Maths

These are resources relevant to tuition in Maths at tomctutor.com.

Student calculators - recommended by tomctutor: ( view detailed pdf file).

Recommended calculators Oxford Maths Set UK
 
 
 
 
 
 
 
 
 
 
 

Visit Youtube resource at: http://www.youtube.com/user/patrickJMT
The justmathtutoring video index is at: http://patrickjmt.com/
These videos are short 10min productions created by PatrickJMT in Texas for tuition in Maths . Patrick uses a whiteboard with marker and works solutions to problems and explains necessary theory; his videos are some of the best in the subject - clear and concise, suitable for StandardGrade to Advanced Higher, A-Level and indeed right through to Graduate University level:
I have compiled a downloadable index of  links to his videos (click here) in Word format.
 

 
Resource downloadable from this site.
See my tutorial videos on Calculus of Inverse-trig Functions suitable for Adv. Higher Maths (SQA),
 A2 Maths and UGMaths 1:
There is also Powerpoint presentation as well as
a summary suitable for print (click -here..pending).


Wolfram|Alpha. This is not a forum – it’s a “computational knowledge engine”. Many forum questions I saw can easily be solved using Wolfram|Alpha, for example “Convert 6 inches to cm.” or “Factor r^6 – 3r^4 +3r^2 -1″. And the answer will be correct!
You can also enter questions from almost any topic into the engine, e.g. science, news, history, biology and so on ad you are sure to get a meaningfull response: e.g. try "Newtons second law".
 Note: better interaction with Wolfram Alpha
if you register with them for free and use your login!

 

Note - due to different browsers rendition of files you need to download these pdf's then view them offline:

SQA Maths..
National Mathematics CfE (SQA link on the right side-bar):
Here are the course units support notes -summaries for the new CfE Scottish curricula... 
SQA Support-notes (course unit specs); 
 N3-Maths (LifeskillsNumeracy), 
LTS Summary guidance and support notes for the CfE applied Advanced Higher Maths options; Advanced Higher Mathematics of MechanicsAdvanced Higher Statistics.

Student Notes;
CfE Level4 Maths;
Level4-RevisionExercises (pdf-76pg - 9Mb)I-can students log tick-sheet.

CfE National4 Maths; 
N4Maths_homework-set1Q (pdf-15pg), 
N4Maths_AVUassessmentrevision (pdf-26pg), N4Maths_numeracytestQnA,  I-can students log tick-sheet.

CfE National5 Maths;
N5Maths-homework-booklet (pdf-18pg), I-can students log tick-sheet.
N5Maths-RevisionBooklet  questions (pdf-82pg) (here are the solutions-pending), 
N5_trig-revision -1, trig-revision-2, trig-revision-3, N5-vectors. 
Practice Papers AA_answersBCDEF.

N5Maths-Lifeskills-SQP(Paper1, paper2).
N3-N5-Progression and Guidance, CfEMaths-progression-flowchart, revision material and mind maps can be found at mathsrevision.

CfE Higher Maths;
 Higher-homework-booklet (pdf- 28pg), I-can student's log tick-sheet.
Course notes and weekly homework sheets can be found at MissDeely.weebly site. 
MissDeely'- HMaths Skill-Builder revision Questions (download this) (pdf- 60pg covering all three outcomes), Skill-Builder Answers-only (pdf- 40pg).
Recommended:- original HSN notes for current CfE and older NQ Higher Maths (link) - 
ps-  the CfEHigherMaths  has essentially same content as original NQ Higher Maths only assessment is different
I have attached my own examples, notes and exercise for R&Cunit- Applying algebraic skills to solve equations- polynomials Q-only (6pg-pdf), solutions pdf- suitable for prelim and exam revision.
(note: I intend to add a similar notes and exercises for inequalities and curve intersections soon).
Higher Maths practice papers for exam revision (yes do the multiple-choice also): 
Papers A, A_answers, B, C, D, E, F.

Casio FX-83GTPlus

For videos on youtube for National4 and 5 (and  through CfEHigher also) check out YouKenMaths playlist (link to his youtube channel); he uses the usual Casio Fx-83GT calculator and explains answers, markings against the relevant spec. outcomes- very clear- I recommend these.

Spec. of the FX-83GTPlus> Casio site.



National 4/5, Higher maths  Millburn Acadamy there is mind-maps, support notes and links to most past papers (inc. older NQ) at all levels from S1-S6 (link).
For Higher Homework (following older NQ course) from Hillhead S5 (link), 
and Higher Worksheets each outcome (this is suitable also for newer CfE course) (link).

Advanced Higher Maths _Oxford _for SQA CfE (2015)
CfE Advanced Higher Maths;
 Notes, past-papers mi's and homework at Millburn Acy (link), here is a comprehensive formulae-sheet (pdf) suitable for your studies, thanks to D. Watkins. 
SQA-Question paper formula-sheet (2pg),
Prelim AHMaths diagnostic test (Q-only)- my own! (worked soln pdf) 
sample AHMaths-prelim-with marking scheme (from 2009 pdf)
PastPapers-cross reference from NQ to newer CfE curriculum units (Knox Academy) 
Here's my own notes on vectors-lines-planes etc for AHMaths:- notes , examples (pdf)
An investigation into parametric-curves using WolframAlpha:- Lissajous pattern (pdf), Wolfram solutions.
My differentiation practice- exercise pdf (- answers pdf).
My short guide (with problems) to Complex Numbers and applications of DeMoivre' Theorem (-pdf 4pg) - answers (-pdf)
My First-Order Differential Equations practice notes  with exercise -pdf  (3-pg)  and their solutions- pdf

(for goodness sake- at this level I recommend to learn to use a graphics calculator!)
DLBMaths_youtube_channel

DLBMaths is at it again, see his half-hour video all about 1ODEs (First Order Differential Equations), very good at explaining all the various types, e.g. Linear, Seperable, Exact,  Integrating Factor and so on:


Here is a calculus Integral-Table (courtesy http://integral-table.com/) -pdf (14-pg)
Calculus Differential Equations summary guide - pdf (2-pg)
Laplace transforms table - pdf (1-pg).

How to use the Ti-84 (Ti-83) Plus Graphing Calculator (by Mike Floersch)-  half hour guide with examples in graphs, trig, statistics and programming:

For GCSE Maths (Foundation, Higher) a great revision guide in one 2hr video by
Primrose Kitten covering how to answer typical exam style questions:

The whole of GCSE 9-1 Maths in only 2 hours!! Higher and Foundation Revision for Edexcel, AQA or OCR

Primrose Kitten logo 
(Here is Primrose Kitten's website - link - recommended by myself)


Entertaining and educational presentation videos published by Youtube Mathloger
on all sorts of mathematical proofs such as irrationality of Pi, Fermat's Last Theorem,
Euler Number e and so on, he also includes videos for junior school as well as PostGraduate
level content:  Here's my abstract document of his channel(s) (pdf). (new*)
Mathloger: Epicycles, complex Fourier series and Homer Simpson's orbit (Youtube)..


Multivariable Calculus 
Course Assistant by Wolfram Alpha..
If you are having difficulty understanding and solving multivariate calculus problems in your course you might want to download the App from Wolfram Alpha (website):
    

Also Pauls's online maths notes (link) is a free source of notes, examples and assignments related to Calculus at this level. Also a set of online videos by 

Prof. Denis Auroux at MIT -see right hand side margin>



anorman728_Maxima CAS Tutorials_youtube


MAXIMA 5 CAS.

Here is an excellent short series of online (youtube) videos, by anorman728,
for this software CAS. The program is free to use on your PC, Mac or tablet.
I have produced a download (3pg pdf) of his playlist- pdf.

Here is a short 10-min tutorial (-pdf) on Maxima prepared by AntonioCangiano

Here also is my sample Matrices script which will open directly in the program if you have it installed!-zip file, here's also the printout of the script running in wmMaxima:
solving matrices EROs- script printout, working with matrices - script printout.
(I am producing a set of Maxima scripts for common problems upto UGMaths level soon).
UGMaths scripts - Laplace transform, inverse-transform and shift examples -zip fileEx script printout pdf .(new*)

The Open University Maths module Essential mathematics 1 (MST124) (link)
as well as other educational bodies, use this software- I recommend it (Maxima i.e.) for students of college, university or engineering courses (the program is similar to Maple).

 Maths examples and solutions  (grades Higher - PGrad) _ ExampleProblems.com is the first user-supported
free content online database of higher mathematics example problems.

Maths from the BBC (grades Standard - Higher)

Scottish Qualifications Authority

RSS Feed: SQA

 CfE - National Curriculum
(SQA Maths  link)
for N4-5-H-AH etc

 Wolfrom Research:    -

 International Baccalaureate
Maths:-
SL/HL/Studies/
IGCSE - free resources recommended site:
Adrian Sparrows Maths Pages 
 IB Subject assessment guide (view)
IBMathsSL(2014)-spec
 IGCSE (EdExcel)
2009-spec and forms 
TI_Nspire CX

TI-NspireCX recommend
(not the CAS)
also Ti-83/84
(not Ti-89/92)
unsure- see the approved list-pdf.


 GCSE Maths Tutor
This is a site with free revision books, worksheets, videos etc.. covering
Number, Algebra, Shape space, Information handling.
Exam papers from Edexcel and AQA.

Maths Tutor
This is a site covering
arithmetic, algebra, geometry, functions and calculus for A-Level and UnderGraduate.
Videos and supporting documentation.

 Examsolutions
 This site  is a GCSE,
AS and A-level Maths revision site with over
1200 free maths video tutorials and worked solutions to past papers.
(recommended)

UK-universities.net
Scotland Mathematics University Programs.

 Linear Algebra
MIT OpenCourseware.
Video lectures by Prof. Gilbert Strang (yes he whom wrote the book).
The material covers UG  year 1 and 2 of most university syllabus in Linear Algebra.
videos index | download Course Materials (zip 14MB)
Introduction to Linear Algebra 4th ed. 
- the book contents.

HNC Engineering Maths (for colleges)
recommended book:
Engineering Mathematics - K.A.Stroud 7th Edition
Engineering Mathematics-
K.A.Stroud & D.J.Booth currently 7th edition.
 - book contents -
Complete collection of  interactive Powerpoint slides and questions at support-  palgrave.com

SQA's Maths for Engineering-2 course:
Is a mandatory unit in most HND engineering courses- covers differentiation, integration and its application from an engineering perspective- DG4L-34 complete notes (pdf-without answers!).

 Calculus
Lifesaver series by
Prof. A. Banner
Princeton (videos)
I thoroughly recommend this resource as A. Banner
is a great teacher and his course covers most of the material found at Uni. single variable calculus course.
 
The book I recommend is>
Calculus7E-0538498846_cover
Calculus Early Transcendentals, 7 edition-J. Stewart
(about)-Stewarts's site.
 
I also recommend:
MathDrBob videos on youtube >  playlists
(don't be freightened by his Jiu Jitsu stuff - he's really nice chap!)
 
More advanced students: Complex Analysis as taught by Jose F. O'Farrill (Edinburgh Uni.) - link albeit as a physicist is still maths rigorous.

Multivariable Calculus  

taught by Prof. Denis Auroux

MIT 18.02 (2007) - link vectors, partials.

 
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