JC Maths Tuition Bishan – Vignette of Math I

JC Maths Tuition – Vignette of Math (I)
by Sufique Math Tutorials

Issue : Tackling the Square-Root Function related integrand by the simple standard form.
Theorem : JC Maths Tuition Bishan - Vignette of Math - Equation 1
eg

JC Maths Tuition Bishan - Vignette of Math - Equation 2

What is currently being taught by most jc math teachers to tackle a similar/identical problem:
By means of intellectual observation, allude the integrand at hand to a semi-specific form of the anti-chain rule of differentiation
ie ,

JC Maths Tuition Bishan - Vignette of Math - Equation 3
and then modify it accordingly to apply.
eg:

JC Maths Tuition Bishan - Vignette of Math - Equation 4

[observe and reflect that

JC Maths Tuition Bishan - Vignette of Math - Equation 5

may be re-expressed as

JC Maths Tuition Bishan - Vignette of Math - Equation 6

JC Maths Tuition Bishan - Vignette of Math - Equation 7

Commentary on the above 2 methods :
In the example where a simple standard form is used, the student need only observe for a visually congruent form and apply homologously. This method of work is almost a reflex skill taking the merest of seconds that amount to less than a minute during exams.

In the method taught by most jcs and their math teachers, the student under the distress of exam and its time constraint, has to intellectually observe (not an easy task during exams) and re-hash the original problem form quite radically and take an extra 2 steps to reach the solution. Note that the time taken for unnecessary, extra steps and thought in exams translates to opportunity costs of tackling other questions better and fuller.

Why most of our school teachers, by insisting on teaching such an inconvenient method quite exclusively and hence present themselves more as an added obstacle rather than an ally in the travails of their students’ pursuit for excellence in academic exams, till today keeps me in indignant astonishment.
Try this : JC Maths Tuition Bishan - Vignette of Math - Equation 8

Contributed by : Rafiq A. Tan Tzu Yen