Exam Technique Dr J Frost jfrosttiffinkingstonschuk wwwdrfrostmathscom Last modified 15 th November 2015 I used to do maths for robots where A slide from my talk titled Dude wheres my cat ID: 400108
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Slide1
Maths in Action ::
Exam Technique
Dr J Frost (jfrost@tiffin.kingston.sch.uk)www.drfrostmaths.com
Last modified: 15th November 2015Slide2
I used to do maths for robots!Slide3
where
A slide from my talk titled…
“Dude, where’s my cat?”
(c) Simon’s CatSlide4
But what the devil is that maths doing?
Each preposition in the English language, such as ‘behind’, ‘between’, ‘near’, ‘left of’, has a probabilistic model built for it. My algorithm generates descriptions of objects that disambiguates their location.
Algorithm output:
“The sculpture is right of 101, just left of you and near the laboratory in front of me”
RobotSlide5
Things I really hate…
Generic Talks
So I’ll keep the advice practical!Slide6
TIP #1 ::
Know Your
Calculatrice
*
*French for calculator
First Tip
:
GET A SILVER CASIO CALCULATOR
There’s a remarkable number of A Level questions these will allow you to fully check answers.
B?
S?
Modules
(Edexcel)
Operation
Quadratic/cubic solver. All
Solve 2/3 simultaneous
eqns
Multiply/inverse matrices FP1,FP3
,
,
complex numbers FP1,FP2
Solve any equation.† C2
(e.g. log equations)
Calculate standard deviation, S1
Mean, PMCC (
), line of best
f
it.
† Using numerical methods. Thus only (at most) 1 solution will be found, and it won’t be exact.
Definite integration C2,C4
Slide7
TIP #1 ::
Know Your
Calculatrice
*
*French for calculator
First Tip
:
GET A SILVER CASIO CALCULATOR
There’s a remarkable number of A Level questions these will allow you to fully check answers.
B?
S?
Modules
(Edexcel)
Operation
Find gradient for any
-value Core
for any equation.
Generate tables of values Core
(e.g.
for
between -3 and +3
)
Look up Z-table values S1-3
(but sadly not in reverse)
Slide8
TIP #1 ::
Know Your
Calculatrice
Shameless Self Promotion Alert!
On my website you can find a ‘virtual calculator’ (both Silver and Black) which explains every single button and mode.
www.drfrostmaths.com
KS5 Virtual CalculatorSlide9
TIP #2 ::
Document Your Errors
I once tutored a student who had previously failed to meet their Cambridge History offer, because of their maths A2 result, and reapplied whilst retaking maths.
He was very bright and ‘got’ the questions, but regularly made silly errors.
We kept a log of his errors each time he made one, but while abroad for a few months (where he learnt Portuguese), he came up with various acronyms for Portuguese phrases, that he would write on relevant questions
BEFORE
he even started it!
NMSPN
(
Não
misturar
-se
positiva
e
negative)Slide10
TIP #2 ::
Document Your Errors
Proactively
think about the types of errors you might make as you embark on a question, if you are liable to make them.
e.g. Rounding errors or giving too little accuracy.
Common General Errors
Sign
errors (e.g.
)
Being
clumsy/careless with your calculator (particular applies to S1)
,
Dividing
an equation by a variable instead of factorising, e.g.
…
Common General Errors
Being
clumsy/careless with your calculator (particular applies to S1)
…
Topic
Specific Errors
Doing
for gradient instead of
for gradient, or being inconsistent in the
‘to’ and ‘from’ point for
and
.
Forgetting
/
-intercepts
on graph sketches.
Mixing up summation and n
th
term formulae for arithmetic/geometric series.
Forgetting the +c after integrating.
…
Topic
Specific Errors
Mixing up summation and n
th
term formulae for arithmetic/geometric series.
Forgetting the +c after integrating.
…
GENERAL ERROR
:
Sign errors, e.g.
Give a mini-cheer if you see a mistake you’ve made before.
GENERAL ERROR
:
Being clumsy punching numbers into your calculator (particularly in S1)
GENERAL ERROR
:
,
GENERAL ERROR
:
GENERAL ERROR
:
TOPIC SPECIFIC ERROR
:
TOPIC SPECIFIC ERROR
:
TOPIC SPECIFIC ERROR
:
For arithmetic sequences, mixing up n
th
term and summation formulae.
TOPIC SPECIFIC ERROR
:
Forgetting +c when doing indefinite integration.
TOPIC SPECIFIC ERROR
:
Click to Start Royal Boat Parade of Maths
ErrornessSlide11
TIP #2 ::
Document Your Errors
You are welcome to use my revision notes, which point out common errors.
Shameless Self Promotion Alert!Slide12
TIP #3 ::
Know your Mark Schemes
You will more reliably answer an exam question correctly if you know
exactly where the marks typically come from
for that type of question.
“Find the mean time taken (2)”.
What you might be tempted to write:
But all you need to write:
M1
A1
You could exploit the ‘sum’ menu in STATS mode.
This is particularly important for common larger mark questions (e.g. hypothesis testing).Slide13
TIP #4 ::
Don’t rely
just
on your textbook
Some textbooks have some drawbacks, e.g. the Edexcel ones:
Certain types of exam questions are underemphasised with limited practice, e.g.
Forming an inequality from a discriminant (C1).
Solving more complex log equations (C2)
On the rare occasion the book prescribes a method that is not consistent with the main method in mark scheme.
e.g. Linear interpolation (S1) mark schemes use idea of ‘fraction across the interval’ (much simpler!) whereas textbook uses similar triangles.Slide14
TIP #4 ::
Don’t rely
just
on your textbook
Sometimes there’s an ‘alternative method’ (indicated as such in the mark scheme) that might work better, again not covered in the textbook.
e.g. For showing divisibility in proof by induction (FP1).
Practice past papers! (including Solomon, ‘Gold/Silver/Bronze’ papers, etc.
HOWEVER: Don’t risk the opposite, revising just to the exam and hence lacking versatility to deal with less routine questions.
Revision videos (e.g.
www.examsolutions.net
).
(or slides on my website
)
A simple solution…Slide15
TIP #5 ::
Know your wordy questions
There’s sneaky last parts to questions (typically on applied modules), which are either wordy or require some form of explanation.
I
t helps to know the standard response in advance.
“Explain whether the mean or median would be the more suitable average to use.”
If real roots,
.
But
and hence
C1
S1Slide16
Shameless Self Promotion Alert!
e.g. From my S2 revision notes:
TIP #5 ::
Know your wordy questionsSlide17
TIP #6 ::
Learn Formulae Effectively
Quick bit of maths! Try finding the gradient of the following two points
in your head
:
If you plugged directly into the formula:
you would have had to contend with various double negatives. It’s a faff and prone to errors.
If however you just thought of the formula as:
Then we can clearly see without the need for subtraction that the
value increases by 12 and the
value decreases by 6.
We get
with much less effort.
Slide18
TIP #6 ::
Learn Formulae Effectively
Another example is the formula for calculating variance of data.
If you remember as:
Rather than the explicit formulae then the benefits are that:
You will memorise the formula more easily.
You can plug in numbers with more confidence because you have a better appreciation of components of the formula.
You get 3 different formulae for the price of one!
“the mean of the squares minus the square of the mean”
Slide19
TIP #7 ::
Reduce dependence on mark schemes
Sound familiar?
(While working on past paper)
I’m a bit stuck with this part of the problem.
MarkSchemesRUs.com
Cool beans. I know how to proceed with this question now.
(Finishes practice paper)
Wicked cool. I got 85%. I feel confident on this material.
DOES REAL EXAM
FAILS EXAM
Joins the circus.Slide20
TIP #7 ::
Reduce dependence on mark schemes
NEVER…
…have the full mark scheme next to you when you do a past paper.
This will give you too much of a safety net and prevent opportunity to make (and hence learn from) mistakes, or build understanding.
BUT FEEL FREE TO…
…have
numerical answers
available.
These provide the final answers only without any explanation. You can check whether you’re right as you go along without getting any assistance on the question.
Numerical answers can be found on various websites
(including my own
).
Shameless Self Promotion Alert!Slide21
TIP #8 ::
Show clear structured working
Your working should tell a story, and it should be clear to the examiner
what you’re calculating at any stage of your working
.
Classic examples of unhelpful working:
If
, find
There should be a
here, otherwise it’s not clear when they’ve just simplified and when they’ve differentiated.
They’ve already integrated, so why is the
still there?
General tips:
Work down the page.
If you have subsidiary results to show, ensure it’s clear when you’re answering the original question again.
Use helpful variable names.
e.g.
U
se
for the gradient function but
for specific gradients. Distinguish between the gradient of a tangent (e.g.
or just
) and the gradient of a normal (
or
)
Slide22
TIP #9 ::
Plan for all types and subtypes of question
Often the mentality when preparing for exams is “prepare as much as I can and get a high as mark as possible”.
It’s the kind of mentality where you’re pleased if you’ve got the bulk of most of the questions right, and content you’ve perhaps got the odd last part of a question wrong or made a slip here and there.
The “0%+ mentality”
The “100%- mentality”
It’s an approach where you meticulously plan in order to
reduce the marks you lose
,
rather than thinking of it as maximising the marks you gain
.
It requires a combination of what we’ve looked at, including:
Full appreciation of the exact types and subtypes of questions, including wordy questions.
A deep appreciation of the content rather than blindly applying processes.
Algebraic dexterity.
Identifying mistakes you’ve made in the past and proactively being mindful of avoiding them.Slide23
TIP #9 ::
Plan for all types and subtypes of question
Without needing to do the questions
, look through a large number of past papers
and
make a list for each chapter of what points come up
.
Shameless Self Promotion Alert!
In some revision notes (on my website) I’ve already done this for you.
But there’s plenty of other notes out there…Slide24
TIP #10 ::
Shallow understanding breeds misconceptions
Some errors are due to silly mistakes. Some are due to lack of preparation. But some are exposed when a superficial understanding of material is surfaced by non-routine questions.
What is
?
For anyone who has covered logarithms:
Solution:
.
Such an expression has never come up in an A Level exam. But if you understand
and
as
inverse functions of each other
, then you can appreciate that the two functions cancel each other out in this example.
The key to being a successful ‘Mathematician’ (rather than an ‘A Level mathematician’) is your capacity to
internalise
concepts successfully in such a way that techniques can be applied in unfamiliar settings.
If you enjoy maths, MAT and STEP questions are perhaps the best way to enrich your skills of maths within the core A Level curriculum.
https://
www.maths.ox.ac.uk/study-here/undergraduate-study/maths-admissions-test
Slide25
Fini
www.drfrostmaths.com
VISIT IT – Everything is free
(Go on, you know you want to)
http
://
www.examsolutions.net
Videos explaining pretty much everything in the A Level syllabus.
http://
www.mrbartonmaths.com/alevelcore.htm
Links to various revision notes and websites.
Sites you might be interested in: