A-Maths Tuition

What You Need To Know To Do Well In Plane Geometry - Part 1

Plane Geometry is the new topic added in the new syllabus. There are hardly any calculations but lots of proving to be done.
We know students dislike proving, be it in Plane Geometry, Trigonometry, Quadratic Equations, Differentiation . . .

To score As in your exam, you must be good in proving.

Plane Geometry has proven to be a challenging topic for many students due to the nature of the diagrams, questions. Many a times, students do not know when to begin, not to mention which theorems to apply. I am going to share with you in this post on the key concepts you need to know at your fingertips for Plane Geometry.

There are 2 basic shapes in Plane Geometry: Triangle & Circle

In Triangle,

You must know the different Congruency Tests & Similarity Tests. These are extremely important in proving plane geometry questions. Teachers did not emphasize on this as students are expected to know these concepts well from E-Math. But I realize many many students did not like Congruency & Similarity as it involves proving (which is a very systematic approach of thinking) and hence many did not understand these 2 concepts well.
Mid point theorem (This is not exactly your mid point formulae in Co-ordinate Geometry)

D and E are the midpoints of AC and AB respectively.

Intercept theorem

When DE//CB, AD/DC = AE/EB

I will be adding on specific properties for circle in my next post. If you like to be updated, subscribe to my feed by clicking HERE

What Happens When Integration Question Is in the form of Product?

I posted an interesting question on Integration here.

Allow me to repeat. There isn’t any product rule nor quotient rule in Integration.

So to Integrate the question, some "extra" work must be done to "dissolve" the product nature of the question.

These are the steps that must be taken even before Integration beings:

Factorise the terms inside the Square Root
Combine common term (2x+1) by applying Indices Law
Remember to + c as this is a indefinite integral aka no limits given

Integration Mixed With Differentiation

In Integration, unlike Differentiation, there isn't any product rule nor quotient rule. Having said this, examiners always like to present question in that form of either product or quotient. Students who aren't able to see through their plot to confuse your mind will fall straight into their trap.
So LOOK OUT!

The question most students will ask next will be what to do when the Integration is presented in the manner as if we can use product or quotient rule aka the given question is in the form of a fraction.

These are the few ways you can work around it

Simplifying either by breaking up the numerator
Simplification by applying Indices Law (very useful when you are working with exponential or bases-powers)
Apply partial fraction concept

Look at this question:
$\int (2x+1)\sqrt{8x+4} dx$

It is expressed as two product. How do we integrate?

Discuss your approach in the comment box below.

I will reveal the step by step approach by end of this week. Be sure to subscribe to www.singaporeolevelmaths.com/feed so that you will be notified of latest updates

Cheers!

Does Stubborness Earn You More Marks?

I was doing Factor, Remainder Theorem with one of my students. She's a brilliant girl but has yet to achieve the results she truly deserves. I think she knows the reasons clearly :-)

She likes to do things her way.

And I am totally fine with students having their own style. Afterall, my best method might not be their best method. However, if their style is not helping them in terms of scoring, time management..., this is where I step in to influence and get them to better understand how my strategy (usually a much shorter way as I am a lazy person :-)) might help them to understand and get the answer faster and easily.

I get them to buy my idea. And most of the time, my idea sells out :)

Today post will be on Identity covered with Factor-Remainder Theorem.

There are 2 main methods to solve the question. And for me, I choose the "lazy" method again. Simply because it is easy, fast and accurate!