Description 
1 online resource (186 pages) 

text txt rdacontent 

computer c rdamedia 

online resource cr rdacarrier 

data file 
Series 
OBP series in mathematics, 23871134 ; v. 1 

OBP series in mathematics ; v. 1. 23871134

Note 
This work is licensed under a Creative Commons Attribution 4.0 International license (CC BYSA 4.0), http://creativecommons.org/licenses/bysa/4.0. 
Summary 
"This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematicsrelated subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to universitystyle mathematics. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the Alevel core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently."Publisher's website 
Contents 
About this book  STEP  Worked Problems ; Worked problem 1 ; Worked problem 2 ; Problems  P1 An integer equation P2 Partitions of 10 and 20 P3 Mathematical deduction P4 Divisibility P5 The modulus function P6 The regular Reuleaux heptagon P7 Chain of equations P8 Trig. equations P9 Integration by substitution P10 True or false P11 Egyptian fractions P12 Maximising with constraints P13 Binomial expansion P14 Sketching subsets of the plane P15 More sketching subsets of the plane P16 Nonlinear simultaneous equations P17 Inequalities P18 Inequalities from cubics P19 Logarithms P20 Cosmological models P21 Melting snowballs P22 Gregory's series P23 Intersection of ellipses P24 Sketching x m ( 1 − x ) n P25 Inequalities by area estimates P26 Simultaneous integral equations P27 Relation between coefficients of quartic for real roots P28 Fermat numbers P29 Telescoping series P30 Integer solutions of cubics P31 The harmonic series P32 Integration by substitution P33 More curve sketching P34 Trig sum P35 Roots of a cubic equation P36 Root counting P37 Irrationality of e P38 Discontinuous integrands P39 A difficult integral P40 Estimating the value of an integral P41 Integrating the modulus function P42 Geometry P43 The t substitution P44 A differentialdifference equation P45 Lagrange's identity P46 Bernoulli polynomials P47 Vector geometry P48 Solving a quartic P49 Areas and volumes P50 More curve sketching P51 Spherical loaf P52 Snowploughing P53 Tortoise and hare P54 How did the chicken cross the road? P55 Hank's gold mine P56 A chocolate orange P57 Lorry on bend P58 Fielding P59 Equilibrium of rod of nonuniform density P60 Newton's cradle P61 Kinematics of rotating target P62 Particle on wedge P63 Sphere on step P64 Elastic band on cylinder P65 A knockout tournament P66 Harry the calculating horse P67 PIN guessing P68 Breaking plates P69 Lottery P70 Bodies in the fridge P71 Choosing keys P72 Commuting by train P73 Collecting voles P74 Breaking a stick P75 Random quadratics  Syllabus 
Subject 
Mathematics  Study and teaching (Higher)


Calculus  Problems, exercises, etc.


Geometry  Problems, exercises, etc.


Probabilities  Problems, exercises, etc.


Mathematics  Problems, exercises, etc.


Mathematics  Examinations, questions, etc.


Mathematics and science.


Mathematics.


MATHEMATICS  Geometry  General.


MATHEMATICS  Essays.


MATHEMATICS  PreCalculus.


MATHEMATICS  Reference.


Calculus. (OCoLC)fst00844119


Geometry. (OCoLC)fst00940864


Mathematics. (OCoLC)fst01012163


Mathematics  Study and teaching (Higher)
(OCoLC)fst01012286


Probabilities. (OCoLC)fst01077737

Genre/Form 
Electronic books.


Examinations. (OCoLC)fst01423780


Problems and exercises. (OCoLC)fst01423783


Problems and exercises.


Examinations.

ISBN 
1783741449 (electronic bk.) 

9781783741441 (electronic bk.) 

1783741457 

9781783741465 

1783741465 

9781783741458 (electronic bk.) 

9781783741427 (pbk.) 
Standard No. 
AU@ 000058393066 

CHNEW 000912645 

AU@ 000066974152 
