Intro -- Contents -- About this book -- STEP -- What is STEP? -- What is the purpose of STEP? -- STEP vs A-level -- STEP vs Olympiad -- STEP Questions -- Advice to candidates -- Worked Problems -- Worked problem 1 -- Worked problem 2 -- Problems -- 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 -- Syllabus.

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