Daniel F. A Level Maths tutor, A Level Further Mathematics  tutor, GC...

Daniel F.

£20 - £22 /hr

Currently unavailable: for regular students

Studying: Maths and Philosophy (Bachelors) - Durham University

5.0
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4 reviews| 28 completed tutorials

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About me

About Me:

Hi, I'm Dan and I am in my third year of studying Maths and Philosophy at Durham University. I have a real interest in my subjects and hope that this level of understanding and enthusiam comes across in my tutorials.

I also have teaching experience, having assisted in lessons at GCSE and A Level, as well as more informal sessions among friends.

Outside of my studies, I love playing piano, going to live gigs and cooking.

About the Tutorials

With these sessions, you will be the one who decides what we cover. I look to address any issues you may have with your studies, and leave you with both the understanding and problem-solving ability to go out and tackle future problems yourself.

I also understand that learning is not something that happens in hour-long sessions, but something that takes time. Because of this I'm always happy for my students to message me whenever you need help.

I look forward to meeting you!

About Me:

Hi, I'm Dan and I am in my third year of studying Maths and Philosophy at Durham University. I have a real interest in my subjects and hope that this level of understanding and enthusiam comes across in my tutorials.

I also have teaching experience, having assisted in lessons at GCSE and A Level, as well as more informal sessions among friends.

Outside of my studies, I love playing piano, going to live gigs and cooking.

About the Tutorials

With these sessions, you will be the one who decides what we cover. I look to address any issues you may have with your studies, and leave you with both the understanding and problem-solving ability to go out and tackle future problems yourself.

I also understand that learning is not something that happens in hour-long sessions, but something that takes time. Because of this I'm always happy for my students to message me whenever you need help.

I look forward to meeting you!

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Ratings & Reviews

5from 4 customer reviews
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Bilal (Student)

January 20 2016

Very excellent tutor who goes over concepts efficiently! He also goes the extra mile for students by providing them with full detailed answers, homework type questions and help beyond tutorials. Would honesty recommend this tutor to any struggling Maths students. Thanks Daniel!

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Matthew (Parent)

May 11 2015

Daniel helped our daughter with A level maths in the few weeks leading up to her final exam. He was flexible, interested and helped to explain concepts in a way that was different to school. We would recommend him to other parents.

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Matthew (Parent)

May 1 2015

going well

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Matthew (Parent)

April 22 2015

Off to a great start.

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Qualifications

SubjectQualificationGrade
MathsA-level (A2)A*
Further MathsA-level (A2)A*
Philosophy and EthicsA-level (A2)A
English LiteratureA-level (A2)A
MusicA-level (A2)A

General Availability

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

Subjects offered

SubjectQualificationPrices
Further Mathematics A Level£22 /hr
MathsA Level£22 /hr
MathsGCSE£20 /hr

Questions Daniel has answered

How do I integrate cos^2(x)?

The key to solving any integral of this form is to use the cosine rule:

cos(2x) = cos2(x) - sin2(x) = 2cos2(x) - 1 = 1 - 2sin2(x)

All of these forms are really helpful when solving problems such as this, and it's great if you can remmeber them, though if you get stuck in an exam, they can all be derived from the addition formulae that are probably on your fomula sheet!

So, using the above idenities, we know that:

2cos2(x) - 1 = cos(2x)

2cos2(x) = cos(2x) + 1

cos2(x) = (cos(2x) + 1)/2

So instead, we perform the integral of (cos(2x) + 1)/2, which we already know how to do.

=> (sin(2x))/4 + x/2

The key to solving any integral of this form is to use the cosine rule:

cos(2x) = cos2(x) - sin2(x) = 2cos2(x) - 1 = 1 - 2sin2(x)

All of these forms are really helpful when solving problems such as this, and it's great if you can remmeber them, though if you get stuck in an exam, they can all be derived from the addition formulae that are probably on your fomula sheet!

So, using the above idenities, we know that:

2cos2(x) - 1 = cos(2x)

2cos2(x) = cos(2x) + 1

cos2(x) = (cos(2x) + 1)/2

So instead, we perform the integral of (cos(2x) + 1)/2, which we already know how to do.

=> (sin(2x))/4 + x/2

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3 years ago

860 views

How do I integrate log(x) or ln(x)?

The integral of log(x) is not necessarily straight-forward. Though we can use the fact that d/dx(log(x)) = 1/x to help us.

Rather than simply trying to integrate log(x), we can use integration by parts on 1 x log(x) (as in 'one times' log(x)).

So we can differentiate the log(x) part and integrate the 1 part to give:

xlog(x) - ∫ 1 dx = xlog(x) - x

Note: if the middle step isn't clear, we can write it more explicitly as

u = log(x)  v' = 1

u' = 1/x     v = x

Where the rule for integration by parts is written as:

uv' = uv - ∫ u'v    ,  where u and v are functions of x

The integral of log(x) is not necessarily straight-forward. Though we can use the fact that d/dx(log(x)) = 1/x to help us.

Rather than simply trying to integrate log(x), we can use integration by parts on 1 x log(x) (as in 'one times' log(x)).

So we can differentiate the log(x) part and integrate the 1 part to give:

xlog(x) - ∫ 1 dx = xlog(x) - x

Note: if the middle step isn't clear, we can write it more explicitly as

u = log(x)  v' = 1

u' = 1/x     v = x

Where the rule for integration by parts is written as:

uv' = uv - ∫ u'v    ,  where u and v are functions of x

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3 years ago

1762 views

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