Daniel V. GCSE Maths tutor, A Level Maths tutor, Mentoring -Personal ...

Daniel V.

£18 - £22 /hr

Currently unavailable: for regular students

Studying: Economics (Bachelors) - Cambridge University

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About me

I am a student at Cambridge University, completing a degree in Economics.

Maths tutoring:

Mathematics has played a large role in both my secondary school eduaction and at university. Thus, while I know how enjoyable and satisfying it can be to study it is also important for students to aquire a good level of mathematical understanding in order to tackle the questions that can push them into that next grade.

During sessions I am happy to cover any questions that students have. We will explore both the understanding behind a solution and how to execute the answer in the best way possible. The use of words, equations, diagrams and even drawings all come in handy when discussing problems and we can tailor the sessions to your preffered style of learning

University applications:

I am also available to discuss and develop personal statements as well as university preparation (interviews/tests etc.), particularly for economics related degrees.

I have recent experience of writing my own personal statement and so I know how hard they can be to get going! However, we will be able to look at my own, as well as other model personal statements in order to create a fantastic piece of writing for you. 

As well as personal statements, interviews form a large part of university applications, particularly for oxbridge applicants. Again, I am willing to share my own experience, develop your interview/communication skills and perform mock interviews in order to prepare you in the best possible way. Having been through the interview process myself and having spoken to academics at Cambridge I can offer great advice to hopeful applicants.

I am a student at Cambridge University, completing a degree in Economics.

Maths tutoring:

Mathematics has played a large role in both my secondary school eduaction and at university. Thus, while I know how enjoyable and satisfying it can be to study it is also important for students to aquire a good level of mathematical understanding in order to tackle the questions that can push them into that next grade.

During sessions I am happy to cover any questions that students have. We will explore both the understanding behind a solution and how to execute the answer in the best way possible. The use of words, equations, diagrams and even drawings all come in handy when discussing problems and we can tailor the sessions to your preffered style of learning

University applications:

I am also available to discuss and develop personal statements as well as university preparation (interviews/tests etc.), particularly for economics related degrees.

I have recent experience of writing my own personal statement and so I know how hard they can be to get going! However, we will be able to look at my own, as well as other model personal statements in order to create a fantastic piece of writing for you. 

As well as personal statements, interviews form a large part of university applications, particularly for oxbridge applicants. Again, I am willing to share my own experience, develop your interview/communication skills and perform mock interviews in order to prepare you in the best possible way. Having been through the interview process myself and having spoken to academics at Cambridge I can offer great advice to hopeful applicants.

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Qualifications

SubjectQualificationGrade
MathsA-level (A2)A*
Further Maths A-level (A2)A*
Physics A-level (A2)A*
Economics A-level (A2)A

General Availability

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

Subjects offered

SubjectQualificationPrices
EconomicsA Level£20 /hr
MathsGCSE£18 /hr
-Oxbridge Preparation-Mentoring£22 /hr
-Personal Statements-Mentoring£22 /hr

Questions Daniel has answered

Integrate the function f(x) = (1/6)*x^3 + 1/(3*x^2) with respect to x, between x = 1 and x = 3^(1/2), giving your answer in the form a + b*3^(1/2) where a and b are constants to be determined.

We can imagine our function as a curve. We have x values on the x axis and f(x) values on the y axis of our graph. 

The question is essentially asking us to find the area between the curve, the x axis and the lines x=1 and x=31/2. It is a definite integral.

To integrate our function we simply use the rule that the integral of xis [1/(n+1)]*xn+1.

To make the function easier to work with we can rewrite f(x) as (1/6)*x3 + (1/3)*x-2.

Using the rule above we can integrate this function easily, with respect to x, to get (1/24)*x4 - (1/3)*x-1. Call this new function g(x).

To check we have obtained the correct integral, we can simply differentiate this new function, g(x). If the differential of g(x) is equal to f(x) then we have got the correct integral. It is always smart to do this check when working with integration.

The next step of our solution is to integrate f(x) between the given limits: x = 1 and x = 31/2. To do this we evaluate g(x) at x = 31/2, by simply subbing in the value for x, and then subtract from this answer the value of g(x) at x = 1. 

We should get [3/8 - (1/9)*31/2] - [-7/24].

The final part of our solution is to rearrange our answer to get it in the form a + b*31/2.

The final answer to the question is: 2/3 - (1/9)*31/2.

We can imagine our function as a curve. We have x values on the x axis and f(x) values on the y axis of our graph. 

The question is essentially asking us to find the area between the curve, the x axis and the lines x=1 and x=31/2. It is a definite integral.

To integrate our function we simply use the rule that the integral of xis [1/(n+1)]*xn+1.

To make the function easier to work with we can rewrite f(x) as (1/6)*x3 + (1/3)*x-2.

Using the rule above we can integrate this function easily, with respect to x, to get (1/24)*x4 - (1/3)*x-1. Call this new function g(x).

To check we have obtained the correct integral, we can simply differentiate this new function, g(x). If the differential of g(x) is equal to f(x) then we have got the correct integral. It is always smart to do this check when working with integration.

The next step of our solution is to integrate f(x) between the given limits: x = 1 and x = 31/2. To do this we evaluate g(x) at x = 31/2, by simply subbing in the value for x, and then subtract from this answer the value of g(x) at x = 1. 

We should get [3/8 - (1/9)*31/2] - [-7/24].

The final part of our solution is to rearrange our answer to get it in the form a + b*31/2.

The final answer to the question is: 2/3 - (1/9)*31/2.

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1 year ago

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