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STEP Support Programme

STEP Questions Database


Step: 1

Question: 12 Lottery (17-S1-Q12)
Question: 13 Sliced loaf (17-S1-Q13)

Step: 2

Question: 1 arctan integral (17-S2-Q1)
Question: 2 Periodic sequences (17-S2-Q2)
Question: 3 Trigonometric equations (17-S2-Q3)
Question: 4 Schwarz inequality (17-S2-Q4)
Question: 5 Parabola and circle (17-S2-Q5)
Question: 6 Inverse square root series (17-S2-Q6)
Question: 7 x to the power x to the power x (17-S2-Q7)
Question: 8 Vector geometry (17-S2-Q8)
Question: 9 Plank on cylinders (17-S2-Q9)
Question: 10 Car with air and rolling resistance (17-S2-Q10)
Question: 11 Projectile (17-S2-Q11)
Question: 12 Fishing (17-S2-Q12)
Question: 13 Game show (17-S2-Q13)

Step: 3

Question: 1 Inverse cube series (17-S3-Q1)
Question: 2 Transformations (17-S3-Q2)
Question: 3 Quartic equation (17-S3-Q3)
Question: 4 Geomtric mean (17-S3-Q4)
Question: 5 Polar equations (17-S3-Q5)
Question: 6 Arctan (17-S3-Q6)
Question: 7 Ellipse (17-S3-Q7)
Question: 8 Trigonometric sums (17-S3-Q8)
Question: 9 Particles connected by spring (17-S3-Q9)
Question: 10 Hinged rod (17-S3-Q10)
Question: 11 Gun carriage (17-S3-Q11)
Question: 12 Discrete random variable (17-S3-Q12)
Question: 13 Variance (17-S3-Q13)


Step: 1

Question: 1 Graphs of floor functions (16-S1-Q1)
Question: 4 Touching circles (16-S1-Q4)
Question: 5 Curvature (16-S1-Q5)
Question: 6 Vector geometry (16-S1-Q6)
Question: 7 Integer sets (16-S1-Q7)
Question: 8 Generating functions (16-S1-Q8)
Question: 9 Static equilibrium: wall and rod (16-S1-Q9)
Question: 10 Particle collisions (16-S1-Q10)
Question: 11 Projectile and tower (16-S1-Q11)
Question: 12 Coin tossing (16-S1-Q12)
Question: 13 Internet tester (16-S1-Q13)

Step: 2

Question: 1 Coordinate geometry (16-S2-Q1)
Question: 2 Factor theorem (16-S2-Q2)
Question: 3 Roots of polynomial (16-S2-Q3)
Question: 4 Inequalities for rational function (16-S2-Q4)
Question: 5 Binomial identities (16-S2-Q5)
Question: 6 Quadratic differential equation (16-S2-Q6)
Question: 7 Trigonometric integrals (16-S2-Q7)
Question: 8 Approximating sums using integrals (16-S2-Q8)
Question: 9 Bullet fired into block (16-S2-Q9)
Question: 10 Hanging triangle (16-S2-Q10)
Question: 11 Projectile and target (16-S2-Q11)

Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

Admissions Testing Service: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)