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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 Online Lessons. In my Online Lessons, 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 Online 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.

We first consider 1/z=(cosx+isinx)^(-1). Application of De Moivre's theorem for integer n: (cosx+isinx)^(n)=cosnx+isinnx yields the result 1/z=cosx-isinx. Addition of the two forms z and z^(-1) steers us to the result, albeit with this being double the result.

Roots:
2x^2 -5x-12 = (2x+3)(x-4)
x=-3/2 or x=-4
Complete the square:
2x^2 -5x-12 = 2((x-5/4)^2)-12/8

Answered by Dorothy B.

Studies Chemical Engineering at Imperial College London

Think about the point a+bi on the complex plane. Specifically, a is how far along the x (real) axis, and b is how far up the y (imaginary) axis the point is. If you draw a line connecting the origin and the point a+bi then notice that you've constructed a triangle with sides a, b, and sqrt(a^2+b^2). Recall that tan of an angle = opp/adj, applying this to the triangle gives that the angle between the x-axis and the line from the origin is equal to arctan(b/a). This is exactly what the argument of a complex number is, the angle between the x-axis and the line connecting the number and the origin.

Answered by Martin S.

Studies MMORSE (Master of Mathematics, Statistics, Economics, and Operational Research) at Warwick

We will look at an example. (I will show the example in the online lesson space)
First we have to know the formulas we will need to use. We have to look at the example and choose all of the formulas that seem relevant. After that, we will use the formulas while also manipullating the functon to get at our result.

We have that the Taylor series of a function infinitely differentiable at a *x* = *a* is given by the expansion:
f(*x*) = f(*a*) + f'(*a*)(*x - a*) + f''(*a*)(*x - a*)^{2}/2! + f'''(*a*)(*x - a*)^{3}/3! + f^{(4)}(*a*)(*x - a*)^{4}/4! +...
Thus we differentiate f(*x*) 5 times and evaluate at zero (as in this case *a* = 0) in order to obtain all our coefficients.
f(*x*) = tan(*x*), f(0) = tan(0) = 0
f'(*x*) = sec^{2}(*x*) = 1 + tan^{2}(*x*) = 1 + f(*x*)^{2}, thus f'(0) = 1 + f(0)^{2} = 1 [by writing f'(*x*) in terms of f(*x*), we can skip differentiating reciprocal trig functions and simply leave the derivates in terms of f(*x*) and its derivatives of lower order]
f''(*x*) = 2f'(*x*)f(*x*), f''(0) = 0
f'''(*x*) = 2(f''(*x*)f(*x*) + f'(*x*)^{2}), f'''(0) = 2
f^{(4)}(*x*) = 2(f'''(*x*)f(*x*) + 3f''(*x*)f'(*x*)), f^{(4)}(0) = 0
f^{(5)}(*x*) = 2(f^{(4)}(*x*)f(*x*) + 4f'''(*x*)f'(*x*) + 3f''(*x*)^{2}), f^{(5)}(0) = 16
Thus the first three non-zero terms of the Taylor series for tan(x) are: x + 2x^{3}/3! + 16x^{5}/5! = x + x^{3}/3 + 2x^{5}/15

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Version: | 3.56.1 |

Build: | 24f1c972e5be-RR |

Time: | 2018-01-15T15:29:36Z |

Our Further Maths A Level Tutors 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 a Further Maths A-Level Tutor. Your Maths A Level Tutor 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.