Jφss Sticks Tuition Centre

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

Updated on 29 August 2008

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 …

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.

Write down an expression for in terms of a and b.
Mark and label clearly on the grid the point Q such that = a – b.
The point R is such that and = 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:

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 .
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.