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!

Weekly Question

See the question below, this should be a simple and common question for differentiation and integration, weekly, we will post different questions to prepare students for the exam. Answer with explanation will be posted together to facilitate students in studying.

Question 20 July 2009:



Answer:
(i) To get the acceleration, we need to differentiate the velocity equation.

If acceleration is zero,

Remember to change the mode of calculator when calculating the t.
To find v, we have to substitute the answers we got previously.


(ii) In order to find the total distance, we have to integrate the velocity equation.
Total distance travelled for the first 1.5s:
Note: Remember to write the answers in 3 significant figures and don't forget about the unit as well, if applies.

Additional Maths Module 1 Exam

Hi boys and girls!

Hope all those who have taken the exam did well. For those who made lots of careless mistakes/errors during the exam, please read the comments that I have written for you.

The average score for this paper for all those who taken is 65(B3). If you have noticed, some of the questions were from the regular quiz questions that we did during the previous lessons. (Aha! Good for those who got my hint!)

Take note that the whole rationale of sitting for this exam is to condition yourself in an exam environment and applying your "brains" on the questions. Only under such circumstances, you will REALLY realise what are the things that you know, and the things that you do not know. Scientists have done researches and found out that the human brain, works most efficiently under condusive environment coupled with a little stress which can be created during an exam.

Thus I have stressed the importance of taking this exam as it will gear you up for the coming Preliminary Exams that you will taking in Mid August, and followed by the O Levels in October.

Let's see how things go then. See you all during Module 2! Take care for now!

Sean
The Tutor

Additional Maths Module 1 Lesson 4

Hi Students! Today makes the end of our Additional Maths Module 1. I hope you have enjoyed your stay with us. The topics covered during this lesson are:

1.)Coordinate Geometry
2.)Linear Law

For Coordinate Geometry, do remember the following formulae:

• Distance between 2 points
• Mid point between 2 points
• Gradient of line joining 2 points
• Proving collinearity
• 3 ways to find the equation of a line
• Finding the equation of perpendicular bisector
• Finding the perpendicular distance
• Area of a polygon (shoelace method)
• Proving for parallelogram (using mid point formula)

Once you master them, you should be able to solve any Coordinate Geometry question!

For Linear Law, do remember the following:

• Converting a non-linear equation to a linear equation
• To find the gradient from the linear graph to solve for unknowns
• To find the Y-intercept from the linear graph to solve for unknowns.

That should be all. Please prepare for the Additional Maths Module 1 Exam on the 5th of July from 3pm-7pm. ( The paper will last 2hr 30min, explanation of the solutions will last 1hr 30min)

This is purely optional but I highly encourage students to attend it. If you have friends who are interested, please bring them to attend as well. No charges will be imposed for new comers.

Oh yes, remember to bring your stationary, calculator, long ruler! Ok see you guys!! =)

Additional Maths Module 1 Lesson 3

Yo Students! We have covered the following during lesson 3.

1.)Logarithms

2.)Exponential

3.)Modulus Functions

Let's not forget the common mistakes that we have gone through during the class. Please complete your homework and submit to me next lesson. See you then!

Additional Maths Module 1 Lesson 2

Yo Students! We have covered the following topics in Lesson 2:

1)Simultaneous Equations in Two Variables
2)Partial Fractions
3)Binomial Theorem

Pls do your homework and submit on the coming Sunday 21st Jun! See ya!

Additional Maths Module 1 Lesson 1

Yo students! I hope Lesson 1 had not been too boring! Ok, let us do a quick recap of the topics we had covered in Lesson 1:

1.)Quadratic Equations and Inequalities
2.)Surds and Indices
3.)Polynomials (Remainder and Factor Theorem)


Quadratic Equations and Inequalities
I am sure everyone remembers the "Discriminant" right?
Always remember that for an expression/curve/quadratic equation that is always positive, the parabola faces upwards (smiling curve) and will never cross/touch the x-axis, which means no roots (imaginary roots) Therefore...

For an expression/curve/quadratic equation that is never negative the parabola faces downwards (frowning curve) and it may either cut the x-axis at two distinct points or just touch the x-axis at one point. This means that it may have 2 distinct roots or repeated roots. Therefore ...

As for the Alpha/Beta section, things to note when solving such questions:

• Find the coefficients of the quadratic equation (a,b,c)
• Find the sum of roots.
• Find the product of roots.
  

You will be asked to find the new roots,which you will need to manipulate the equation to the original sum and product of roots. By substituiting them, you will get the new sum and product of roots. Following that always remember that you must an additional minus sign (-) for the new sum of roots for the new equation. That should solve the question. =)

Surds and Indices
Remember the law of indices on page 19 of the course book....
For surds, rationalising the denominator will be common and always remember the following:

Polynomials (Remainder and Factor Theorem)

For solving of cubic equations, do you remember how to use the equation mode in the calculator? Under Mode, choose Eqn. Choose 3. Plug in the values of a,b,c,d. Press “=” and you will get all the 3 roots. Use the first root as the factor and perform long division. From there, you will be able to factorise the quadratic equation.

Thats all for now! See you in Lesson 2!!!

Cambridge O Level Question 2002Q1

A curve has gradient ,

at point (x, y). Given that the curve passes through the point (0,3), find the equation of the curve.

Answer:
We need to integrate the equation of gradient in order to find the equation of the curve.

How to practice more A-Maths questions in shortest time.

Often, when the exam is coming soon, students will encounter a problem while trying to practice more questions.

Below are a few tips to practice more questions in short period:


1. Do more challenging questions first.

• Normally, in an assessment book, the easier questions come first, followed by the tougher question. If the assessment book is in topical format, you may try the last question, normally denoted with a *, or highlighted by the book. If you are comfortable in solving a few of such questions, you may proceed to do another topic.

2.Think, with no writiing.

• It maybe very time consuming if you want to write down all the steps and working to get the answer. Furthermore, normally students are facing the problem of understanding the questions during exam, rather than don't know certain topic. Hence, this is to practice the students on understanding the question pattern and hence help in solving question in shorter time.

3.Learn beyond scope.

• Normally, experience help when solving question. If the scope of learning is only to know how to solve simple questions, find more challenging questions to do. It will not be a waste to know more than current scope, as eventually students will learn it in higher level, however, keep in mind that, if we know how to solve the questions of higher level, normally to solve lower level questions will not be tough.
  

4.Practice, Practice, and Practice

• Although we have summarize on how to practice more effectively, practices are still something that must not be missed. Students need to do a lot of practices, to prepare for the high tension environment during exam. For students with more practices, normally the questions will be solved with ease.
  

All the best for the coming exam. In Flexi Tuition Learning Group website, we will keep posting questions , some with answers to help students in preparing for the exam.:

For E-Maths:
http://ftemaths.blogspot.com/