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William U.

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Degree: Mathematics (Masters) - Oxford, St John's College University

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About me

About Me

I am a Mathematics student at Oxford University, and have a real interest in helping those who are in a similar position to my own a few years ago. I am passionate about science and mathematics, and believe that a firm understanding of the basics is absolutely essential for mastering these subjects at higher level, and also provides fascinating insight on the world!

Academic Qualifications

I achieved 100% at GCSE and A Level Maths, and also over 99% in A Level Further Maths. In 2014 I sat and passed the MAT paper.

Lessons

During lessons, I can teach to any syllabus, and am very willing to explain whatever you find most useful, while ensuring that all necessary material is covered. I encourage two-way learning, and will provide opportunity for you to explain topics to me and to submit work for marking and feedback. I like to use several teaching methods, and believe that content should be demonstated with clear, relevant examples.

Contact Me!

You can send me a message through "WebMail", or book a "Meet the Tutor Session", using this website. Please let me know which exam and board you would like help with, as well as any specific topics.

Subjects offered

SubjectLevelMy prices
Further Mathematics A Level £24 /hr
Maths A Level £24 /hr

Qualifications

QualificationLevelGrade
MathsA-LevelA*
Further MathsA-LevelA*
PhysicsA-LevelA*
ChemistryA-LevelA*
Disclosure and Barring Service

CRB/DBS Standard

No

CRB/DBS Enhanced

No

Currently unavailable: for new students

Ratings and reviews

5from 54 customer reviews

Barinov (Student) November 22 2016

Very kind and intelligent person Very good explanations and examples

Joseph (Student) June 19 2016

Last session with Will and it went very good. Couldn't have asked for a better tutor to help me through my Further Maths exams!

Muniza (Parent) May 30 2016

Very helpful tutorial as always. Thank you.

Muniza (Parent) June 2 2016

Great tutorial. Thanks.
See all reviews

Questions William has answered

[FP2] Solve: 3 cosh x - 4 sinh x = 7

First write cosh and sinh as exponentials, from their respective definitions: sinh x = 1/2 (ex  - e-x) cosh x = 1/2 (ex  + e-x​) So:   3 * 1/2 (ex  + e-x​) - 4 * 1/2 (ex  - e-x) = 7 Multiply by 2:  3 * (ex  + e-x​) - 4 * (ex  - e-x) = 14 Expanding gives:   3 * ex  + 3 * e-x  - 4 * ex + 4 * e...

First write cosh and sinh as exponentials, from their respective definitions:

sinh x = 1/2 (e - e-x)

cosh x = 1/2 (e + e-x​)

So:   3 * 1/2 (e + e-x​) - 4 * 1/2 (e - e-x) = 7

Multiply by 2:  3 * (e + e-x​) - 4 * (e - e-x) = 14

Expanding gives:   3 * e + 3 * e-x  - 4 * e+ 4 * e-x = 14

Collecting terms:   -ex + 7 * e-x = 14

So:   ex - 7 * e-x + 14 = 0

Since ex is not 0, we can multiply by it:

ex * ex - 7 * e-x *e+ 14 * ex = 0

e2x - 7 + 14 * ex = 0

This is a quadratic in ex, and we can use the quadratic formula to obtain:

ex = -7 +- 2 root 14

But ex > 0, so we discount the negative root:

ex = -7 + 2 root 14

x = ln ( -7 + 2 root 14)

Which can easily be checked with a calculator.

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11 months ago

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