Tuesday, May 5, 2015

[S2_20150501AXC] 2011: Chunking and Substitution with Algebra

Question

Introduction
This lower secondary algebra question seems complicated, doesn’t it?  Can you spot any chunk that is repeated, or almost the same?  This is one of the keys to solving the problem.  Another key that you need is the relevant algebraic identities and tricks.

Reminders
First, let us review some of these useful formulas.
Looking back at the question, do you notice anything that is repeated?  Can you see any chunks that are the same or almost the same?  (n – 2011)  is almost the same as  (2012 – n)  isn’t it?  Whenever you see a repeated chunk, it is a good idea to substitute that chunk with another variable that you invent.  To name this new variable, you can use any letter that is not used before, so as not to conflict with existing letter(s).

Solution

Summary
To solve the given problem, we have used the following:-
(1)  square-of-difference identity
(2)  swapping technique
(3)  observation of repeated chunks
(4)  using substitution with the chunks

H04. Look for pattern(s)  e.g. chunking, observation
H09. Restate the problem in another way  e.g. swapping, identities
H10. Simplify the problem e.g. substitution for chunks
H11. Solve part of the problem
H12* Think of a related problem
H13* Use Equation / write a Mathematical Sentence

Suitable Levels
· Lower Secondary Mathematics
· other syllabuses that involve whole numbers and ratios