[AM_20160115SEAV] Simultaneous equations? Absolutely!

Problem / Question

Introduction

     This question was from a Facebook group not dedicated to “Singapore math”.  The thing is, mathematics is really an international experience, especially with modern social media.

     Simultaneous equations can pose a challenge to students, but this one is absolutely more challenging, because of the absolute value.

The Absolute Value

Strategy

     The problem is: we do not know whether each of  x  and  y  is negative or otherwise.  That potentially raises complications.  There seems to be  4  cases to check.  However, by making assumptions  [H08]  separately and checking for contradictions [H07], we can narrow down the possibilities.  [H10]  Finally, we can simplify the problem to a regular pair of simultaneous linear equations   [H10]  and solve it by the method of elimination.  [H10, H11]

Solution

Heuristics Used

H04. Look for pattern(s)        [deciding what to eliminate]

H07. Use guess and check     [is x negative?  is  y negative?]

H08. Make suppositions        [is x negative?  is  y negative?]

H10. Simplify the problem

H11. Solve part of the problem

H13* Use Equation / write a Mathematical Sentence

Suitable Levels

* Lower Secondary Olympiad

* GCE ‘O’ Level Additional Mathematics, “IP Mathematics” (challenge)

* other syllabuses that involve simultaneous equations and absolute values

* any precocious or independent learner who wants his/her mind tickled

[JCH2BXQNSR_20150429] Binomial Expansion for a Quotient

Question

Solution

Comment

     Note in the above working that  3(x + kx²)² = 3(x² + 2kx³ + k²x⁴),  but since we do not need the  x³  and  x⁴  terms, we omit them and just write “3(x² + ... )”.

Heuristics Used

H12* Think of a related problem

H13* Use Equation / write a Mathematical Sentence

Suitable Levels

* revision for GCE ‘A’ Level H2 Mathematics

* AP Calculus

* other syllabuses infinite binomial series