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Trigonometry - Proving Questions Are Good!

(4)
Posted at 7:11 pm by Miss Loi in A-Maths Questions

Proving questions are good.
Proving questions are important.
Proving questions helps you remember the formulas.
So don't be lazy and don't always skip the proving questions in your homework!

Show that

{2-cosec^2 x}/{cosec^2 x+2 cot x}={sin x-cos x}/{sin x+cos x}

Ignore at your peril!

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Similarity - Ratios Fetish

(4)
Posted at 7:02 pm by Miss Loi in E-Maths Questions

It has been a holy weekend with an unholy schedule for Miss Loi. As this hectic weekend (thankfully) comes to an end, Miss Loi would like to leave you with a question on Similarity. Miss Loi's students will know that she has an unnatural fetish for these questions (triangles and all) as they sometimes tend to pop up uninvited and unannounced in Vectors area as well.

Diagram

ABCD is a quadrilateral with AB parallel to DC. AC and BD meet at E where BE = 6 cm and DE = 9 cm.

  1. Given than AC = 35 cm, find the length of AE.
  2. Find the ratio of area of triangle BCE : area of triangle CDE.
  3. Find the ratio of area of triangle ABE : area of triangle CDE.
  4. Find the ratio of area of triangle BCE : area of triangle ADE.

Ok that's all for now while Miss Loi takes a sip of coffee and enjoys the brilliant sunset in front of her, contrary to what is being reported in her Ever-Reliable Apple Weather Widget *sigh!*

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The Ever-Reliable Apple Weather Widget

(1)
Posted at 8:50 pm by Miss Loi in Miss Loi's Car

Apple Weather Widget Screenshot

Apple Weather Widget in Miss Loi's Mac (7 April ~3pm)

Rainy BKE

BKE looking like a road to Mordor (7 April ~3pm)

Made Miss Loi nearly late for her tuition today. Tsk tsk!

Disclaimer: Photo from car and widget screenshot taken by Miss Loi's passenger, as doing such things while driving is a punishable offence in Singapore, and er, probably anywhere else in the world.

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Small Increments & Approximations - A Familiar-Looking Inverted Cone of Water

(9)
Posted at 7:07 pm by Miss Loi in A-Maths Questions

After thwarting the Persians with the three Spartans, Miss Loi will be busily lighting up many many joss sticks to 'celebrate' this long weekend!

To spice up your holidays, she will leave you with a commonly-asked question starring an enigmatic inverted cone of water that has been sighted many many times ...

Diagram of a very familiar inverted cone of waterThe diagram shows a vertical cross-section of an inverted cone of height 10 cm and base radius 6 cm. Water is poured in to a height of x cm.

  1. Show that the volume, V cm3, of water in the container is (3π/25)x3 cm3.
  2. Find the approximate increase in V when x increases from 3 to 3.02 cm.

Next time, instead of daydreaming at the water dispensor, why not think about how familiar the little cone you're drinking from is going to be in your exam? :)

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Numbers - The Three Spartans

(5)
Posted at 5:08 pm by Miss Loi in E-Maths Questions

Nevermind if you are too young to know who the Spartans were. But because they tend to appear (whether as Spartans or not) in your E-Maths Paper 1, so STUDENTS!!! PREPARE YOUR HOMEWORK!!!!!!!!!!!!!

Spartan ShieldTo warn King Leonidas of the approaching Persian army, three Spartan scouts are assigned to send signals from three different posts at 0600 hours everyday. The first Spartan signals every 16 seconds, the second Spartan signals every 40 seconds and the third Spartan signals every 64 seconds.

Find the time, correct to the nearest minute, when the three Spartan scouts signal simultaneously.

HAROOH!!! HAROOH!!! HAROOH!!!

P.S. If thou art still stuck, do climb a mountain and seek the Oracle in the form of Miss Loi's wise old primary school teacher friend Mdm Lau Chio Min. But please be gentle to her and don't shout "HAROOH!!!" into her face.

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