Challenge and Thrill of Pre-College MathematicsChallenge And Thrill Of Pre-College 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 Life-Long 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 Robot-Type 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. |
Contents
Number Systems | 1 |
Arithmetic of Integers | 17 |
GeometryStraight Lines and Triangles | 45 |
GeometryCircles | 111 |
Quadratic Equations and Expressions | 232 |
Trigonometry | 264 |
7 | 345 |
Systems of Linear Equations | 411 |
11 | 520 |
Elementary Combinatorics | 555 |
Beginning of Probability Theory | 579 |
Beginnings of Number Theory | 599 |
Finite Series | 615 |
De Moivres Theorem and Its Applications | 647 |
Miscellaneous Problems | 658 |
ANSWERS to selected Questions | 673 |
Common terms and phrases
a₁ AABC ABCD altitude b₁ bisects c₁ chord circle with centre circumcentre circumcircle circumradius coefficients collinear common divisor common tangent complex number Construction Corollary cyclic quadrilateral d₁ d₂ divides equal equilateral EXAMPLE Find the sum function given circle gives graph Hence implies incentre incircle integer internal bisector intersection isosceles line segment Mathematics midpoint multiple natural numbers nine-point circle orthic triangle orthocentre P₁ P₂ pair parallel parallelogram pedal triangle permutations perpendicular polynomial positive integer prime problem Proof Let prove quadratic equation quadrilateral r₁ r₂ radius ratio real numbers respectively right angled roots S₁ S₂ sample space Show sides BC Similarly Simson line sin² solution Solve straight line subset Suppose tangent Theorem triangle ABC u₁ vertices x₁ y₁ zero