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

Miss Loi’s neglected car
click to see how horribly dirty it is

With the return of the haze and Miss Loi’s recent absence away in the Plane of Geometry, the poor car is looking a little neglected these days.

Dismayed and feeling depressed like a guilty parent each time she saw the dismal state of its paintwork, Miss Loi decided to send the car for a long-overdue wash plus pamper it with one of those much-touted “car grooming” sessions.

When she collected her car later in the day, her depression was cured instantly by the uplifting sight of its dazzling shine.

Words could not describe the silky sensation as she ran her slim fingers slowly across its smooth immaculately-waxed body, now free of the minuscule scratches and parabolic swirls that once scarred it.

It was almost like getting a new car, and this feeling stayed with her throughout her drive to a new student’s home, situated at the end of a straight road in a carpark-deprived area, for her next tuition session.

Bird’s eye view
- Miss Loi’s somewhere down there

As she slowly walked away, turning her head every few steps to admire the shine of her parked car, little did she realize that this glint of a shine would attract the attention of a little bird perched on a large tree at the end of the road.

Before long the area was slowly draped by a large shadow that caused Miss Loi to stop in her tracks, look up, and stare in utter horror at a huge fleet of birds flying towards her direction in an aggressive-looking formation, each with its … umm … “crosshairs” trained on the car.

The air raid siren in her mind sounded, and it was sheer luck that got her to the car in time before these terrors in the sky rained destruction upon the land.

When heroes are born

In heroic scenes that followed, left and right she swerved her car as she strived to save it from the relentless onslaught, narrowly avoiding bomb after bomb of waste matter that whistled through the air before landing with a sickening *splat* inches away from her.

Just when it seemed certain the car would be martyred on this very day, the flock began to turn back, as Miss Loi charged her way to freedom beyond the bombing range, immensely relieved that her superb driving skills had somehow saved her from the pounding.

But now she’s stuck at the end of the road, in a tense face-off with the evil birds on the tree at the opposite end readying themselves for the next bombing run, while her new student waits patiently for her in her house …

Noticing the pattern of the impact points along the road, Miss Loi suspects that their distance d from the centre of the road and the distance x along the road is connected by the equation

Bravely measuring a few samples along certain intervals on the road, Miss Loi recorded the following sets of values:

x (m)	5	10	15	20	25	30
d (m)	2.50	0.9	3.21	2.85	2.50	2.20

Given there’s nowhere else she can park her car other than along the centre of the narrow road (inside the bombing range), *use a suitable graph to examine the validity of Miss Loi’s equation, and estimate the values of a and b.

At which point (x) along the road should Miss Loi park her car to minimize the chances of it being hit i.e. where d is maximum?

*This is a Linear Law question requiring you to plot a graph on a piece of graph paper. You may generate a piece of graph paper online should you not to have one with you.

As Miss Loi doesn’t have any graph paper with her (shame on her!), can you please help her find the safest spot to park her shiny car so that she can start her new student’s tuition session on time with peace of mind?