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Amaths Modulus Function Graphs

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Ophelia, Wanchi, Olivia & Zoey

I understand you are studying this topic now. Please do the following 3 questions and hand up next lesson. Thanks!

***do remember to find and indicate y-intercept, x-intercept and turning point for sketching of graphs!! 🙂




Introduction to Classification of things: Living & Non-living things

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Here is a introduction quiz for my little P3 students who are taking Science subject for the first time next year!

Kindly complete this worksheet in 15 minutes. I will be going through this in class this week.

More interesting questions on classification of animals and plants are coming!

I will inform your mummies when those questions are ready!


Additional Maths – Trigonometry Functions and Equations, Proofing Trigo Identities

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For my sec 3 Amaths students,

Here are the trigonometry revision questions,

Before you attempt trigo questions, please study and remember the addition angle, double angle and trigo factor formulaes.

Speaking with not a bit of sarcasm tone**   🙂

“Seriously, there is no point doing and practicing the trigo questions without memorising the formulaes. You can do those simple practices for the start but you will face a lot of ‘stuck’ moments, with you trying to flip through the formulae page and the question page when you are solving the more challenging problems.”

Totally ineffective and waste of time. 😦

If you are still unsure on the R-formulae, here are some notes.

For the R-formulae,

It is actually from the addition formulaes.

R cos (x+α)
R [cosxcosα-sinxsinα] ( Think Addition Formula)
(R cosα)cosx-(R sinα)sinx

Hence, if we need to express 5 cos x – 7 sin x in the form of R formulae. (i.e R cos (x+α),

We just compare with the (R cosα) with 5 and (R sinα) with 7. (See that?)

tan α = 7/5 ⇒ α = 60.5°

To find R, we square everything.
R2cos2α+R2sin2α = 52+72
R2[cos2α+sin2α] = 74 ⇒ R =

∴ 5 cos x – 7 sin x =  cos(x+60.5°)


  • Re-arrange the sine and cosine terms depending on how the question wants you to express the R function.

x sin θ + y cos θ → if you require R sin (θ + α)

  • For R-function, always ensure first term is positive!

  • Double angle formulaes can be applied for all values of x, i.e 4x, 5x, 6x, 7x etc. Not only for the even number coefficients ones.

 cos 7x = cos (2 ( 7/2  ))

  • Only use Double Angle formulae when you can express whole expression in terms of one trigo function (i.e sin, cos, tan)


Now, ready?

Try these 5 questions. 🙂

1)                  Solve the following equations for O≤x≤3600

(a)   4 tan x + 2 tan (x-450)  –>Hint: Addition formulae

(b)   5 cos x – 2 sin ( x/2  ) =2 –>Hint: Half Angle formulae and work out the range for the half angle

(c)    cos 8x – 3 cos 4x = -1 –>Hint: Double Angle formulae and work out the range for the double angle identified.

(d)   4 cos x – 3 sin x = 4 –>Hint: R function formulae

(e)   2sin 2x = 7cos2x -2  —>Hint: Not Double Angle formulae. Only use Double Angle formulae when you can express whole expression in terms of one trigo function (i.e sin, cos, tan)


Well, another FAMOUS portion of AMaths Trigonometry is proofing identifies.

From what I observed from my previous students, those who are familiar with the trigonometry formulaes, did well naturally. It is actually quite thrilling for these students because they know they definitely got the marks in their pockets when they are able to proof LHS=RHS! woot!

2)                  Prove the following identities

(a)   tan A + cot A = 2cosec 2A

(b)   cosec 2B – cot 2B = tan B

(c)    (tan C +cot C)sin2C =2

(d)   cos D cos 2D – sin D sin 4D = cos 2D cos 3D

(e)  (1+sinE)/(1-sinE)  = (tan E+ sec E)2

Solutions will be posted next week if we did not manage to go through all of them in class. 🙂

P5 Science – Cells

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Teaching Cells to my P5 students this week.

Take a look at animal and plant cell. We are doing comparison of these 2 cells and learning the different parts and functions of a cell.

This is a plant cell.

Try to fill in the blanks with the cell parts below!

We will also be covering cell division, unicellular living compounds and also how cells form tissue and then organ. A few organs form a system.

Take a look at the questions below. I will be going through in class next week. 🙂

P5 Maths – Percentage

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This week, I am teaching a new topic to my P4 students. They will be in P5 next year and they are pretty excited about it.

Usually, I will cover those topics that they will be facing for the first time in P5. ( For instance, percentage, rate and average).

Here are this week exercises on percentage.

(You should already get the worksheets during lesson. If you lose it, please print from my website). 🙂

Parents and students, please do not get frustrated or discouraged if you are still unable to do the questions.

This is only the first lesson on percentage. I will be going through the questions next week.

See you all soon.

Hannahtuition Primary School Students 2012 SA2 Results! 100% Passes, 75% Band 2 and 15% Band 3!!

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Had been so tied up with my holiday program after my Europe trip.

Finally have time to tabulate my primary school students SA2 results.

I am happy for 100% passes! 🙂

Yet a bit disappointed that there is no Band 1 achievements. One of my boys got 82 and 83 for his maths and science, so its a little frustrating because it is just a few marks away from Band 1 (85).

In fact, several of them achieve more than 70. 🙂

For the past few weeks, I received more primary school sign-up for 2013.

Thank God for His faithfulness.

I will continue to do my best. I know I just do what i can do, God will do what I cant do. 🙂


Yes, I did work hard and I am proud of my achievements.

I thank God for bringing these children under my coaching and I will continue to mentor them in the best way i know how. 🙂

Sec 2 Express Maths & Science Group Tuition (Yishun) Monday night

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Greetings to all parents,

This is a special post.

I have a sec 2 boy waiting to form Maths & Science group tuition on Monday night (7-9pm).

I have another sec 2 group slot but its full. ( I only take in a maximum of 4 students in a class)

Parents of my sec 2 class, kindly let me know if you want to change your child to Mon night class. Thanks!

Location: My tuition room in Yishun – Just beside Yishun MRT ( Contact me at 82888792 for full address). 🙂

Fees: $170 (4 sessions – 2 hours each)

Material fees: $20 ( includes hannahtuition notes, worksheets and 10 sets of sch papers)

FYI. Regarding my lesson plans, my style is fine-tuned from tuition centres’ programmes. Because my class size is kept small, I am able to know and teach the topics that the students are learning in school concurrently. Usually, the discrepancy is only 2 topics for my group tuition.

In a nutshell,  I will spend 30 mins on the maths topics overview (including foundation quiz). Then students will do the questions on those topics that are covered or ask me questions from their homework. This 30 minutes of question time, I work with students individually to know their understanding level.  The next hour, similar process is carried out for Science.

Hannahtuition on holiday till 8Nov12

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Good day to all, 🙂

I received a few sms past few days regarding hannahtuition 2013 lesson timings.

I’m on holiday (in Europe) now and will only be back on 8Nov. I will revert with the details when I am back. 🙂

For enquiries on lesson rates and timing, kindly leave me your details (child’s level, previous grades, short description on child’s learning progress) at


Here are some of the lovely pictures I took in Italy. 🙂










The first 2012 primary school student SA2 results I received! Marvellous!

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Yesterday, I received a sms from one of my P4 boy’s mum.

My boy whom i start coaching from mid July this year has wonderful news for me.

I thought to myself: “What a good start. ”

A deep sense of peace settled in my heart and i somehow know that all of my primary school students will do well for this end of year examinations.

It has been a tiring period for the past few weeks, rushing for revision lesson after lesson. First for my secondary kids then for my primary kids… I am thankful that the taxing period is now over and I am confident that I have prepared them well for their examinations.

More good news awaits. 🙂

Hannahtuition Secondary Students Results! 100% passes! 73% Distinctions! 15% Bs and 12% Cs!

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I have completed about 120 lessons in the last 2 weeks of Sep and first week of Oct for my secondary students!

It is So tiring! But i declare that its all worth it as I stare at my harvest now. 😀

I had received all my secondary students’ results from sms and whatsapp over the past week and tabulated the results as follows;

Although I am happy for Hannahtuition’s secondary students 100% passes on Maths and Science,

I am quite shocked at some of my students’ Maths results. Some of them whom i thought can easily secure a A1 end up with a B3 instead. 😦

Although it didn’t hit my target of 80% distinctions, I have done my best and will continue to do so.  I believe I will have a bigger harvest next year!

* PS: My Hannahtuition secondary students, kindly drop me a note if you think i reflected the results wrongly. 🙂

Enjoy your holidays!!

As spoken, our lessons start second week of November! Dont’t miss me too much and See you! 🙂