Hi! My name is Alex, and I am currently a student at Durham University, studying Accountancy! I came to Durham from The Netherlands, having spent my entire life there, but have British and French parents. Having gone to an international school, and learned from people of all sorts of cultures and backgrounds, I have a unique take on many subjects in that I have learned many concepts in a different way to how most schools teach them. For me, understanding the concept is the most important part of learning -- if a student doesn't have an understanding of what is happening, then there is no way that he or she will be able to apply it in the future!
This international understanding can also help with University applications, as I have applied and received offers from several top European and American institutions.
Learning is meant to be fun, and it is often not the student's fault if a concept is difficult to grasp -- it is usually the teacher who is at fault for not making the lessons memorable, and for not helping the student where it is necessary. I can provide support throughout the day, and can offer early morning and late night support sessions if such is necessary, as well as on weekends. My support goes beyond these one to one sessions, as I am always available to mark and look at past papers, homework and assignments in order to ensure that the progession towards mastering subjects is continual.
Remember that learning is not all about grades -- it is about understanding, and if the understanding is in place, then you will succeed!
|Dutch||A Level||£20 /hr|
|French||A Level||£20 /hr|
|Business Studies||GCSE||£18 /hr|
|English Language||GCSE||£18 /hr|
|English Literature||GCSE||£18 /hr|
|Business Studies||IB||£20 /hr|
|French||13 Plus||£18 /hr|
|Maths||13 Plus||£18 /hr|
|Maths||11 Plus||£18 /hr|
|-Personal Statements-||Mentoring||£20 /hr|
|IB Business and Management||Baccalaureate||7|
|Before 12pm||12pm - 5pm||After 5pm|
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There are many methods of expanding quadratic equations, however there is one method which I find to be far easier than the others. This method is called the "box method", and allows this to be done quickly and reliably!
Here is an example. Take this example question : Expand the quadratic equation ( x + 2 ) * ( x + 3 ).
First, you must draw a box divided into 4 quarters, as shown:
Then, you need to place one of the brackets on the top and on the left side of this box, as below:
Then all you need to do is muliply the number or variable on the top of the box, and on the side of the box.
Box A therefore is : x * x = x2
Box B therefore is 3 * x = 3x
Box C therefore is 2 * x = 2x
Box C therefore is 3 * 2 = 6
Then just add up all of the results and simplify : x2 + 3x + 2x + 6 = x2 + 5x + 6
This method also works if you have more than two figures in each bracket, so if you get asked to expand the following, you simply follow the steps again!
Expand (x3 + 4x2 + 5x + 7) * (x + 2)
First, you must draw a rectangle of two boxes in height, but simply make it longer!
2 |____e____|_____f ____|______g___|_____h____|
Then follow the same steps again, multiplying one side of the box by the other
Box A : x3 * x = x4
Box B : 4x2 * x = 4x3
Box C : x * 5x = 5x2
Box D : 7 * x = 7x
Box E : 2 * x3 = 2x3
Box F : 4x2 * 2 = 8x2
Box G : 2 * 5x = 10x
Box H : 2 * 7 = 14
Add them all up to get : x4 + 4x3 + 2x3 + 5x2 + 8x2 + 7x +10x +14 = x4 + 6x3 + 13x2 + 17x +14.
And there you go! The easiest and quickest way to expand a quadratic equation!see more