Hi! I am a second year mathematics student at the University of Warwick, with a love for pure maths - in fact since 14 I've been set on becoming a mathematician. My intense fascination with this field not only motivated me to study new concepts on my own, but also led to my continued experimenting with simple concepts in order to gain a deep and intuitive understanding. I hope to pass this intuition on to all of my tutees, along with useful methods that I have picked up, and most importantly an engagement with the subject, which I feel is the best route to success.

Throughout my time studying for A levels I frequently helped other students to understand and grasp new concepts, often to an extent where I was an impromptu teaching assistant, and in one particular case I taught my A level class about the Taylor expansion. I also spent one term helping to teach a younger class mathematics, during which I learnt how to simplify ideas into understandable chunks. In year 13, I undertook a project in which I wrote a concise guide to a pure branch of mathematics, group theory. I had to write with an intriguing tone, and also make use of pedagogic features like in-depth examples and analogies. All of this experience is still fresh in my memory, and so I am well-placed to tutor GCSE and A Level material at a high standard.

Hi! I am a second year mathematics student at the University of Warwick, with a love for pure maths - in fact since 14 I've been set on becoming a mathematician. My intense fascination with this field not only motivated me to study new concepts on my own, but also led to my continued experimenting with simple concepts in order to gain a deep and intuitive understanding. I hope to pass this intuition on to all of my tutees, along with useful methods that I have picked up, and most importantly an engagement with the subject, which I feel is the best route to success.

Throughout my time studying for A levels I frequently helped other students to understand and grasp new concepts, often to an extent where I was an impromptu teaching assistant, and in one particular case I taught my A level class about the Taylor expansion. I also spent one term helping to teach a younger class mathematics, during which I learnt how to simplify ideas into understandable chunks. In year 13, I undertook a project in which I wrote a concise guide to a pure branch of mathematics, group theory. I had to write with an intriguing tone, and also make use of pedagogic features like in-depth examples and analogies. All of this experience is still fresh in my memory, and so I am well-placed to tutor GCSE and A Level material at a high standard.

No DBS Check

Solving cubics is an interesting problem: while there is a formula which can find the roots of every cubic equation, it isn't taught and is not generally worth learning. Instead, exam questions will often give you a root of a cubic, and from that you are expected to fully factorise it, and hence find the roots. Let's look at an example!

Q: Given that -2 is a root of 2x^3 + 9x^2 - 2x - 24, find all roots.

A: Firstly, we know by the factor theorem that if ** a** is a root of a polynomial (a cubic, for instance), then

**2x^3 + 9x^2 - 2x - 24 = (x + 2)( )**

Now, we know that in the brackets there will be an * x^2* term, an

**2x^3 + 9x^2 - 2x - 24 = (x + 2)(2x^2 )**

Similarly, the constant term must be -12, because we need a -24 after multiplying out the brackets, and the **only** way to get a constant term here is by multiplying the two constant terms.

**2x^3 + 9x^2 - 2x - 24 = (x + 2)(2x^2 - 12)**

Now the ** x** term. if we start to multiply out, we see that we have

**2x^3 + 9x^2 - 2x - 24 = (x + 2)(2x^2 + 5x - 12)**

Finally, we just have to factorise the quadratic in the bracket. Using inspection, or failing that the quadratic formula (though this is more prone to error), we find that:

**2x^3 + 9x^2 - 2x - 24 = (x + 2)(2x - 3)(x + 4)**

Applying the factor theorem again, we find that the roots are -4, -2 and 3/2.

Solving cubics is an interesting problem: while there is a formula which can find the roots of every cubic equation, it isn't taught and is not generally worth learning. Instead, exam questions will often give you a root of a cubic, and from that you are expected to fully factorise it, and hence find the roots. Let's look at an example!

Q: Given that -2 is a root of 2x^3 + 9x^2 - 2x - 24, find all roots.

A: Firstly, we know by the factor theorem that if ** a** is a root of a polynomial (a cubic, for instance), then

**2x^3 + 9x^2 - 2x - 24 = (x + 2)( )**

Now, we know that in the brackets there will be an * x^2* term, an

**2x^3 + 9x^2 - 2x - 24 = (x + 2)(2x^2 )**

Similarly, the constant term must be -12, because we need a -24 after multiplying out the brackets, and the **only** way to get a constant term here is by multiplying the two constant terms.

**2x^3 + 9x^2 - 2x - 24 = (x + 2)(2x^2 - 12)**

Now the ** x** term. if we start to multiply out, we see that we have

**2x^3 + 9x^2 - 2x - 24 = (x + 2)(2x^2 + 5x - 12)**

Finally, we just have to factorise the quadratic in the bracket. Using inspection, or failing that the quadratic formula (though this is more prone to error), we find that:

**2x^3 + 9x^2 - 2x - 24 = (x + 2)(2x - 3)(x + 4)**

Applying the factor theorem again, we find that the roots are -4, -2 and 3/2.