 15000.

**Since there is no gap between the largest number you’d round down to 15000 and the smallest number you’d round up to the next thousand, the upper bound for 15000 is the same as the lower bound for 16000, i.e. 15500.**

So 15000 to the nearest thousand could be **any value from 14500 up to but not including 15500**.

Similarly, if you were rounding to the nearest hundred miles then the lower and upper bounds would be 14950 and 15050 respectively.

So 15000 to the nearest hundred could be **any value from 14950 up to but not including 15050**.

Questions for you to try: (*Answers at the bottom of the page)*

- If a footpath was 260 m long, measured to the nearest 20 m, what would be the upper and lower bounds for its length?
- If a vehicle weighs 1200 kg to 2 significant figures, what are the upper and lower bounds for its mass?

An error interval is simply the lower and upper bounds expressed as a double-ended inequality.

For the examples in the last section, they look like this:

Remember, with discrete data you include the upper bound; if n = 15000 to the nearest thousand then n could be any integer from 14500 up to *and including* 15499, or

If n = 15000 to the nearest hundred then n could be any integer from 14950 up to *and including* 15049, or

What would the error interval look like for 350 china elephants rounded to the nearest 50? *Answer at the bottom of the page.*

If n = 15000 to the nearest thousand then n could be any value from 14500 up to *but not including* 15500, or

If n = 15000 to the nearest hundred then n could be any value from 14950 up to *but not including* 15050, or

What would the error interval look like for a footpath of length 260 m rounded to the nearest 20 m? *Answer at the bottom of the page.*

Truncation is a kind of “lazy rounding”: you don’t bother to decide whether to round up or down, you just chop the number off at the specified place value (and pad out with zeroes if necessary).

So 15000 truncated at the thousands column could be any number starting with 15 thousand…

… so the lower bound is **15000 **and the upper bound is **16000 **for continuous data, or **15999 **for discrete (if counted in ones).

What would the error interval look like for a mass of 7 kg truncated to the nearest kg? *Answer at the bottom of the page.*

Here’s a video lesson from the Grade 4 Essentials for GCSE Maths course, covering the same material as the Foundation content of this article. Take a look at the course if you feel you’d benefit from a bit of extra support to hit that magic Grade 4.

When you use bounds in calculations, it can take some thought to decide which bound is going to give the result you want.

A rectangle has a length of 16 cm, measured to the nearest cm, and a width of 7.5 cm, measured to the nearest 0.5 cm. What are the upper and lower bounds for the area and perimeter of the shape?

For 16 cm, LB = 15.5 cm and UB = 16.5 cm

For 7.5 cm, LB = 7.25 cm and UB = 7.75 cm

To find the area we multiply. To get the biggest possible answer we need to multiply both upper bounds, and for the smallest possible answer we need to multiply both lower bounds.

So max area = 16.5 x 7.75 = 127.875 cm²

and min area = 15.5 x 7.25 = 112.375 cm²

**What if you were asked to give the area of the rectangle “to an appropriate degree of accuracy”?** (With a question like this you probably wouldn’t be explicitly asked to find the upper and lower bounds of the area, but it would be expected.)

The initial measurements are only given to 2 significant figures so your final answer can’t possibly be more accurate than that. But if you rounded 127.875 to 2 s.f. then you’d get 130, and 112.375 rounded to 2 s.f. would be 110. You need a single value that covers the full range of possible areas, so you’d have to reduce the number of significant figures to one. Therefore the answer would have to be just 100 cm²… which of course wouldn’t be very helpful, as it would imply that the area could be anything between 50 and 150 cm²!

Now your turn: Work out the upper and lower bounds for the perimeter. *Answers at the bottom of the page.*

Given that

a = 230 to 2 s.f.

b = 140 to 3 s.f.

c = 300 to 1 s.f.

find the maximum possible value of

(a) (b)

These are a bit trickier. When you’re subtracting, you’ll get a bigger difference if you subtract a small number from a big one than vice versa. So to get the biggest possible difference, we need to start with the upper bound of one value and subtract the lower bound of the other value.

Similarly, when you’re dividing, if you divide by a bigger number then you’re going to get a smaller answer. In this case we’re looking for a big answer, so we want the *biggest *possible number on the *top *of the formula and the *smallest *possible number on the *bottom*.

What are the upper and lower bounds for each of a, b and c?

a: LB = 225; UB = 235

b: LB = 139.5; UB = 140.5

c: LB = 250; UB = 350

So for (a) the answer will be 235 x 140.5 – 250 = **132.07**.

What will the answer be for (b)? Scroll down to the bottom to check.

So that covers the topic on upper and lower bounds. If you’ve found this post helpful then please share it, and if you’d like to receive my monthly email updates then please subscribe to my mailing list using the link in the footer of this page.

For more on how I can help you with your Maths, please visit this page.

China elephants: LB = 325; UB = 374

Footpath length: LB = 250 m; UB = 270 m

Vehicle mass: the 2nd s.f. is the hundreds column so it’s rounded to the nearest 100.

Therefore LB = 1150 kg; UB = 1250 kg

Error intervals: ;

Truncation:

Rectangle perimeter: LB = 45.5 cm; UB = 48.5 cm

Calculation:

]]>*Last Updated on 2 March 2021 *

For both Foundation and Higher GCSE – and also for other Level 2 Maths qualifications – you need to know how to round numbers:

- to the nearest whole number, ten, hundred or thousand
- to the nearest tenth or hundredth
- to a specified number of decimal places
- to a specified number of significant figures.

The first two categories could also be described as rounding by place value .

**Rounding to the nearest whole number means rounding to the units column. On the image above, the units digit is the 5. So the number is 12,345-and-a-bit.**

Now we need to decide whether the number we have is closer to 12,345 or 12,346. To do that, look at the digit AFTER the one you’re interested in. If that next digit is 5 or more then that tells us that we’re at least half way to the next whole number, so we should round UP.

In this case the next digit is a 6, which tells us that the number is more than 12,345 and a half, so we need to round the 5 up to a 6, giving 12,346 to the nearest whole number.

To round to the nearest ten, identify which is the tens digit.

On the image above, it would be the 4.

Now we need to decide whether the number we have is closer to 12,340 or 12,350. Again, look at the next digit AFTER the one you’re interested in. If that next digit is 5 or more then that tells us that we’re at least half way to the next tens digit.

In this case the next digit is a 5 so we know that the number is actually at least 12,345, which means it’s closer to 12,350 than to 12,340. So we round the 4 up to a 5, and pad out the remaining space to the decimal point with a zero, so that all the digits are still in the right place value columns (giving 12350 rather than 1235, which is a much smaller number).

The number in the hundreds column is the 3, so the question is, is our number closer to 12,300 or 12,400?

Look at the next digit: it’s a 4, so the number must be twelve thousand, three hundred and forty-something; in order words, it’s definitely less than 12,350, so it’s closer to 12,300 than to 12,400.

So in this case we DON’T round the 3 up, but just leave it as a 3. Again, we need to pad out the gap to the decimal point with zeroes, to keep the digits in the right columns… so we get 12,300 rather than the much smaller 123.

Now try rounding the same number to the nearest tenth. Can you predict what the answer will be?

The tenths column is the first one after the decimal point, so it’s the 6.

The digit immediately after it is a 7, so we’re more than half way up from 12,345.6 to 12,345.7, so the 6 needs to rounded up, and the rounded value is 12,345.7.

(No need to pad out with zeroes in this case, because we can already see where the decimal point is.)

Once you’ve got your head around rounding to the nearest tenth, hundredth or thousandth, this is easy.

Rounding to 1 decimal place is the same as rounding to the nearest tenth;

rounding to 2 decimal places is the same as rounding to the nearest hundredth;

rounding to 3 decimal places is the same as rounding to the nearest thousandth;

and so on.

So what would 34.527 be if you rounded it (a) to 1 d.p.? (b) to 2 d.p.?

Answers: (a) 34.5; (b) 34.53

This is a little harder to get to grips with. The tricky bit is identifying which digit you’re interested in. Once you’ve done that, it’s just the same as the other approaches.

The first significant figure is the first digit that isn’t a zero. After that, EVERY digit is a significant figure, including zeroes.

So in 3805, the first significant figure is the 3, the second is the 8 and the third is the 0.

What would this number be to 1, 2 and 3 s.f.?

1 significant figure: First s.f. is the 3. Next digit after the 3 is 8, which is “5 or more”, so we round the 3 up to a 4 and pad out with zeroes so that it stays in the thousands column, giving 4000.

2 significant figures: Second s.f. is the 8. Next digit after the 8 is a 0, which is NOT “5 or more”, so we leave the 8 as an 8 and pad out with zeroes, giving 3800.

3 significant figures: Third s.f. is the 0. Next digit after the 0 is a 5, which is “5 or more” so we round the 0 up to a 1, and pad out with zeroes, giving 3810.

Now can you round 0.04097 to 1, 2 and 3 s.f.?

1 s.f.: First s.f. is the 4. Next digit after the 4 is 0, which is NOT “5 or more”, so we leave the 4 as it is, giving 0.04.

2 s.f.: Second s.f. is the 0. Next digit after the 0 is a 9, which is “5 or more”, so we round the 0 up to a 1, giving 0.041.

3 s.f.: Third s.f. is the 9. Next digit after the 9 is a 7, which is “5 or more” so we round the 9 up to a 10… which means that the 1 has to be added onto the next column to the left, giving 0.410.

*When dealing with decimal places, DO NOT add any extra zeroes at the end, or it makes it sound as if you’re being more accurate than you actually are. Remember, extra zeroes are only needed to show the positions of the digits in relation to the decimal point.*

This video lesson, showing you how to round numbers, is an extract from my **Grade 4 Essentials for GCSE Maths** course (Number & Ratio module). You can read more about the course on this page, and find the course itself at mathscourses.co.uk.

Now that you know how to round numbers, you can use this table for more practice. It’s entirely up to you whether you use all the columns; if you’re confident going straight to the answer column without filling the others in then that’s great.

Answers below.

**Answers:** 2) 5600; 3) 249; 4) 120.6; 5) 120.58; 6) 390; 7) 795.1; 8) 795.06; 9) 4000; 10) 0.03; 11) 301; 12) 0.098; 13) 0.10 (since the 2nd s.f. in the original number was the hundredths digit so we’re rounding to the nearest hundredth); 14) 90; 15) 0.0701

*Last Updated on 16 January 2021 *

You’re in Year 11 and your GCSE Maths is all going swimmingly – a few bits of it are tricky, but mostly it’s fine. You should easily get a Grade 6, hopefully a 7 or maybe even an 8, then of course you’ll be able to carry on into the sixth form and do a Level 3 course, probably either A-level Maths or Core Maths… but what’s the best option?

As you may be aware, the A-level Maths specification taught in sixth forms across England and Wales changed in September 2017. Where previously there were some significant differences between the specifications set by the different exam boards, and some options in what Applied Maths modules you could take, all are now working to exactly the same specification prescribed by Ofqual… though there are still some differences in how the different boards set out their questions and require answers to be presented.

The new A-level Maths isn’t supposed to be any harder than it was before, but, as at GCSE, there’s a greater emphasis on problem solving – which means that the questions offer less “scaffolding” than you’ll find in past papers from the old specifications. The entry requirement is typically a Grade 7 at GCSE, though some institutions might accept a 6 and others might require an 8.

The A-level Maths course is a linear 2-year course, with a separate AS-level qualification. The two are designed to be co-taught so that there is the option of taking the AS-level at the end of the first year of sixth form, but it doesn’t count towards the A-level. Because of the way sixth form education is funded, institutions tend to be reluctant to allow you to do just the AS-level and will usually require you to sign up for the full A-level. And if you want to do the AS-level as well as the full A-level then you’re likely to have to pay for your own AS-level exam entry.

There’s also the option of A-level Statistics (Edexcel only). This provides a good complement to a wide range of other subjects including Business, Economics, Psychology and Biology. Again, there’s also the option of AS-level but that may not be permitted on its own, for funding reasons.

You may also consider a “Level 3 Certificate” qualification in Core Maths. Each exam board has a different version of this qualification (AQA’s is called Mathematical Studies, Edexcel’s is Mathematics in Context, and OCR/MEI offers Core Maths options A and B – and there are others too) but each is equivalent to an AS-level in terms of UCAS points, which means it’s worth 40% of an A-level. Funding has been increased to encourage uptake of Core Maths in the sixth form and it’s rapidly gaining in popularity.

Before you finalise the decision to do A-level Maths, think about which aspects of the subject you enjoy the most. Most of A-level Maths is Pure Maths, which involves a huge amount of algebra, so if rearranging formulae and solving equations is your thing then that will stand you in very good stead. The algebra is very closely intertwined with graph work, so you’ll pick up on the work you’ve done on different graph shapes and go into greater depth with that.

There’s also a lot of trigonometry involved; SOHCAHTOA is just the tip of the iceberg. If you’re aiming for high grades then you’ve probably looked at the sine, cosine and tangent curves; that’s where the trig content of A-level starts from.

If you want to do A-level Physics then you might find that your institution makes it compulsory to also do A-level Maths. That’s an indication of how much maths is involved in A-level Physics; if you don’t like the sound of that then it’s best to avoid both subjects!

On the other hand, if you prefer the Data Handling aspects and are hoping to get that high grade at GCSE without having to do too much algebra then you really should think long and hard about whether A-level Maths is for you; you might enjoy the Statistics content but that’s only about a sixth of it. An A-level in Statistics, on the other hand, might suit you very well – particularly if you’re also doing Psychology, Biology, Business Studies or Economics, as these all involve a significant amount of statistical work.

If your favourite bit of GCSE Maths is Geometry and Measure then you might be disappointed at how little of that there is at A-level! You will meet circles and triangles every now and then but there’s not much on polygons and three-dimensional shapes.

Another option to consider is Core Maths. The emphasis here is on real-world applications of maths. The level of maths skills involved is far less demanding than at A-level, with about 80% of the Core Maths content being at Higher GCSE level, though the remaining 20% does go beyond that.

If you’re *really* keen and want to do twice as much maths as any other subject then there’s the option of taking Further Maths as well as Maths at A-level. This will usually have to be taken as a fourth A-level and will have higher entry requirements than single A-level Maths.

Finally, if you do still decide to go on to study Maths at A-level, be ready to hit the ground running! You might have coasted through Year 11 and not given maths a thought between finishing your GCSE in June and going back to school or college in September, but you will be expected to recall the relevant content, and within a couple of weeks you’ll be moving on to work that’s beyond GCSE level.

The work that you do in the first few weeks of the A-level will form the foundation for the rest of the course, so if you’re struggling at this stage then you can’t afford to stick your head in the sand. You need to either put in the necessary work to get up to speed – in the sixth form you need to take responsibility for your own learning, and it’s usually recommended that you spend about the same amount of time on independent study as you spend in the classroom – or investigate other subject options before it’s too late to change courses.

If you need a refresher course to help you make sure you’re up to speed on the GCSE content that you’ll need at A-level, take a look at my Preparing for A-level Maths course – which will also help you to get the best possible result in your GCSE!

In summary:

- If you love algebra and trigonometry then you should enjoy A-level Maths
- If you REALLY love maths then you could do A-level Further Maths too
- If you prefer the Statistics / Data Handling aspects then consider A-level Statistics
- If you avoid algebra wherever possible then consider other options such as Core Maths, Statistics, Biology, Psychology
- Be ready to hit the ground running and do plenty of independent study if you do opt for A-level Maths!

*Last Updated on 6 January 2021 *

Are you someone who always struggled with maths at school, and has tried to avoid it ever since… but now you find that you really need to become a mature student, or adult learner, and get a Maths qualification to progress in your career?

For most people, the best place for an adult learner to start is your local Futher Education (F.E.) College or Adult Education Service, where you’ll be able to register as a mature student. They have funding to offer free courses and exam sittings to anyone who doesn’t yet have a Level 2 Maths qualification (and the same for English). The main enrolment season is early September but they may have courses for adult learners starting at other times of year too, especially January.

When you enrol, it’s likely that you’ll be asked to take some kind of diagnostic assessment to gauge your level, and they’ll advise you on what level of course would be most appropriate for you. You might be able to go straight in as a mature student on a GCSE course (probably at Foundation Tier; Higher Tier is really only for those aiming at Grades 6 and above and isn’t commonly offered in adult learner settings), but they may recommend that you do a Functional Maths qualification first and work up to GCSE afterwards if you still need it.

If for some reason you are not eligible for, or able to attend, a free course, then you will need to book your exam through a private exam centre local to you, and make your own learning arrangements. More on that here.

A GCSE at Grade 4 or above will open lots of doors to you, but you might find that a Functional Skills qualification is sufficient for your needs. Functional Skills qualifications are available in Maths, English and ICT (Information Communication Technology – that’s what they call IT in education these days). A Functional Maths qualification at Level 2 is equivalent in difficulty to a Grade 4 at GCSE – that’s a Grade C in old money – but it only involves the aspects of Maths that you’re likely to need in everyday life, and focuses on real-life applications of the skills.

It’s a bit like having an automatic driving licence versus having a full licence that also allows you drive a vehicle with manual transmission; either way you need to know how to navigate the roads safely, but if all you want to do is drive an automatic car then the automatic licence is all you need.

The full list of levels for Functional Skills qualifications is Entry 1, 2, 3 and then Level 1 and Level 2. The Entry levels correspond roughly to primary school, and Level 1 is approximately in line with what schools cover in Key Stage 3 (the first three years of secondary school). You can find the subject content at each level for Functional Maths on the Ofqual site here, and the equivalent information for GCSE here.

Both the Functional Maths and GCSE qualifications are offered by several different exam boards and the format of the exams varies to a degree, but in general it’s:

- Sittings available throughout the year
- Either paper-based or online (usually at an exam centre)
- Between 1 h 45 min and 2h 30 min
- Either two papers, or one paper in two sections
- 25% of the marks are non-calculator; a calculator is permitted for the other 75%

- Sittings available in May/June and November
- Always paper-based and held at an exam centre
- Three papers of 1.5 hours each
- Paper 1 is non-calculator; a calculator is permitted for Papers 2 and 3

Don’t worry about being the only mature student in a class of teenagers; there will probably be adult learners of a wide range of ages in the group, from 19-year-olds in their first jobs, to mums who want a maths qualification in order to forge a new career for themselves now that their children have grown up and left home, to pensioners who left school at 15 without any qualifications and just want to prove to themselves that they can do it!

You’re likely to be enrolled on a year-long course consisting of typically two hours per week (a bit more if you’re lucky) of teaching. For an adult learner it might be either a daytime or an evening class. Two hours per week is not a lot, especially for a full GCSE course (in schools it’s typically at least 4 hours a week for Maths or English), so you’ll need to do quite a bit of independent work as well.

If you are enrolled on a course then your institution might subscribe to an online service such as Mathswatch, HegartyMaths, MyMaths, etc., so do make use of that. This blog post provides links to a variety of other resources that you might find helpful, and this one advises on how best to prepare for a GCSE Maths exam (though it’s relevant for other Maths exams too).

You might also like to take a look at my Grade 4 Essentials course for GCSE Maths, ideal for anyone who just wants to cover the topics needed to be confident of getting a Grade 4, either as a supplement to a taught course or to support them as independent learners.

Are you an adult learner who has taken a Maths qualification as a mature student, or looked into doing so? Please share your experience in the Comments below.

]]>*Last Updated on 6 January 2021 *

After many hours of work, I’m proud and delighted to introduce my new sister site, mathscourses.co.uk. As the name suggests, its purpose is to host a range of maths courses. Exciting? Well, maybe not for everyone, but it is for me! It’s been a steep learning curve since my website building skills are elementary at best, but I think it’s looking quite good if I do say so myself!

The first course that I’m launching there is Module 1 of ** Grade 4 Essentials for GCSE Maths**. The full series consists of four modules:

- Number and Ratio
- Geometry and Measure
- Algebra and Graphs
- Statistics and Probability

Module 1 is available now; the others are under construction and will be coming online over the next few months.

For this course series, my aim is to distil my teaching experience into a series of videos and quizzes covering all the topics needed to ensure a secure Grade 4 – or possibly even a 5 – in GCSE Maths. It’s ideal for home educators, adult learners, and anyone else who feels they would benefit from a bit of extra help to get that magic Grade 4.

Even if you’re doing the Higher Tier, you still need to be secure on the Foundation content. If your confidence isn’t quite what it could be then this series of maths courses may be just what you need for that extra boost!

It’s also relevant to those studying the Edexcel International GCSE (IGCSE), since there are only small differences between the two qualifications at Foundation level.

Each course consists of a set of pre-recorded videos – over 6 hours’ worth in Module 1 alone – with lots of built-in opportunities for you to practise the skills being taught, and a series of quizzes for you to test your knowledge and understanding after working through the lessons. You get the first six video lessons of Module 1 – a total running time of over an hour – as a free preview, so it’s worth taking a look even if you have no intention of signing up!

Since the videos are pre-recorded, you can pause them so that you can answer questions in your own time, and repeat sections whenever you like. Of course, this means that if you make full use of them then they’ll take considerably longer than just the actual running time to get through!

You can also redo the quizzes multiple times, so – if you like – you can try them *before *doing the lessons, shortly afterwards (several times if you wish!), and then again a few weeks later. If there’s anything you’re still struggling with then you can always post a question on the Facebook group, where you can get free help. And if the demand is there then I may also run some live workshop tutorials on a PAYG basis.

These maths courses are an absolute steal at just £9.99 for each module – and what’s more, Module 1 is **FREE **until 8th January 2021!

Of course, you’ll want to work through lots of exam questions too. That’s not the focus of this course – it’s more focused on the underlying skills that you’re going to need for the exams – but you are directed to some useful free resources for exam preparation. The advice in this blog post will also help you to prepare effectively.

This course, which I launched in the summer, is aimed at those studying Higher GCSE (or Edexcel IGCSE), with a view to going on to study Maths at A-level. It covers all the top-end parts of the GCSE specification that are assumed prior knowledge for A-level.

Since there’s so much content in the GCSE specification, schools often just have to gloss over some of these top-end topics. They simply don’t have the time to cover them in the depth that you need to get the very best GCSE results and hit the ground running when you start the A-level. This maths course aims to address that, helping you to achieve those top GCSE grades as well as being ready to start the A-level.

It contains approximately 10 hours of video lessons, with plenty of practice opportunities built in – so it will actually take considerably longer for you to work through if you take full advantage of those. The course fee is just £30, and you can get a 25% discount code if you sign up for free membership of this site.

Because I hadn’t yet built the new site when I launched the Preparing for A-level Maths (PFALM) course, it’s currently hosted in Google Classroom and accessed via this site. I do intend to migrate it across to the Maths Courses site, but for now my priority is to complete the remaining modules of the GCSE course. In the meantime I have uploaded a preview of the PFALM course to the Maths Courses site; you can find it here.

The new site, like this one, is built in WordPress. For those not familiar with WordPress – as I wasn’t until a few months ago – it’s the world’s most popular platform for building websites (I believe that something like 40% of the websites in existence use it). It started out as just a platform for bloggers, but these days it’s much more than that.

You choose a theme – a sort of frame on which you construct your site – and install additional programs called plugins that do all sorts of things: security, page building software, backup tools, memberships, photo galleries, and so on.

I built the Maths Courses site using an LMS (Learning Management System) plugin called LearnPress. The basic LearnPress LMS is free, but in order to add some of the functionality I needed/wanted (such as taking credit/debit card payments via Stripe, allowing students to review the maths courses, awarding certificates for course completion, etc.), various add-ons were required, and the most efficient way of getting these was to buy a theme package. The one that I plumped for was called Eduma, mainly on the basis that it was the most popular and included lots of demo sites that you could use as a starting point.

I’m not entirely sure whether the demo site was a help or a hindrance, but after much experimentation and watching numerous YouTube tutorials (in particular I learned a lot from IdeaSpot and Nayyar Shaikh) – and with a bit of help from Phuong at ThimPress Tech Support – I managed to get it looking and working as I wanted it.

So please take a look at the maths courses on offer, and I hope you’ll want to enrol!

]]>*Last Updated on 6 January 2021 *

You might be a little unclear on which calculators are appropriate for which exams. The short answer is that if a calculator is permitted in an exam – at least in England – then ANY calculator is fine*, as long as it’s not one that you can program text into. However, different calculators have different capabilities so here’s a guide to the ones you’re most likely to come across.

For GCSE Maths, you will need a scientific calculator, but just about any model will do; see AQA’s guidance below for a list of the functions you need.

The standard GCSE model in the UK now is the Casio Classwiz fx-83/85GT X (centre in the image). The only difference between the 83 and 85 is that the 85 is dual fuel, i.e. has a solar panel. It replaces the old fx-83/85GT Plus (shown to its left), and usually costs around £15, though if you’re lucky you might find it for £10 or so in a promotion. If you have the older model then it will still do everything you need for GCSE, so don’t worry about that!

Texas Instruments also produces a range of scientific calculators. Any of these – most of which start with TX-30 – are suitable for GCSE, though if you like to be able to enter your fractions as fractions then you’ll need one of the Multiview models. However, Casio pretty much has a stranglehold on the UK market and not many institutions promote the use of TI models.

If you have a really tight budget then you can pick up a scientific calculator in Wilko (they have a model that’s similar to an older Casio) or even Poundland. Just make sure you know where to find all the functions you need for your exam!

It’s also worth considering an A-level model, especially if you’re doing the Higher Tier and there’s a possibility that you might continue to study Maths in some form beyond GCSE.

Here’s an extract from AQA’s guidance for GCSE:

*For GCSE Mathematics exams, calculators should have the following as a minimum requirement:*

*four rules and square**square root**reciprocal and power function**brackets**a memory facility**appropriate exponential, trigonometric and statistical functions.*

*For the purposes of this specification, a ‘calculator’ is any electronic or mechanical device which may be used for the performance of mathematical computations. However, only those permissible in the guidance in the Instructions for conducting examinations are allowed in GCSE mathematics examinations.*

The standard model for A-level is the Casio Classwiz fx-991EX (right in the image above), which usually costs around £25. It has additional functions such as solving quadratics and simultaneous equations which can be useful at GCSE too, as well as Statistics functions that you don’t need until A-level. So if there’s any chance of you continuing with Maths beyond GCSE then it’s a worthwhile investment. (You’ll probably need it if you do Core Maths too, though it does depend on which board and which modules you study. It’s certainly required for the Statistical Techniques option on the AQA spec.)

The Texas Instruments equivalent is the TI-30X Pro Multiview.

Some schools/colleges may require you to buy a graphical calculator for A-level (Casio’s flagship model is the CG-50), but if you can stretch to a Classwiz too then it’s good to have, as it’s easier to use for some functions, and having a second calculator reduces the need to keep switching between modes. Don’t worry, you are allowed to take two into the exam with you!

All of the models mentioned above are allowed in any exam where calculators are permitted*; there is no distinction between a calculator for GCSE and one for A-level as far as JCQ (who make the exam regulations) are concerned. You can find the JCQ regulations in section 10 of this document.

Guidance from the exam boards can be found on these pages from AQA, Edexcel and OCR.

**Note that, unlike the other exam boards, CIE (Cambridge International) does not allow the use of graphical calculators.*

If you want to learn more about the useful things that the Casio calculators in the photo above can do, take a look at this video series on my Facebook page.

Interested in finding more resources to help you with GCSE Maths? Take a look at this blog post.

*Last Updated on 2 January 2021 *

Ever wondered if it’s possible to make a DIY visualiser (document camera) out of kit that you already have at home? It’s actually pretty simple; there’s really no need to spend £50+ on a Hue or similar camera if it’s only going to be for occasional use.

If you’re teaching remotely then a DIY visualiser allows your students to see what you’re doing on the desktop. This setup could also be used by students who are learning remotely, perhaps with an online tutor, and prefer to write on paper rather than on screen. And it’s cheaper than buying a graphics tablet to facilitate on-screen writing.

It could also be useful for live video tutorials, for example involving crafts or cookery. (I’ve done a series of calculator tutorials using mine.)

All you need is a spare smartphone or tablet, a free phone app and some kind of support to hold the phone in place. You don’t even need a SIM card in the phone, since it works over either WiFi or a USB connection.

The photo above shows a cheap gooseneck stand – I recommend a G-clamp design like this, since it won’t topple over as a free-standing phone support might – but you can get away with a stack of food tins at a pinch! Just remember to also put a weight on top of the phone if you’re using that approach. Below is another no-budget (albeit slightly precarious!) setup used by fellow tutor Jennifer Bibby!

There are multiple webcam apps available; just try a few and see which ones you get on best with. They come in two basic varieties:

Type 1: View the output through your browser. If you use this option then you can share the DIY visualiser view with your students (or teacher/tutor) by sharing the screen. The ones that I’ve tried show the IP address as an overlay on the phone screen, and all you need to do is type the IP address into your browser and then bookmark it for future use.

Type 2: Install a client on your computer, which will allow the computer to see the DIY visualiser as a separate camera. This option means that you can select either your main webcam or the phone cam for your main window in Zoom, Google Meet, Microsoft Teams or whatever other video conferencing app you are using.

My own DIY visualiser uses an Android app called CamON, which is free and comes under Type 1. IPWebcam is another example of this type, though I’ve found CamON simpler to use. There’s a lag of half a second or so (over WiFi) but that shouldn’t matter too much.

Type 2 apps include DroidCam and iVCam, but I’ve found that the free versions of these aren’t sufficiently high resolution to allow the sharing of printed material from a text book. There may be others that offer higher resolutions for free; iVCam did at first, and worked very well, but what I didn’t realise was this this was a free trial of the paid version. But if you like the app enough, and want the option of being able to switch between cameras, then you might want to consider the upgrade.

A word of warning, though: these apps all drain the phone battery pretty quickly – mine has about a 2-hour life – so remember to turn the camera off when not in use! If you’re going to use your DIY visualiser for more than a couple of hours at time then it may be worth investing in a purpose-built document camera.

So there you go – an easy way to make a DIY visualiser. I hope you’ve found this helpful; please comment below if you have anything to add. Maybe you’ve tried a different app (perhaps one for iPhone – I can’t comment on those!) and would like to feed back on how well it worked.

If you’d like an introduction to using Zoom and BitPaper for online teaching/learning, take a look at this blog post.

For more help with Maths and online learning, visit my website at https://b28mathstutor.co.uk.

]]>*Last Updated on 4 February 2021 *

There are a huge number of software options for delivering online tuition but I use Zoom and, in my 1-to-1 online tuition, BitPaper. I favour Zoom over Google Meet, Skype and the rest because it’s the only one I know of that allows annotation of a shared screen (by both tutor and student) and allows the tutor to hand control of the mouse over to the student. It also allows the host (the tutor) to end the meeting for everyone, which is less straightforward in the others.

BitPaper is a very versatile whiteboard app that allows you to keep a permanent record of each student’s work.

This post describes the software mainly from the student’s point of view but I hope it will also be of use to tutors. Please share it with anyone who you think might find it helpful.

- A decent broadband Internet connection
- A device with webcam, microphone and preferably a reasonably large screen (for screen sharing)
- Either a touchscreen or a graphics tablet is useful if you want to use the annotation tool, but otherwise isn’t necessary

Go to https://zoom.us/download and download the Zoom Client for Meetings, or click on the link in the email you have received inviting you to join a Zoom meeting and download it from there.

When you have the Zoom app open you will see the icon – a white camera on a blue background – on the taskbar.

When you receive a meeting invitation, simply click on the link. (Zoom meetings are password-protected by default, but if you receive an invitation by email then the password will usually be embedded in it.) If you are asked what app you want to use, check that “Zoom” is selected (it will probably be the only option shown), tick the ”Remember my choice” box and click “Open link”. In future it shouldn’t need to ask you.

Alternatively, if you know the meeting ID and password, you can go into the Zoom app, click on “Join”, and type in the meeting ID and then the password.

Most tutors will use a waiting room so you’ll be sent there when you first join, and will only be able to get into the online tuition session if you’re expected. A free Zoom account allows meetings of unlimited length with only two participants, but as soon as a third person – or device – tries to join the meeting, the time limit is reduced to 40 minutes.

A meeting can take the form of video, audio or just screen sharing. I normally start with video and take it from there. If your Internet connection isn’t great then it may help if you turn the camera off. With larger groups you may find that your camera and microphone are turned off when you join the meeting, but you can normally turn them on using the icons at the bottom of the screen.

Once you’re in the meeting, you’ll see whatever the participants’ webcams are pointing at. You can toggle between “Speaker view” and “Gallery view” using the button in the top right-hand corner (on a desktop machine). If the tutor shares their screen then you’ll see whichever window has been shared with you (website, PowerPoint, spreadsheet, PDF, etc.). When you move your cursor a green bar should appear at the top of the screen, telling you whose screen you are viewing. You can use the menu options on this bar to annotate the shared view (a graphics tablet or touchscreen makes this easier) or to request remote control.

You can also share your screen with other participants – look for the green “Share screen” icon at the bottom of the video window. You can choose to share either just a single window or your whole screen. It’s usually best to share only the window that you want everyone else to see. You can stop the share using the red bar at the top of the screen, or by closing the shared window.

There’s a chat function that can be used for sharing URLs or for asking questions if you’re part of a larger online tuition group. Depending on the host’s (tutor’s) settings, you may be able to choose whom your message goes to, or you might only be able to address the host.

If you minimise the Zoom window before using BitPaper (or other apps) then the video window will float on top, so you don’t lose sight of the person you’re talking to.

If there are ever any problems with Zoom then Google Meet and Jitsi Meet are possible alternative platforms that can be used for online tuition. These both allow screen sharing but don’t have the annotation or remote-control facilities.

BitPaper is a feature-rich online whiteboard that’s designed with online tuition in mind. Zoom has a built-in whiteboard but it’s far more basic. I assign a paper to each of my 1-to-1 students and we use it like an exercise book, so it gives the student a permanent record of what’s been covered in their online tuition. Each paper can have up to 100 sheets, each infinitely extendable in any direction, and so can be used for an extended period. A record of every keystroke is stored, though, so eventually a paper will become slow and you’ll need to start a new one.

- Ideally, a laptop or desktop computer with a graphics tablet plugged in. Any Wacom, Huion or XP-Pen graphics tablet is fine; you can get one with a 6 x 4 inch active area (corresponding to your screen) for around £40, or a smaller one for around £25-30. It will come with its own stylus.
- Failing that, a touchscreen computer or tablet (at least 768 pixels wide, which normally means a 7-inch screen, but bigger is better; phone screens are usually too small to display BitPaper)
- You
*can*get away without either touchscreen or graphics tablet, but freehand writing with a mouse is tricky! - Chrome browser; Firefox or Safari should work too, but BitPaper doesn’t support Internet Explorer and Edge… though I’m told that the new version of Edge (with the blue and green swirly icon) actually works very well, which makes sense since I understand it’s based on the Chromium open-source software.

Open Chrome – support for other browsers, especially Internet Explorer / the older version of Edge, is more limited – and go to the BitPaper.io URL you have been given. The URL is permanent, so the same address can be used multiple times, keeping everything in one place. You can open up the same paper on more than one device if you like.

You can log into BitPaper using either a Facebook or a Google account, or email if you prefer, and you need to do this if you want to be able to use the whiteboard in between your online tuition sessions and save your work. Use Shift-S to save it for the first time, and after that it will appear in “My Papers” and will save any changes automatically. Logging in also allows you to create one free paper of your own per month.

A turquoise rectangle outlined on the screen indicates the field of view for the participant with the smallest screen. If you put anything on the screen outside that window then that person will need to pan around the page to see it.

If for any reason you have difficulty accessing BitPaper then it can still be shared with you via Zoom, though then you’ll only be able to write on it properly if remote control is handed over. (Without remote control you can still write on the screen using the Zoom annotation tool, but that’s like writing on an overlay and doesn’t get saved.)

Use the menu across the bottom of the BitPaper screen or the number keys on the keyboard to select your tool:

- Select pen colour & thickness;
- Use pen or highlighter (if you click on the ruler icon then you’ll get only straight lines, but you can also do this by holding down the Shift button while you draw);
- Use eraser (best avoided since it actually just covers things up rather than removing them; you can delete items properly by selecting them and then pressing the Delete key);
- Select and move items;
- Pan around the page [and since I wrote this post they’ve added the facility to recentre, i.e. jump straight to the beginning of the current page];
- Draw shapes selected from the library;
- Type text;
- Enter mathematical notation using TeX language – a nice new addition if you’re comfortable with TeX, but it’s usually quicker to handwrite!

Top right-hand corner: click on box to bring up menu allowing you to delete the page, add a new blank page or add a duplicate page; click on numbers or up/down arrows to move between pages. I leave the first page blank for my students to experiment with, and suggest that they use to it make a contents list of what’s on the other pages, so it’s easier to find things again later.

Bottom left of screen:

- Upload files (but you can use the Windows Snipping Tool to paste selections directly into the whiteboard);
- Add grid or coloured background (may be helpful for those with dyslexia) to paper;
- Use chat box (or join audio or video call but that costs extra);
- Share URL of whiteboard with someone else;
- Open full menu in sidebar.

Bottom right of screen: undo action; redo action.

Get a full list of BitPaper keyboard shortcuts by pressing K at any time (except when text entry window is open). A few handy ones to remember are:

**<**and > (without the Shift button, so really , and .) to change pages- 1, 2, 3, etc. to change tools
- Z to undo last action (even if it was someone else’s).
- To draw a straight line or maintain the aspect ratio of a shape, hold Shift down while drawing.
- To zoom out (and fit more on the screen): Ctrl and –
- To zoom in: Ctrl and +
- T – show/hide screen icons
- F – toggle fullscreen view (Esc will also get you out of it)

To use the Snipping Tool on Windows 10 (with Creator update installed): Shift+Windows+S, select area to copy, then Ctrl+V to paste. (*Personally I use this ALL the time, so I have it pinned to the taskbar at the bottom of the screen for easy access. You can do this with any app by right-clicking on its taskbar icon (while the app is open) and selecting “Pin to taskbar”.*)

Snipping tool on Mac with Chrome: Shift+Ctrl+Cmd+4 then use cross-hairs to select desired area, then Cmd+V to paste.

If you feel more comfortable doing your working on paper rather than on the screen then take a screenshot of the question (so you don’t lose it if someone else in your online tuition session moves to a different view while you’re working) and do your working-out on paper. When you’re ready, either (a) take a photo of your work, copy it (either the whole thing or a snipped section) and paste it into BitPaper for feedback, or (b) hold it up to the video camera and let the tutor do the copy & paste bit.

To find out how to make a DIY visualiser for free using just an old smartphone, have a read of this blog post.

If you’re interested in finding out more about online tuition with B28 Maths Tutor then click here.

If you’ve found this post helpful, or think there’s something I’ve missed or got wrong, then please let me know in the comments below. If you know someone else who you think might find it helpful then please share it with them too.

What are YOUR favourite video conferencing and whiteboard apps for online tuition, and why?

]]>*Last Updated on 23 February 2021 *

With some subjects, reading your notes and making mind maps and more notes about the content works well.

*Maths isn’t like that.*

Read on for some tips on effective ways to revise GCSE Maths.

To get good at Maths, you need to do LOTS of practice. You may need to do a bit of reading or watching videos to get started, but spend as much time as you can actually attempting questions. Don’t leave it until the exams are in sight; little and often, throughout the year, is the way to go!

If you want to make sure that you have all the basic topics covered for a Grade 4 then take a look at my Grade 4 Essentials for GCSE Maths series of courses. Not free (although you do get a free preview of a full hour’s worth of video lessons), but very inexpensive – and a heck of a lot cheaper than private tuition! Each of the 4 modules consists of several hours of interactive videos with lots of practice opportunities built in, and quizzes for you to check your knowledge and understanding. Membership of this site (which is free) also gets you a discount code for £5 off your first course enrolment, making it an absolute steal!

Try to revise GCSE Maths for a short time every day so that you keep a variety of topics fresh in your mind. Corbettmaths 5-a-day is perfect for this, with sets of questions at several levels ranging from basic numeracy to the top GCSE grades, covering every day for an entire year. You can buy it in workbook form now too! (I don’t have a vested interest, I just think it’s a brilliant resource.)

As soon as you feel reasonably confident with a topic area, start working on exam (or exam-style) questions. Great resources for this are the exam question collections by topic on Maths4Everyone and JustMaths. Solutions are provided on both sites.

When you’ve attempted a few questions, compare your answers with the solutions or mark schemes and try to work out what mistakes you made. (But bear in mind that the solutions provided are not necessarily the *only* correct approach; there may be five or six possible ways of answering a question. Also, there are occasional errors in the JustMaths solutions, as they were compiled very quickly when the new GCSE spec was launched.)

If you can’t work it out on your own then ask someone for help. You’re welcome to join my Facebook group for this!

Then put the exam questions aside and go away and work on any bits you need to – for this I suggest using the “Videos and Worksheets” page on Corbettmaths, or my Grade 4 Essentials courses, though those are by no means the only options. This blog post provides suggestions of other places to look for help.

When you’re feeling a bit more confident, come back and have another go at some exam questions.

Learn to interpret the mark schemes published by the exam boards. That way you’ll develop a better understanding of which marks you would and wouldn’t have got, and you’ll be able to improve your presentation to maximise your marks.

When you first start to revise GCSE Maths, it’s fine to keep your notes and formula sheets handy and refer to them if you need to, but bear in mind that you’re going to have to work up to managing without them. Set yourself a target of not looking at your notes until you’ve done as much as you can of the current set of questions without them. Then you can allow yourself a peek, then put the notes away and see if you can get any further on your own.

If you’re struggling to remember some of the rules and formulae then make yourself some flashcards – making your own is more effective than buying someone else’s – and use those to help you learn them.

Students often seem to think that they should stick to just calculations in their exam answers, but in fact it’s GOOD to use words and phrases to explain what you’re doing; you want to make it easy for the examiner to follow your reasoning and give you marks! Imagine that you’re explaining to another student how to do the question, rather than just trying to find an answer. The more clearly you can do that, the more likely you are to get all the marks. This principle applies especially in the case of proof questions.

On the difficult questions at the end, it’s often quite easy to get the first mark, so try to write down something relevant even if you have no idea where to take it after that! Just ask yourself, “What CAN I do with this information?” Often there’s a mark available for simply taking a step in the right general direction.

And on questions that use any of the words “prove”, “show” or “verify”, remember to always finish off with a ** statement** echoing what the question said, or you might miss out on the last mark.

The AQA papers include some multiple choice questions. If you don’t know how to answer one of those then don’t leave it blank; just circle/tick whichever answer you think looks like the best bet. At least that way you have a 1 in 4 chance of getting the mark!

And it’s likely that there will be one question (though perhaps not on every paper) where there’s a mark *just *for putting the right units in the answer space, even if you don’t do the rest of the question!

By about 6 months before the GCSE exam you should be starting to work through complete papers. Use your notes if you need to, but gradually try to reduce your reliance on them as far as possible. Again, after you’ve marked your work, go away and work on any areas that you feel you could improve on, then come back and have another go, or try another paper.

Gradually work up to doing the papers under exam conditions: no notes or formula sheets, and observing the time limits.

With AQA and Edexcel there are 80 marks on a 90-minute paper. That’s just over a minute per mark, on average (assuming that you’re aiming to complete the whole paper). Don’t worry about it when you’re just starting to look at exam papers, but by the time you get into the last few weeks you need to bear in mind how long you can afford to spend on each question.

Don’t spend 10 minutes wrestling with a 3-mark question; leave it and just come back to it at the end if you have time. And don’t be discouraged if there are bits you can’t do; remember that roughly half the marks on a Higher paper are aimed at Grades 7 and above. You’re only expected to be able to do everything if you’re aiming for the top end of your Tier.

Of course, it’s still worth going back afterwards and finishing off the questions that you didn’t manage in the allotted time, even if you need to use your notes for that.

When you’re working through a whole paper, start off with the questions that you like the look of! If you can get the first few marks under your belt without too much difficulty then it will help your confidence with the rest. It will also help to prevent you from wasting time getting bogged down on a difficult question early on.

Rather than repeating papers, you can revise GCSE Maths using papers from other exam boards; there’s very little difference between them at GCSE, especially if you’re doing Foundation. (Probably the biggest difference is that OCR doesn’t include f(x) notation in their interpretation of the spec prescribed by Ofqual, so if you’re doing OCR Higher then that’s an aspect of AQA and Edexcel questions that might throw you.)

Finally, don’t spend 12 hours a day cramming! Ideally you should take around 10 minutes of break per hour of study (though of course you’ll have to stretch that when you’re working to exam conditions) and a longer break after 2-3 hours. Try to do some physical activity whenever you have a break, and don’t forget to eat well and drink plenty of water.

By all means revise GCSE Maths for a couple of hours each day as the exams approach, but that will usually be plenty; after all, you probably have other subjects to do as well! Most people struggle to maintain concentration for more than about two hours, so the effectiveness of your study will be reduced if you keep going for too long.

So there you are – 12 tips to help you revise GCSE Maths effectively (with a bit of exam technique thrown in too). Do you have any more tips to add? Please comment below if you can think of anything I’ve missed.

As well as the Grade 4 Essentials for GCSE Maths courses I mentioned earlier for those aiming for Grades 4/5, I have a Preparing for A-level Maths course that you’ll find useful if you want to hit a high grade and go on to do Maths at A-level. Free members of my site get discounts on both of these.

]]>*Last Updated on 15 October 2020 *

When I take on a new 1-to-1 tutee for GCSE Maths, the first thing I ask them to do is a basic skills check. They shouldn’t view this as a test; they can look things up and take their time, doing it over two or three short sessions if they choose. The aim is to identify any gaps in the basic skills that they should have covered in Maths before the end of KS3; a lot of it will have been covered in primary school. Most of it should be fairly straightforward, but even with a very able student I can usually show them one or two things they didn’t already know.

Basic skills that they are asked to demonstrate – including showing valid methods of working, and without using a calculator – are:

- Addition, subtraction, multiplication and division (including long multiplication and long division)
- Using place value to sort positive and negative numbers into order
- Rounding to a specified degree of accuracy (nearest 10, nearest tenth, 2 decimal places, 3 significant figures)
- Order of operations (BIDMAS – or GEMA if you prefer) to evaluate an expression
- Fractions: finding a fraction of an amount, working with equivalent fractions, arithmetic with fractions
- Finding simple percentages of amounts
- Multiplying and dividing with decimals
- Solving simple equations

You may think that some of these skills are of little use in the real world. Even so, they are still examined at GCSE… and some of the techniques – for example arithmetic with fractions – will be needed if the student goes on to study Maths at a higher level. It’s surprising how many students starting the A-level Maths course can’t remember how to add two fractions with different denominators!

In our first lesson we’ll go through the exercise – which ideally they’ll already have worked through beforehand (I like to give full value for money!) – and identify the gaps in their basic skills that it reveals. Some of these gaps can be addressed in just a couple of minutes; others will take longer.

We’ll also discuss any areas of the GCSE course that they feel need particular attention, either because they have struggled with the material or because they have missed out on teaching, perhaps due to illness or a change of teaching set.

As an example, here’s the list of topics that I use as a prompt for Foundation GCSE students:

We will of course aim to cover as many of the topics in the relevant exam specification as time permits, but this initial discussion allows me to plan for that particular student’s immediate needs.

From that initial discussion I’ll draw up a provisional plan for a few weeks at a time, listing topics and providing directions to sources of further practice for homework or voluntary independent study. (Corbettmaths is a favourite for this.) The plan is always flexible, so if the student wants to go “off-piste” and spend time looking at something they’ve been struggling with at school that week then I’ll accommodate that (though not to the extent of doing their homework for them!). I generally update a student’s plan roughly once every 4-6 weeks.

If I’m asked to try to coordinate with the school’s scheme of work then I’m happy to do so if the student/parent can provide me with with the necessary information on what skills will be covered when. However, it’s generally better to NOT be in sync, because interleaving topics – revisiting one topic while studying others – helps with memory.

Maths should make sense, and a good tutor can be a great help here. If the basics don’t make sense to the learner then what hope do they have of getting to grips with the harder material in the exam specification?

To find out more about my tuition services, take a look at my Maths Help page. You can sign up there for free membership of the B28 Maths Tutor site to access some useful free resources, and also see what other services I have to offer.

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