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William U.

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

5.0
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148 reviews

This tutor is also part of our Schools Programme. They are trusted by teachers to deliver high-quality 1:1 tuition that complements the school curriculum.

192 completed lessons

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.

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.

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About my sessions

During my lessons I am happy to both teach new material and to help the student practise previous topics. I like to focus on examples, from past papers and from other sources; and make sure to discuss the key observations required to solve them fully. It is helpful for me when students ask questions about anything they don't fully comprehend, as then we can work together on clarifying their understanding.

During my lessons I am happy to both teach new material and to help the student practise previous topics. I like to focus on examples, from past papers and from other sources; and make sure to discuss the key observations required to solve them fully. It is helpful for me when students ask questions about anything they don't fully comprehend, as then we can work together on clarifying their understanding.

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Personally interviewed by MyTutor

We only take tutor applications from candidates who are studying at the UK’s leading universities. Candidates who fulfil our grade criteria then pass to the interview stage, where a member of the MyTutor team will personally assess them for subject knowledge, communication skills and general tutoring approach. About 1 in 7 becomes a tutor on our site.

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Ratings & Reviews

5from 148 customer reviews
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Brendon (Student)

February 24 2018

Very good at simplifying the difficult c4 concepts!

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Manoj (Parent from Watford)

May 27 2017

Will has done an excellent job tutoring further Maths for my son during AS levels. My son achieved 97% UMS for further maths. I will highly recommend William for maths tutoring.

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Ismaeel (Student)

June 15 2017

Helped provide me with tips for C3.

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Ismaeel (Student)

June 3 2017

Helped show me multiple ways to answer a question.

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Qualifications

SubjectQualificationGrade
MathsA-level (A2)A*
Further MathsA-level (A2)A*
PhysicsA-level (A2)A*
ChemistryA-level (A2)A*

General Availability

Pre 12pm12-5pmAfter 5pm
mondays
tuesdays
wednesdays
thursdays
fridays
saturdays
sundays

Subjects offered

SubjectQualificationPrices
Further MathematicsA Level£30 /hr
MathsA Level£30 /hr

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 (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.

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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