PremiumJonathan B. A Level Maths tutor, GCSE Maths tutor, A Level Further Ma...

Jonathan B.

£24 - £26 /hr

Currently unavailable: for new students

Studying: Physics with Astrophysics (Masters) - Manchester University

5.0
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73 reviews| 206 completed tutorials

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About me

Hi! My name is Jonny and I recently graduated with a 2:1 in a Master's degree (MPhys) in Physics with Astronomy from the University of Manchester.

Tutoring Experience: I have been a private tutor for 5 years, initially teaching GCSE Science and Maths and continuing on to A Level Maths and Physics for the last 4 years. I am also a qualified tutor with The Tutor Trust.

Flexibility and availability: I am generally very flexible and will endeavour to find a time that works around your busy schedule!

As a tutor, I aim to share my enthusiasm for science and maths with younger students, and to supplement the material they cover in school. As well as helping students to build confidence in their own abilities, I also strive to provide understanding as to why science and maths are important, and where the skills these subjects teach can be applied in the real world.

I understand the difficulty a student can have in understanding a particular topic, or solving a certain problem, and my lessons will provide a comfortable environment in which they can overcome these challenges. My experience as a tutor has taught me how to adapt to the individual needs of the student and teach in an engaging and enjoyable way.

So, if you think I can help, or you'd simply like to know a little more, please feel free to get in touch. I look forward to hearing from you!

Hi! My name is Jonny and I recently graduated with a 2:1 in a Master's degree (MPhys) in Physics with Astronomy from the University of Manchester.

Tutoring Experience: I have been a private tutor for 5 years, initially teaching GCSE Science and Maths and continuing on to A Level Maths and Physics for the last 4 years. I am also a qualified tutor with The Tutor Trust.

Flexibility and availability: I am generally very flexible and will endeavour to find a time that works around your busy schedule!

As a tutor, I aim to share my enthusiasm for science and maths with younger students, and to supplement the material they cover in school. As well as helping students to build confidence in their own abilities, I also strive to provide understanding as to why science and maths are important, and where the skills these subjects teach can be applied in the real world.

I understand the difficulty a student can have in understanding a particular topic, or solving a certain problem, and my lessons will provide a comfortable environment in which they can overcome these challenges. My experience as a tutor has taught me how to adapt to the individual needs of the student and teach in an engaging and enjoyable way.

So, if you think I can help, or you'd simply like to know a little more, please feel free to get in touch. I look forward to hearing from you!

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Ratings & Reviews

5from 73 customer reviews
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Andreas (Parent)

August 15 2016

Always on time, making complex ideas simple, also very responsible regarding my studies.

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Jack (Student)

June 7 2016

Very clear at explaining concepts - thanks Jonny!

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Andreas (Parent)

April 15 2016

Repeatedly went over a concept that I was stuck in and now I fully understand it. Always on time, concentrated on the topic and very polite. Nothing negative to say.

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Emma (Parent)

October 27 2015

Jonny has helped my son no end to improve his understanding of the subject. Excellent. Thanks Jonny!

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Qualifications

SubjectQualificationGrade
MathematicsA-level (A2)A*
Further MathematicsA-level (A2)A
PhysicsA-level (A2)A
ChemistryA-level (A2)B

General Availability

Before 12pm12pm - 5pmAfter 5pm
mondays
tuesdays
wednesdays
thursdays
fridays
saturdays
sundays

Subjects offered

SubjectQualificationPrices
Further MathematicsA Level£26 /hr
MathsA Level£26 /hr
PhysicsA Level£26 /hr
MathsGCSE£24 /hr
PhysicsGCSE£24 /hr

Questions Jonathan has answered

How do you differentiate arctan(x)?

Differentiation of arctan(x), also written tan^(-1)(x), requires a little knowledge of regular trigonometric algebra and differentiation, and implicit differentiation. 

Let's set y = arctan(x) to start. Then, by the definition the arctan function, tan(y) = x. We recall the derivative of the tan function, d(tan(u))/du = (sec(u))^2.

So, if we differentiate both sides of our equation with respect to x, we find that (dy/dx)((sec(y))^2) = 1, using the rules of implicit differentiation. Now, we can rearrange our equation for dy/dx = 1/((sec(y))^2). 

Thinking about some trigonometric algebra, we know that* (sec(y))^2 = 1 + (tan(y))^2. Additionally, remember that tan(y) = x as we said earlier! Using this information, simple substitution back into our equation yields dy/dx = 1/(1+x^2).

So, d(arctan(x))/dx = 1/(1+x^2).

 

 

 

*For a reminder of where this comes from, think about the trigonometric relation: (sin(y))^2 + (cos(y))^2 = 1.

Differentiation of arctan(x), also written tan^(-1)(x), requires a little knowledge of regular trigonometric algebra and differentiation, and implicit differentiation. 

Let's set y = arctan(x) to start. Then, by the definition the arctan function, tan(y) = x. We recall the derivative of the tan function, d(tan(u))/du = (sec(u))^2.

So, if we differentiate both sides of our equation with respect to x, we find that (dy/dx)((sec(y))^2) = 1, using the rules of implicit differentiation. Now, we can rearrange our equation for dy/dx = 1/((sec(y))^2). 

Thinking about some trigonometric algebra, we know that* (sec(y))^2 = 1 + (tan(y))^2. Additionally, remember that tan(y) = x as we said earlier! Using this information, simple substitution back into our equation yields dy/dx = 1/(1+x^2).

So, d(arctan(x))/dx = 1/(1+x^2).

 

 

 

*For a reminder of where this comes from, think about the trigonometric relation: (sin(y))^2 + (cos(y))^2 = 1.

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3 years ago

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