Intro -- 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 Non-linear 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 xm(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 differential-difference 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 non-uniform 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 knock-out 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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2022. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.