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STEP Support Programme

STEP Questions Database

2009

Step: 1

Question: 2 Cubic equations (09-S1-Q2)
Question: 3 Quadratic equations (09-S1-Q3)
Question: 4 Euclidean geometry (09-S1-Q4)
Question: 5 Optimisation (09-S1-Q5)
Question: 6 Integration by substitution (09-S1-Q6)
Question: 7 Integration by parts (09-S1-Q7)
Question: 8 Euclidean geometry (09-S1-Q8)
Question: 9 Projectile motion (09-S1-Q9)
Question: 10 Wedge (09-S1-Q10)
Question: 11 Collision (09-S1-Q11)
Question: 12 Sampling without replacement (09-S1-Q12)
Question: 13 Combinatorics (09-S1-Q13)

Step: 2

Question: 1 Coordinate geometry (09-S2-Q1)
Question: 2 Functions (09-S2-Q2)
Question: 3 Trigonometry (09-S2-Q3)
Question: 4 Polynomials (09-S2-Q4)
Question: 5 Integration (09-S2-Q5)
Question: 6 Fibonacci numbers (09-S2-Q6)
Question: 7 Integration (09-S2-Q7)
Question: 8 Vector geometry (09-S2-Q8)
Question: 9 Centre of mass (09-S2-Q9)
Question: 10 Collision (09-S2-Q10)
Question: 11 Work and power (09-S2-Q11)
Question: 12 Continuous random variable (09-S2-Q12)
Question: 13 Andover and Basingstoke Rockets (09-S2-Q13)

Step: 3

Question: 1 Coordinate geometry (09-S3-Q1)
Question: 2 Series solutions (09-S3-Q2)
Question: 3 Functions (09-S3-Q3)
Question: 4 Laplace transform (09-S3-Q4)
Question: 5 Simultaneous equations (09-S3-Q5)
Question: 6 Complex Numbers (09-S3-Q6)
Question: 7 Proof by Induction (09-S3-Q7)
Question: 8 Infinite series (09-S3-Q8)
Question: 9 Projectile motion (09-S3-Q9)
Question: 10 SHM (09-S3-Q10)
Question: 11 Differential equation (09-S3-Q11)
Question: 12 Coin toss (09-S3-Q12)
Question: 13 Geometrical probability (09-S3-Q13)

2008

Step: 1

Question: 1 Number theory (08-S1-Q1)
Question: 2 Differentiation (08-S1-Q2)
Question: 3 Inequalities (08-S1-Q3)
Question: 4 Convex functions (08-S1-Q4)
Question: 5 Chebyshev's theorem (08-S1-Q5)
Question: 6 Inverse functions (08-S1-Q6)
Question: 7 Coordinate geometry (08-S1-Q7)
Question: 8 Differential equation (08-S1-Q8)
Question: 9 Kinetic energy (08-S1-Q9)
Question: 10 Projectile motion (08-S1-Q10)
Question: 11 Friction (08-S1-Q11)
Question: 12 Discrete random variables (08-S1-Q12)

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)

OCR: Exam board information about STEP (external link)

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

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