You can learn how to solve hard problems and how to write rigorous proofs
Top UK universities and entrance exams
Top UK universities
usually accept students with good
STEP grades,
please click on the university logos
to access maths admissions webpages:
 STEP I, II, III are the Sixth Term Exam Papers in June, see the STEP webpage. The possible STEP grades are S (excellent), 1 (very good), 2 (good), 3 (satisfactory), U (poor).
 Cambridge may ask for STEP II and III, a usual offer is a grade 1 in both papers.
 Oxford asks to take the MAT paper in November, see the Oxford admissions page.
 Cambridge/Oxford interviews are in December, then Oxford asks for only Alevels.
 Imperial College London now requires the MAT paper, occasionally STEP II or III.
 Warwick accepts a grade 1 in easier STEP I or a grade 2 plus A* in Further Maths.
 University College London accepts a grade 1 in STEP I plus A*A at Alevel Maths.
 Other universities that may ask for STEP: Bath, Bristol, Durham, King's, Loughborough.
 The table below summarises key differences between the
MAT paper and
STEP exams:
exams when entrance to problems and marks MAT early
NovemberOxford, Imperial 10 multiple choice questions (4 marks each) and
4 long questions (15 marks each), total 100 marksSTEP 2nd half
of JuneCambridge, Warwick
and UCL, Bath, Bristolbest solutions to any 6 of 13 problems (8 problems
in pure maths), 20 marks each, total 120 marks  Past students have gained 18 highest grades S in STEP exams.
years/exams STEP I STEP II STEP III all grades S 2016 1 2 3 6 all years 4 5 9 18
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What help you can get for entrance exams
 Read the blog: how to master mathematics and other educational stories.
 Explore many successful study tips for maths candidates to top universities.
 Look at frequent questions on exam preparations, learn about Master Maths.
 Try distance courses for MAT papers, Oxbridge interviews, STEP I, II, III.
 Prices of courses: MAT paper, Oxbridge interviews, STEP I, STEP II, STEP III.
 Dozens alumni of past summer schools have entered top UK universities.
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What you can expect from web tutorials
Each web tutorial covers a long multistep problem split into 4 parts
 in every part: you may attempt several times an interactive quiz that includes randomised parameters, immediate feedback, progressive hints
 after taking the quiz (even if scored 0), you may review detailed answers
 difficulty of quizzes is increasing in each tutorial, you need all previous steps
 if anything is unclear, you may submit your anonymous feedback at the end
 many tutorial problems can be solved in numerous different correct ways, so you may outline your own method: contact us or send anonymous feedback
 your feedback is seriously considered and the tutorials are regularly updated.
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How to access and work through tutorials
 guests have the readonly access, interactive quizzes work only for enrolled users
 selfregister click on Create a New Account, login, navigate to our free tutorial Beyond Pythagoras' theorem and click on enrol me in this tutorial in the left menu
 prepare some draft paper and a pencil for your computations during a tutorial
 if a quiz seems hard, you may finish it and review answers in the next activity
 make frequent breaks and study regularly: learning in small portions is effective
 you could return to every web tutorial at least once a month for your revisions
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The list of 49 available web tutorials (log in as a guest for a quick view):
STEP II  STEP I  MAT  Oxbridge interviews
 Free tutorial: Beyond Pythagoras' theorem and applications

Tutorials on past STEP II exams
(log in as a guest)
 Areas under graphs help prove inequalities
 Converging nonmonotone recurrent sequences
 Signs of roots and graphs of cubic polynomials
 Graphs of rational functions with a double symmetry
 Diaphontine equations with infinitely many solutions
 Using graphs to compare powers with arbitrary bases
 Sketching loci of middle points of variable chords
 Recursive integration of functions with parameters

Tutorials on past STEP I exams
(log in as a guest)
 Minimum distances between points on the plane
 Periodic recurrent sequences with a 3term relation
 The graphs and real roots of quartic parabolas
 Symmetric tangents and normals to a hyperbola
 Homogeneous first order differential equations
 Integrating trigonometric functions with a logarithm
 Inequalities between areas under graphs of functions
 Angles of elevation in a pyramid over a rightangled triangle
 Tangents and normals to transformed hyperbolas
 Two intersecting tangents to a horizontal parabola
 Trigonometric identities with products and sums
 Graphs and extrema of trigonometric functions
 Basic integration by substitution and by parts
 Evaluations of infinite binomial expansions
 Diaphontine equations with finitely many solutions
 Differential equations of flows and leaks in a bath

Tutorials on past MAT papers
(log in as a guest)
 Algebraic expressions: squares, equations, estimates
 Tangent lines to circles and graphs of polynomials
 Computing areas of triangular regions in a disk
 Integration and areas under graphs of functions
 Repeated compositions of two linear functions
 Turning points and the area under a cubic parabola
 How a circle and a parabola can touch each other
 A cyborg executing a computergenerated code
 Logical analysis of exam results in a large class
 Best strategies to win a number game modulo 3
 Counting combinatorial choices: jumps and wins
 Inequalities and recurrence relations for sequences
 Recurrence relations between multiple sequences
 Equations: polynomial, trigonometric, exponential
 Plane geometry: rectangles, circles and angles
 Sketching graphs of functions and applications
 Tangent lines and areas bounded by cubic parabolas
 Global extrema of a 2variable function over a region
 Logical analysis of multiple claims for crime detection
 Linear pattern recognition in competitive games

4 tutorials on Oxbridge interviews
(log in as a guest)
 Combinatorial choices of rooks, words and signs
 Rates of increase, cubes of roots and binary numbers
 Properties of primes, factorials, recurrent sequences
 Counting roots of complicated graphs of functions
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Successful students at top UK universities
 69 students entered top universities after the courses,
read success stories
Universities Cambridge Oxford Warwick Imperial all students all years 27 13 16 13 69  100% students who completed the STEP courses in 2016 were accepted at Cambridge.
 The table contains only confirmed destinations, not all students have replied (one success case from 2012 was confirmed by a school teacher only in 2013).
 Other destinations not counted in the table above include University College London (UCL), King's College London, Universities of Bath, Bristol, Durham, Edinburgh, Sheffield, Southampton, St Andrews, London School of Economics, Columbia University (USA), Waterloo University (Canada).
 Following former students' request, you can ask us about degree level tuition.
 The offered training courses are completely independent of any universities.
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