**by Stephen Siklos**

DescriptionTable of ContentsDetailsHashtagsReport an issue ### Book Description

This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.

Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and 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.

This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics. ### Table of Contents

### Book Details

### Related Books

Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and 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.

This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

This open book is licensed under a Creative Commons License (CC BY). You can download Advanced Problems in Mathematics ebook for free in PDF format (2.0 MB).

Problem 1

An integer equation

Problem 2

Partitions of 10 and 20

Problem 3

Mathematical deduction

Problem 4

Divisibility

Problem 5

The modulus function

Problem 6

The regular Reuleaux heptagon

Problem 7

Chain of equations

Problem 8

Trig. equations

Problem 9

Integration by substitution

Problem 10

True or false

Problem 11

Egyptian fractions

Problem 12

Maximising with constraints

Problem 13

Binomial expansion

Problem 14

Sketching subsets of the plane

Problem 15

More sketching subsets of the plane

Problem 16

Non-linear simultaneous equations

Problem 17

Inequalities

Problem 18

Inequalities from cubics

Problem 19

Logarithms

Problem 20

Cosmological models

Problem 21

Melting snowballs

Problem 22

Gregory's series

Problem 23

Intersection of ellipses

Problem 24

Sketching x^m(1 - x)^n

Problem 25

Inequalities by area estimates

Problem 26

Simultaneous integral equations

Problem 27

Relation between coefficients of quartic for real roots

Problem 28

Fermat numbers

Problem 29

Telescoping series

Problem 30

Integer solutions of cubics

Problem 31

The harmonic series

Problem 32

Integration by substitution

Problem 33

More curve sketching

Problem 34

Trig. sum

Problem 35

Roots of a cubic equation

Problem 36

Root counting

Problem 37

Irrationality of e

Problem 38

Discontinuous integrands

Problem 39

A difficult integral

Problem 40

Estimating the value of an integral

Problem 41

Integrating the modulus function

Problem 42

Geometry

Problem 43

The t substitution

Problem 44

A differential-difference equation

Problem 45

Lagrange's identity

Problem 46

Bernoulli polynomials

Problem 47

Vector geometry

Problem 48

Solving a quartic

Problem 49

Areas and volumes

Problem 50

More curve sketching

Problem 51

Spherical loaf

Problem 52

Snowploughing

Problem 53

Tortoise and hare

Problem 54

How did the chicken cross the road?

Problem 55

Hank's gold mine

Problem 56

A chocolate orange

Problem 57

Lorry on bend

Problem 58

Fielding

Problem 59

Equilibrium of rod of non-uniform density

Problem 60

Newton's cradle

Problem 61

Kinematics of rotating target

Problem 62

Particle on wedge

Problem 63

Sphere on step

Problem 64

Elastic band on cylinder

Problem 65

A knock-out tournament

Problem 66

Harry the calculating horse

Problem 67

PIN guessing

Problem 68

Breaking plates

Problem 69

Lottery

Problem 70

Bodies in the fridge

Problem 71

Choosing keys

Problem 72

Commuting by train

Problem 73

Collecting voles

Problem 74

Breaking a stick

Problem 75

Random quadratics

Subject

Science and Mathematics

Publisher

Open Book Publishers

Published

2019

Pages

186

Edition

1

Language

English

ISBN13

9781783747764

ISBN10

1783747765

ISBN13 Digital

9781783747771

ISBN10 Digital

1783747773

PDF Size

2.0 MB

License

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