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William U.

Currently unavailable: for new students

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

SubjectQualificationPrices
Further Mathematics A Level £30 /hr
Maths A Level £30 /hr

Qualifications

SubjectQualificationLevelGrade
MathsA-levelA2A*
Further MathsA-levelA2A*
PhysicsA-levelA2A*
ChemistryA-levelA2A*
Disclosure and Barring Service

CRB/DBS Standard

No

CRB/DBS Enhanced

No

Ratings and reviews

5from 135 customer reviews

Ismaeel (Student) June 15 2017

Helped provide me with tips for C3.

Ismaeel (Student) June 3 2017

Helped show me multiple ways to answer a question.

Ismaeel (Student) April 25 2017

He helped me with a difficult topic.

Shenal (Student) April 6 2017

Good session learnt a lot!
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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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2 years ago

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