Miss Loi avatar

Till Death Do Us Part

Tuition given in the topic of E-Maths Tuition Questions from the desk of Miss Loi at 9:38 am (Singapore time)

Updated on

On a quiet day, Miss Loi sat in a lotus position in the Zen-like confines of The Temple to mark her students’ homework.

The gentle air-con breeze caressed her silky hair as, with a singular mind and soul that’s free from the worries of the world, she proceeded to ruthlessly splash red ink across those horrid lines of unintelligible workings.

A buzzing sound broke the Zen-like calm, as a fly settled on an opened page of the Vectors Chapter of her E-Maths textbook.

Down came Miss Loi’s 1000-Newton 如来神掌 (Explosive Buddha Palm???) upon the poor fly, to deliver swift justice for its trespassing.

Or so it seemed.

As someone who prides herself as a one-hit-one-kill ace, she watched in disbelief as the fly did a little flight of triumph before settling on another part of the Vectors page of the textbook.

Down came another 1000-Newton 如来神掌 … and another … and another, with the wily fly constantly able to avoid its fate at the last minute with each passing slam.

Nursing her swollen red palm, it suddenly dawned on her that, given The Temple‘s propensity to heighten the learning abilities of all living things in its proximity, the fly might have actually been reading and understanding the Vectors Chapter that it rested on, for it somehow managed to fly away with just the right speed (magnitude) and direction regardless of where Miss Loi’s lethal palm came hurling from.

But as a great leader once hypothesized, complacency can affect all of us. After the latest miss by Miss Loi, the fly was apparently finished with its Vectors page and settled instead on a piece of graph paper this time, taunting her with an arrogant glint on its eyes …

Vector Grid

With the grids on the graph paper to guide her, Miss Loi pin-points the fly at position P. Recalling her mathematical powers, she calculated that she needs to place her palm at a starting position Q and slam the fly at point R.

  1. Write down an expression for vec{OP} in terms of a and b.
  2. Mark and label clearly on the grid the point Q such that vec{OQ} = ab.
  3. The point R is such that vec{OR} = h vec{OQ} and vec{PR} = kb.

    1. Mark and label clearly on the grid the point R.
    2. Find the value of h and k.

Note: Grids are labeled here to facilitate readers’ answers. They are normally unlabeled in actual exams as you’ll need to plot out the answers directly on the paper itself.

Can you help Miss Loi to 如来神掌 the fly into oblivion once and for all?

Vectors questions in your E-Maths exam can be broadly classified into two types:

  1. Those that end up asking you to mark on a grid diagram certain points that are expressed in terms of other vectors (like in the question of this blog post) or using the grid to find some column vector [matrix{2}{1}{a b}].
  2. Those that end up asking you to make use or calculate the ratios of two areas or lines like in this example, often requiring knowledge from other topics like similar triangles as well.

Regardless of the type of question, you’ll frequently end up using these basic vector properties:

Vectors Fundamentals


Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

  1. Leave A Comment!
Comments & Reactions


  1. Li-sa's Avatar
    Li-sa commented in tuition class


    Usually when you see vector questions involving a grid like this one, expect to do some 'shifting'/'lengthening' of the vectors to form a couple of triangles (as shown in the ADDITION/SUBTRACTION OF VECTORS section of the notes above)

    1. 3a-4b

    Vector grid answer 1

    Pretty straightforward to form the triangle consisting of 3 units of vector a and 4 units of b. Looking at the direction of the arrows, you can see that

    3a = vec{OP} + 4b
    vec{OP} = 3a - 4b

    2. Q:(F,3)

    Vector grid answer 2

    Shifting a and b to form a triangle with a point at O (since we're finding vec{OQ} so one end has to be at O) we can then locate Q to be a (F, 3).

    3i. R:(D,3)
    ii. h=3, k=-1

    Vector grid answer 3

    Now, vec{OR} = h vec{OQ} which means that vec{OR} is parallel to vec{OQ} (from the Scalar Multiple portion of the notes above). Furthermore, since there's a common point O this means that R must lie somewhere along grid-line #3.

    vec{PR} = kb means that vec{PR} has to be parallel to b. And with the vector originating from point P, this means that R must lie somewhere along grid-line #D.

    So from this info, we can locate R at (D, 3) in the grid.

    And looking at the diagram,

    vec{OR} is three times longer than vec{OQ} and in the same direction ⇒ h = 3
    vec{PR} is the same length as b and in the same direction ⇒ k = 1

    Care to share how you got k = -1 in your answer when vec{PR} is in the SAME DIRECTION as b??? *scratch head*

  2. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    如 ... 来 ... 神 ... 掌!!! (in the direction of vec{QR})


  3. Li-sa's Avatar
    Li-sa commented in tuition class


    Good thing you pointed that out. It implies that

  4. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

  5. cendrine's Avatar
    cendrine commented in tuition class


    erm....why such a title ? Dun sound good lei in this month... 🙂

  6. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    Cendrine: Thanks for your feedback 🙂

    *Scraps title of next blog post: "Welcome To Hell"*

  7. .l's Avatar
    .l commented in tuition class


    Maybe "Li-sa" got k = -1 because she had somehow forgotten the question. Instead of subtracting vec{OP} by vec{OR} she added vec{OR} to vec{RP}.

  8. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    .I: Perhaps. That's why it's always important to note the order of the letters in vectors e.g. vec{AB} = -vec{BA}

    Speaking of which, Li-sa seems to have disappeared after leaving that mysterious truncated comment. Could she have been trapped in a recurrent time warp like what happened to Miss Loi awhile ago?

Post a Comment

  • * Required field
  • Your email will never, ever be published nor shared with a Nigerian banker or a pharmaceutical company.
  • Spam filter in operation.
    DO NOT re-submit if your comment doesn't appear.
  • Spammers often suffer terrible fates.

Impress Miss Loi with beautiful mathematical equations in your comment by enclosing them within alluring \LaTeX [tex][/tex] tags (syntax guide | online editor), or the older [pmath][/pmath] tags (syntax guide). Please PREVIEW your equations before posting!


Whatsapp Instagram Twitter Facebook Close Search Login Access RSS Joss Sticks Sessions Suggested Solutions Preview O Level Additional Mathematics O Level Elementary Mathematics Secondary Three Additional Mathematics Secondary Three Elementary Mathematics Secondary Two Mathematics Secondary One Mathematics Additional Mathematics 4038 Additional Mathematics 4018 Elementary Mathematics 4017 Virus Zoom Date Modified Address Telephone 非常に人気の Popular Slot! Cart Exam Paper Cart