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Category Archives: Secondary

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°)

EXAM TIPS:

  • 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. 🙂

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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.

Sec 2 Maths Quiz (Direct, Inverse proportions, Scales, Congruence & Similarity) 2 top scorers this time!

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There are 2 top scorers for this quiz!

Score: 78%

  • Jasmine Toh ( Sengkang Secondary School)
  • Justin Lim ( Nan Chiau High School)

Jasmine is a hardworking and very positive girl. She is focused on her goals and I am very sure her goals are not too far away from her. Kudos!

Justin is intelligent. Someone who grasps Mathematical and Science concepts very fast but he needs to be more careful in his work. I am sure he can attain higher grades with focus. Lastly, I am very impressed with the delicious mooncakes he made with his mum. *thumbs up*. 🙂

 

Lower Sec Maths – Simultaneous Equations and Linear Graphs Quiz

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Top Scorer: 85%

Justin Lim

(NAN CHIAU HIGH SCHOOL)

Justin is a intelligent boy. However, he needs to focus and be CAREFUL in his work. 🙂

I believe he can do well in the coming end of year examinations! 🙂

Forming Simultaneous Equations from word problem VIDEO

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Hey Jessie,

Here you go!

I have looked through your workings below and realise you are unable to form the 2 simultaneous equations because you didnt realise that Toby and Sheryl age are not the same 5 years ago, 5 years later and presently. 😦

Its ok. Do a few more of these practice questions and I am sure you will get the drift. 🙂

 

Please attempt the question again after watching the video and also another similar question that i have send to you via watsapp.

Do submit these 2 questions to me this Thurs. 🙂

Lower Secondary Inequality Question (Mathematics) VIDEO

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Hey Jas T,

look at the video to solve the inequality question you sent me today.

 

Let me know if you still have any questions.

Good night! 🙂

 

 

Sec 2 Algebra Quiz ( Top Scorer: Jasmine Toh , Sengkang Secondary School)

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Sec 2 Algebra Quiz ( Top Scorer: Jasmine Toh , Sengkang Secondary School)

Top Scorer: Jasmine Toh

(Sengkang Secondary School)

Jasmine scored 20 out of 25 which is a pretty 80%.

I have 7 Secondary 2 students (both NA and Express). I gave them the same paper and I am proud to see that a few of my NA students did very well. 😀

I think it shows that it is OK that you are not one of the PSLE top scorers. As long as you work hard in secondary school, you can still catch up. I believe everything is possible and we should give the young ones hope. 🙂