Challenge and Thrill of PreCollege MathematicsChallenge And Thrill Of PreCollege Mathematics Is An Unusual Enrichment Text For Mathematics Of Classes 9, 10, 11 And 12 For Use By Students And Teachers Who Are Not Content With The Average Level That Routine Text Dare Not Transcend In View Of Their Mass Clientele. It Covers Geometry, Algebra And Trigonometry Plus A Little Of Combinatorics. Number Theory And Probability. It Is Written Specifically For The Top Half Whose Ambition Is To Excel And Rise To The Peak Without Finding The Journey A Forced Uphill Task.The Undercurrent Of The Book Is To Motivate The Student To Enjoy The Pleasures Of A Mathematical Pursuit And Of Problem Solving. More Than 300 Worked Out Problems (Several Of Them From National And International Olympiads) Share With The Student The Strategy, The Excitement, Motivation, Modeling, Manipulation, Abstraction, Notation And Ingenuity That Together Make Mathematics. This Would Be The Starting Point For The Student, Of A LifeLong Friendship With A Sound Mathematical Way Of Thinking.There Are Two Reasons Why The Book Should Be In The Hands Of Every School Or College Student, (Whether He Belongs To A Mathematics Stream Or Not) One, If He Likes Mathematics And, Two, If He Does Not Like Mathematics The Former, So That The Cramped RobotType Treatment In The Classroom Does Not Make Him Into The Latter; And The Latter So That By The Time He Is Halfway Through The Book, He Will Invite Himself Into The Former. 
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All 7 reviews »Seriously amazing book, recommended for olympiads and higher math enthusiasts. Covers a variety of topics and that too in depth. I really enjoyed reading it.
Contents
A Prologue for the StudentReader  1 
Arithmetic of Integers  17 
GeometryStraight Lines and Triangles  45 
GeometryCircles  111 
Quadratic Equations and Expressions  232 
Trigonometry  264 
iii  281 
17  298 
Common terms and phrases
AABC ABCD altitude bisects Chapter chord circle with centre circumcentre circumcircle circumradius coefficients common divisor common tangent complex number congruent Construction Corollary coso cyclic quadrilateral defined divides division Draw elementary events equal equilateral Euler line EXAMPLE EXERCISE Find the sum function given circle gives graph Hence implies incentre incircle internal bisector intersection isosceles line segment mathematics midpoint multiple natural numbers ninepoint circle Note orthic triangle orthocentre pair parallel parallelogram pedal triangle permutations perpendicular polygon polynomial positive integer prime problem Proof Let prove quadratic equation quadrilateral radius ratio real numbers respectively roots roots of unity sample space sequence Show sides BC Similarly Simson line solution Solve straight line subset Suppose Theorem triangle ABC values vertices zero