Wednesday, May 13, 2015

[H2_20150512GSS] A Square Spiral in Geometric Progression

Question

Introduction
     This is a type of question that has become quite common in H2 Mathematics at Junior College level.  I was not told where this question came from, but I seem to get a bout of déjà vu.  It is quite a common practice for the Singapore junior colleges to mimic questions from the GCE ‘A’ Levels and/or one another.

Solution



Summary
     The keys to solving this question are:-
          (1)  if a coordinate frame is needed but not given it the question, we invent our own.
          (2)  see whether we need to care about the direction or not, and then apply the
                 geometric series formula.
          (3)  When applying the geometric series formula, always identify correctly the first term,
                 the common ratio, and the number of terms to be summed.

H02. Use a diagram / model
H04. Look for pattern(s)
H09. Restate the problem in another way
H10. Simplify the problem
H11. Solve part of the problem
H13* Use Equation / write a Mathematical Sentence

Suitable Levels
GCE ‘A’ Level H2 Mathematics
* other syllabuses that involve geometric series


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