Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favorite Private Tutor

Let us pray …

Oh our dear Heavens, look down on us
your elite crack GCE O Level 2009 A-MATHS students,
who are doomed to suffer the 2nd-half of the Week of Mathematical Armageddon,
and watch with envy the next two days
our single-maths brethrens and sisters in their decadent ways.

We thank you again for answering our prayers!
For sending us an another easy EMaths Paper!

SO EASY!

Should be can leh. 2 questions you did before came out leh o.O

No construction question came out at all! How awesome is that??

While others burn their maths books as we speak,
for us, its only halfway through The Week.
So once again your blessings we seek!

• Give us this day divine guidance
  that we may see the earthly errors of our common careless mistakes
  like how ≠
  and how ≠
  and how sin² x ≠ sin x² (DUH)
  and how sin x + cos x ≠ 1 (DUH!!!)

• Grant us the strength to summon the right technique of differentiating and integrating various functions
  however confusing they may be.

  • Give us the sight
    to see that minus sign in
    and the absence of it in

  • Give us the wisdom
    to deal with exponential functions
    so we DON’T subtract 1 from its power when differentiating
    i.e. ≠
    or add 1 to/divide by its power when integrating
    i.e.
    ≠
    ≠

  • Give us more wisdom
    to avoid attempting a nigh-impossible integration/differentiation
    when they both appear together in a Hence question

  • And when we rejoice in our successful integration,
    we pray that you remind us in our finest moment
    to write our dx and + c(for indefinite integrals).

• May we not lose our Identity Matrix, I =
  and may we be wise not to ‘anyhow’ play with the order of our matrix equation:

  AX = B ⇒ X = A^-1B ≠ BA^-1

  XA = B ⇒ X = BA^-1 ≠ A^-1B

• May we be enlightened enough
  to embrace the oft-misunderstood Laws of Logarithm.

  Should we be called upon
  to sketch an exponential graph like y=10−10e^−0.5t
  to trace the riotous journey of some crazy kinematic particle,
  we pray that you hold our hands steady
  and assure us that everything begins with y=e^t
  (i.e. shift up/down, flip up/down/left/right …)

  And should we be called upon to sketch a logarithmic curve
  we pray we remember that y=ln(x−1) cuts the x-axis at x=2.

• Grant us the power to discipline p(x)/q(x) in Partial Fractions
  with a long division should it be IMPROPER
  Grant us the instinct to look out for repeated linear factors

  ≠

• We implore you to plant these handy expressions:

  α² + β² = (α + β)² − 2αβ ≠ (α + β)²
  (α − β)² = (α + β)² − 4αβ

  deep in the roots in our subconsciousness
  that we may find our Sum & Product of Roots with ease.

• Should the phrase “Line MEETS curve” be encountered,
  bless us with the instinct to recognize that it’s
  b² − 4ac ≥ 0
  NOT b² − 4ac > 0

• Last but not least,
  please, please, please,
  for the sake of our 7-9 marks,
  just let our 阴阳眼s of Plane Geometry come.

Forgive Miss Loi once more
for not saying more than what’s been said before (read only the AMaths portion).

But show no mercy on us
if our minds begin to wander near the end.
For remind us you must
to check our answers while we can.
Especially the part (i)s that affect parts (ii) and (iii)
and those near the end with higher weightage they carry.

So lead us, oh dear Heavens, to our Mathematical LIBERATION!
That we may lead a fair life free from calculus and quadratic inequalities
at least until our poly/JC term starts.