William continues to provide, excellent support to my son - helping him to go beyond being able to answer a complex question with a by rote, step by step approach - to having a much fuller understanding of the concepts. This mean that he feels much better equipped to deal with what the exam might throw at him. Thanks very much Will : )

Susan, Parent from Hertfordshire

Why limit yourself to someone who lives nearby, when you can choose from tutors across the UK?

By removing time spent travelling, you make tuition more convenient, flexible and affordable

We've combined live video with a shared whiteboard, so you can work through problems together

All your tutorials are recorded. Make the most out of your live session, then play it back after

Usually we cover both subject knowledge and exam technique, although that can change depending on each individual student. Then we go through diagrams, and they ask questions, and we go from there.

Lots of students say that the classes are too big in school, or that they don't have time to ask teachers after lessons. In my tutorials, we take time to explore things in a little in a bit more detail.

I always look up the board my students are taking so the lessons are really relevant. Then we go through past papers or set texts, whatever the student finds helpful.

I use the shared whiteboard. We make diagrams together and label them, and often the student prints it off because they know it's right and they completely understand it.

After tutoring one girl went and told all her friends the new explanation I gave her. And she was so excited about what she wrote in the exam she emailed me immediately afterwards.

There was one girl who had her exam on Monday. She wanted tuition on Friday, Saturday and Sunday beforehand. It was very intense, but she said the exam went well.

First we must establish how to differentiate terms individually. This is done by using the simple method of multiplying the X by the power, and subtracting one away from the power.
To make it easier we will differentiate each term individually and then put the equation back together at the end.
1. x^2
2*x^(2-1) =2x
2. 9x
1*9x^(1-1) = 9x^0
=9*1 = 9
3. 8
0*8^(0-1) = 0
Therefore dy/dx = 2x+9
This would be useful if the gradient needed to be found. To find the gradient at a point all you need to do is substitute in the X value.

Start by moving all the terms to one side of the inequality. In this case it's easiest to move the 6x to the left hand side by subtracting 6x from both sides, so that you are left with x^3 + x^2 - 6x > 0. Then factorise the cubic equation so that you get x(x+3)(x-2) > 0. From this form you can see that x=0 ; x= -3 and x= 2 solve the cubic equation, so these are the points, where the graph of y= x^3 + x^2 - 6x crosses the line y=0 (the x axis). Next sketch the cubic graph and you will be able to see clearly, which values solve the inequality. In this case, since x^3 + x^2 - 6x >0 it will be all the parts of the graph above the x axis, which are -3 < x < 0 and x > 2.

Answered by Miron S.

Studies Physics at Edinburgh

first the definition of the rank of a matrix is "maximal number of linearly independent column vectors in the matrix"

then the question could be rephrased to " how many independent column vectors are there".

so what we want to do is actually to find how many independent column vectors this matrix has.

to find the number of independent columns, use Elementary Row Operations (would be demonstrated with an example matrix in detail in real class) to find the rank.

Something further things to note after covering the main thing above:

1. The above method can be used to find the rank of a matrix, be it square or not.

2. To save the calculation, determininant of a square matrix can be checked beforehand, if it is non zero then the rank is its number of columns (rows).

3. If the matrix is a zero matrix, its rank is 0.

Answered by Yilin S.

Studies Mathematics and Statistics at Oxford, St Anne's College

First, let's think of how many different possibilities we have to seat 6 people at a 'normal' table, i.e. in a straight line. Let's call the people A, B, C, D, E, F. We now have 6 seats:

__ __ __ __ __

When we pick who gets to sit on the first seat, we have 6 options to choose from. For the second seat, there are still 5 people left to choose from, 4 for the third, 3 for the fourth, 2 for the fifth and only one person is left over to sit on the last seat. So we have:

6 x 5 x 4 x 3 x 2 x 1 = 6! = 720 possibilities.

Now if instead the table is round, there is 'no first seat'. If everybody rotates through one seat to the left, each person still has the same people to their left and right and we say the configuration is identical. There are 6 different seats for A to seat on that correspond to identical configurations (simply keep rotating the whole group through) - so compared to the 'normal' table, we have overcounted by a factor of 6. The number of possibilities is now:

6! / 6 = 720 / 6 = 120

Answered by Sjoerd B.

Studies Natural Sciences (Physics and Maths) at Durham

(bx+d)(bx-d)=b^2x^2-d^2

(ax-c)(bx+d)(bx-d)=(ax-c)(b^2x^2-d^2)=ab^2x^3-ad^2x-b^2cx^2+cd^2

ab^2=3

b^2c=2

ad^2=147

-cd^2=98

From equations:

a=3/b^2

c=2/b^2

d^2=49b^2

Since a, b, c, d are positive integers, b must be 1. Then a=3, c=2, d=7

The procedure of mathematical induction is as following:

Firstly prove the base case is true i.e. when n=1, the statement is true.

Then assume for some integer n=k the statement is true, and then prove the case n=k+1, the statement is true.

Make a conclusion that by mathematical induction, the statement is true.

For this particular question, the base case is when n=0, the statement is true, since it is asked for 'all non-negative integers'. It is because 11^{2x0}+25^{0}+22=24 is divisible by 24 (24=24x1).

Then let's say P(n) is the proposition that 11^{2n} + 25^{n} + 22 is divisible by 24. Assuming that P(k) is true for some integer k=n, then 11^{2k} + 25^{k}+ 22 is divisible by 24.

The most important step comes: we then prove that P(k+1) is true. i.e. 11^{2k+2} + 25^{k+1} + 22 is divisible by 24.

It is true because 11^{2k+2} + 25^{k+1} + 22=121x 11^{2k}+25x25^{k}+22=(120 + 1)11^{2k} + (24 + 1)25^{k} + 22= (120 x11^{2k} + 24 x25^{k})+ (11^{2k} + 25^{k}+ 22). Expressions in both brackets are divisible by 24. so P(k+1) is true.

Then we are done. We could conclude that by mathematical induction the statement is true for all non-negative integers.

Answered by Xunrui Z.

Studies Mathematics and Economics at LSE

Company information

Popular requests

Cookies:

Are you there? â€“ We have noticed a period of inactivity, click yes to stay logged in or you will be logged out in 2 minutes

Your session has timed out after a period of inactivity.

Please click the link below to continue (you will probably have to log in again)

Every tutor on our site is from a **top UK university** and has been** personally interviewed** and ID checked. With over 7 applications for each tutor place, you can rest assured you’re getting the best.

As well as offering **free tutor meetings**, we **guarantee every tutor who has yet to be reviewed on this site,** no matter how much prior experience they have. Please let us know within 48 hours if you’re not completely satisfied and we’ll **refund you in full.**

Every time a student and parent lets us know they have enjoyed a tutorial with a tutor, one 'happy student' is added to the tutor's profile.

mtw:mercury1:status:ok

Version: | 3.27.1 |

Build: | 979bcece8e5d |

Time: | 2017-01-03T14:51:33Z |

Your message has been sent and you'll receive an email to let you know when responds.

Tutors typically reply within 24 hours.

Tutors typically reply within 24 hours.

Thanks , your message has been sent and we’ll drop you an email when replies. You should hear back within 24 hours.

After that, we recommend you set up a free, 15 minute meeting. They’re a great way to make sure the tutor you’ve chosen is right for you.

Thanks , your message has been sent and we’ll drop you an email when replies. You should hear back within 24 hours.

After that, we recommend you set up a free, 15 minute meeting. They’re a great way to make sure the tutor you’ve chosen is right for you.

**Limit reached ***(don't worry though, your email has still been sent)*

Now you've sent a few messages, we'd like to **give the tutors a chance to respond**.

Our team has been notified that you're waiting, but please contact us via

support@mytutor.co.uk or **drop us a call on +44 (0)203 773 6020** if you're in a rush.

**Office hours are 8am to 7pm**, Monday to Friday, and we pick up emails on weekends.

Thanks,

The MyTutor team

**Limit reached ***(don't worry though, your email has still been sent)*

Now you've sent a few messages, we'd like to **give the tutors a chance to respond**.

Our team has been notified that you're waiting, but please contact us via

support@mytutor.co.uk or **drop us a call on +44 (0)203 773 6020** if you're in a rush.

**Office hours are 8am to 7pm**, Monday to Friday, and we pick up emails on weekends.

Thanks,

The MyTutor team

**Limit exceeded ***(Your message will not be sent)*

You should have recieved a notification with your previous message, and **our team have also been notified that you're waiting.**

If you're in a rush, please contact us via support@mytutor.co.uk or **drop us a call on +44 (0)203 773 6020** .

**Office hours are 8am to 7pm**, Monday to Friday. We also pick up emails on weekends.

Thanks,

The MyTutor team

**Limit exceeded ***(Your message will not be sent)*

You should have recieved a notification with your previous message, and **our team have also been notified that you're waiting.**

If you're in a rush, please contact us via support@mytutor.co.uk or **drop us a call on +44 (0)203 773 6020** .

**Office hours are 8am to 7pm**, Monday to Friday. We also pick up emails on weekends.

Thanks,

The MyTutor team

OurÂ FurtherÂ Maths A Level TutorsÂ will give you that focused, individual attention which could make all the difference to your grade. Gaps in your learning, careless mistakes and ineffective time-management during the exams can all be overcome with the expert guidance of aÂ FurtherÂ Maths A-Level Tutor.Â YourÂ Maths A Level TutorÂ will also ensure you have plenty of past papers to complete, as practice, repetition and excellent exam technique are key to Maths A Level success.