Plane Geometry

Let us start from a simple question. This is more to learn on how to study a question. By having this skill, students will not need to worry about any kind of question.

ABC and DBC are equilateral triangles. Prove that
Think:
Whenever we attempt to a question, we should start from all the information given in the question and form a complete diagram from it.

Information we can get from the question:
equilateral triangle: means all 3 sides have same length, and all 3 angles included are the same.

Answer:
For those angles that we need to prove, first let them as an unknown for easier in visualization.


As ABC and DBC are equilateral triangles, and both triangles share BC,
AC = CD

EC is side shared by triangle EAC and triangle EDC.
Therefore, Triangle EAC and triangle EDC are congruent (SAS).

Plane Geometry

Dear students, I am pretty sure that plane geometry might looked complicated at the first sight. This few days, i am going to teach you all on how to simplify the complexity of plane geometry questions with step by step guide and tips on attempting this kind of questions.

Below is the link to the summary on what you need to equip yourself before attempting plane geometry. In a nutshell, plane geometry is nothing but just application on everything you have learnt in solving geometry question such as, trigonometry (sine rule, cosine rule and etc.), Pythagoras Theorem, Properties of circles, inner angles and external angles of polygons, similarity and congruency of triangles.

Have fun and email your question to flexituition@gmail.com if you have any.

Plane Geometry Note 1

Plane Geometry Note 2

A Good Question from a Student (Jason)

Oh yes, I was being challenged by Jason with this question. It was pretty tricky and I almost fell for it too. Hehe. There you go, attached the question with full solutions. Find the area bounded by the curves and y-axis.

Additional Maths Module 2 Lesson 4

Yo Students! Today marks the end of the Module 2! As things were pretty rush, I tried my best to answer every question that was being brought up by everyone. I hope everyone understood the topics covered today.

1.)Integration
2.)Application of Integration I : Area Under a Curve
3.)Application of Integration II: Kinematics

Under the topic of integration, always remember that if you are not sure of your answer, try to differentiate your answer to see if you can obtain the original form.

Integration of exponential terms, trigo functions have all been gone through today. Some ways of solving integration problems is to split the equation into its simpler terms, either by applying the partial fraction method, or the individual fraction terms.

For Area Under a Curve, always note what the question wants you to find. It is normal to find the intersecting points of 2 curves, thus from there you can find the lower and the higher limit of the integral order. Lastly, use regular shapes like triangles,trapezium,rectangles to speed up the finding of the area under the curve.

For Kinematics, most important thing you must note is the original equation that is provided.
s denotes displacement
v denotes velocity
a denotes acceleration

We differentiate s to get v, differentiate v to get a, while we integrate a to get v, integrate v to get s. Take note of the constants during integration from a to v or from v to s. Constants are normally provided, when t=0s.

Ok, that is all for now, I hope its clear for everyone. Its been good knowing everyone, especially those who went through more than 32 grueling hours of maths solving with me, your efforts will definitely be paid off. I wish you all the best for coming Module 2 Exam that I've prepared for you all this coming Sunday 9th of August. There will only be one paper of 18 questions, 100 marks, to be completed in 2.5hrs

Morning Paper is at 10am-12.30pm
Afternoon Paper is at 3pm-5.30pm

Pls "read" through the quiz questions before coming for the Exam. Lastly, before I pen off, have lots of rest and drink lots of water during this period of time. All the best!