Josh O. A Level Maths tutor, A Level Further Mathematics  tutor, GCSE...

Josh O.

£18 - £25 /hr

Currently unavailable: for regular students

Studying: Mathematics (Bachelors) - Warwick University

5.0
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1 review| 15 completed tutorials

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About me

I am an experienced mathematics tutor who specialises in teaching A-Level and GCSE mathematics. A less rigid learning structure enables students to understand how interconnected concepts are, which helps them in the long run. This approach is useful at A-Level and especially with STEP preparation, where papers aren’t as predictable. I'm welcoming and responsive when a student doesn’t quite grasp a concept. I’m available on Saturdays after 15:00. and all day on Sundays. Lastly, I am incredibly excited and enthusiastic about my subject. I won't go into too much detail here, but be reassured that I am a tutor who loves his work. Get in touch if you want to know more.I am an experienced mathematics tutor who specialises in teaching A-Level and GCSE mathematics. A less rigid learning structure enables students to understand how interconnected concepts are, which helps them in the long run. This approach is useful at A-Level and especially with STEP preparation, where papers aren’t as predictable. I'm welcoming and responsive when a student doesn’t quite grasp a concept. I’m available on Saturdays after 15:00. and all day on Sundays. Lastly, I am incredibly excited and enthusiastic about my subject. I won't go into too much detail here, but be reassured that I am a tutor who loves his work. Get in touch if you want to know more.

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About my sessions

Earlier in an academic year, sessions are usually pure theory, demonstrated with examples. Closer to exam season, many students understandably prefer to make use of past papers. For maths, they are an invaluable resource. I studied Edexcel mathematics at school, and I’m very familiar with their A-Level syllabus. If needed I can read up on another exam board's syllabus and tutor it. I prefer to hold regular sessions with a student over the course of a term or a year. This way I get to measure progress as well as carefully plan each session. I also (when needed or wanted) give homework, mostly to A-Level students. They go away and complete the questions and come back with any issues. In the next session, before doing any new work, I go thoroughly go through any mistakes on the previous homework.Earlier in an academic year, sessions are usually pure theory, demonstrated with examples. Closer to exam season, many students understandably prefer to make use of past papers. For maths, they are an invaluable resource. I studied Edexcel mathematics at school, and I’m very familiar with their A-Level syllabus. If needed I can read up on another exam board's syllabus and tutor it. I prefer to hold regular sessions with a student over the course of a term or a year. This way I get to measure progress as well as carefully plan each session. I also (when needed or wanted) give homework, mostly to A-Level students. They go away and complete the questions and come back with any issues. In the next session, before doing any new work, I go thoroughly go through any mistakes on the previous homework.

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Ratings & Reviews

5from 1 customer review
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Gill (Parent)

May 7 2017

Jack really enjoyed and benefited from your first tutorial. Your explanations were simple and very effective and he is enthused again ! Phew. Great job Josh

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Qualifications

SubjectQualificationGrade
MathematicsA-level (A2)A*
Further MathematicsA-level (A2)A*
BiologyA-level (A2)B
STEP IUni admission test1
STEP IIUni admission test2
STEP IIIUni admission test1
AEAUni admission testDISTINCTION

General Availability

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

Subjects offered

SubjectQualificationPrices
Further MathematicsA Level£20 /hr
MathsA Level£20 /hr
MathsGCSE£18 /hr
.STEP.Uni Admissions Test£25 /hr

Questions Josh has answered

Are we able to represent linear matrix transformations with complex numbers?

Absolutely. Consider a point (a,b). This may be represented by the complex number a+bi and also by the column vector (a;b), where the semicolon means 'new line'.

To translate the point by +(c,d), in complex numbers, this is done by adding c+di to a+bi.  In 2D space, this is done by adding (c;d) to (a;b).

To scale the point by a factor of r, in complex numbers, this is done by multiplying by r.  In 2D space, we do the very same thing.

To rotate the point about (0,0) by angle t in the counterclockwise direction, in complex numbers, we do this by multiplying by e^it. In 2D space, we multiply on the left hand side by the matrix ((cost,-sint);(sint,cost)).

To conclude, if we were to translate a point (a,b) by +(c,d), scale it by factor r and rotate it about the origin by angle t in the counterclockwise direction, then the following are two representations of it:

(a+bi)(re^it)+(c+di)

r((cost,-sint);(sint,cost))(a;b)+(c;d)

Absolutely. Consider a point (a,b). This may be represented by the complex number a+bi and also by the column vector (a;b), where the semicolon means 'new line'.

To translate the point by +(c,d), in complex numbers, this is done by adding c+di to a+bi.  In 2D space, this is done by adding (c;d) to (a;b).

To scale the point by a factor of r, in complex numbers, this is done by multiplying by r.  In 2D space, we do the very same thing.

To rotate the point about (0,0) by angle t in the counterclockwise direction, in complex numbers, we do this by multiplying by e^it. In 2D space, we multiply on the left hand side by the matrix ((cost,-sint);(sint,cost)).

To conclude, if we were to translate a point (a,b) by +(c,d), scale it by factor r and rotate it about the origin by angle t in the counterclockwise direction, then the following are two representations of it:

(a+bi)(re^it)+(c+di)

r((cost,-sint);(sint,cost))(a;b)+(c;d)

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2 years ago

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