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

FRONTLINE UPDATE:

As forecasted, the dense fog cleared at 2.30pm this afternoon, revealing for a historical first time the likes of Partial Fractions, Double-Angle Formulae and Addition Formulae upon the A-Maths battleground.

After an agonizing informational blackout for hours, word began filtering through to The Temple:

I COULD DO ALL THE QUESTIONS! 🙂 Just hope no careless mistakes.

IT WAS OKAY I SURVIVED! Guess I could think better at the last-minute. (Miss Loi: -_-)

Can do all questions! Hehe. I hope all correct. Hehe.

I was thinking of you throughout the paper haha

And so, like last year, it appears that the enemy was annihilated in today’s opening skirmish.

Narrowing her eyes with guarded optimism, though, Miss Loi now know that the pivotal AMaths battle will be fought this Friday, where the weightage and stakes are higher, and where she knows for certain that the following heavyweights will be unleashed:

1. Plane Geometry
2. Curves & Circles
3. Modulus Functions
4. Sum & Product of Quadratic Roots
5. Trigonometry – R-Formula
6. Trigonometry – Factor-Formula
7. Trigonometry – Equations & Graphs
8. Rate of Change
9. Integration – Area Under Curve(s)
10. Coordinate Geometry
11. You’ll still need to revise your general Differentiation, Integration, Trigonometry!

Hail to all who fought well today! Rest well and conserve your energies, for Mathematical Armageddon awaits on Friday!

Onward we march to Super Friday!

P.S. Do spare a thought and pray for Miss Loi’s lungs too as she chokes on the hundreds and thousands of joss sticks that are being burnt at The Temple in preparation for this Friday’s Mathematical Armageddon.

• If you’re stuck or can’t prove the earlier part of a proving question, a Show question, or a Hence question, CONTINUE to do the next part using the ‘proven’ expression (even though you couldn’t prove it). Don’t leave the second part blank!

• Remember that:

  mega/million = 106 giga/billion = 109 tera/trillion = 1012

  micro = 10-6 nano = 10-9 pico = 10-12

• Do a final practice to ensure that you know which buttons (e.g. DATA, σn etc.) to use in YOUR calculator for mean and standard deviation calculations.
• Pay attention to the axes and extreme ends of the cumulative frequency curve, and be familiar with how to derive a box-and-whisker plot from it.
• Always double-check if angles in a question are in degrees or radians (when expressed in π i.e. π radians = 180°)
• When calculating arc length (s = rθ), or the area of sector (A = 1/2r²θ) i.e. that θ must always be in radians!

A-MATHS Specific

• Take note of this table of the Principal Values of inverse trigonometric functions:

  Function	Domain	Range (Principal Value)
  y=sin-1x	-1 ≤ x ≤ 1	–π/2 ≤ y ≤ π/2 (1st & 4th quadrants)
  y=cos-1x	-1 ≤ x ≤ 1	0 ≤ y ≤ π (1st & 2nd quadrants)
  y=tan-1x	Real Numbers	–π/2 < y < π/2 (1st & 4th quadrants)

  Some sample questions on this obscure but EXAMINABLE topic …

  • Find the principal value of sin^-1(1/2).

    Ans: Let sin^-1(1/2) = y
    ⇒ sin y = 1/2
    ⇒ y = π/6 (In the principal value range (-π/2 ≤ y ≤ π/2), y has to be in 1st quadrant for sin y to be positive)
    ∴ sin^-1(1/2) = π/6

  • Find the principal value of cos^-1(-1/2).

    Ans: Let cos^-1(-1/2) = y
    ⇒ cos y = -1/2
    ⇒ y = 2π/3
    (In the principal value range (0 ≤ y ≤ π), y has to be in 2nd quadrant for cos y to be negative)
    ∴ cos^-1(-1/2) = 2π/3

  • If A is the principal value of tan^-1(-7/24), find, without using calculator, the value of sin(-A).

    Ans:
    
    In the principal value range (-π/2 < A < π/2), A has to be in 4th quadrant for tan A to be negative, and we can obtain the values in the diagram via Pythagoras’ Theorem.

    From the diagram, sin A = -7/25
    So sin(-A) = -sin A = -(-7/25) = 7/25

• Be familiar with the shapes of the curves of y = ax², ax³, , , a√x, a ³√x and y² = ax, for BOTH a > 0 and a < 0.
• Know the steps to deriving the Trigonometry R-Formula (look under ‘Deriving The R-Formula’ in the notes), especially when high marks are allocated to the part of the question.
• Go through these Plane Geometry questions one more time, for many tend to forget their own proving methods/solutions upon revisiting them.