skip to content

STEP Support Programme

STEP Questions Database


Step: 2

Question: 12 Old hat probability problem (16-S2-Q12)
Question: 13 Binomial distribution approximations (16-S2-Q13)

Step: 3

Question: 1 Integral reduction (16-S3-Q1)
Question: 2 Parabola normals (16-S3-Q2)
Question: 3 Integration (16-S3-Q3)
Question: 4 Telescoping sums (16-S3-Q4)
Question: 5 Prime number distribution (16-S3-Q5)
Question: 6 Intersecting curves number (16-S3-Q6)
Question: 7 Argand geometry (16-S3-Q7)
Question: 8 Functional equations (16-S3-Q8)
Question: 9 Simple harmonic motion (16-S3-Q9)
Question: 10 Motion on a plane (16-S3-Q10)
Question: 11 Accelerating car (16-S3-Q11)
Question: 12 Chebyshev's inequality (16-S3-Q12)
Question: 13 Kurtosis (16-S3-Q13)


Step: 1

Question: 1 Curve sketching (15-S1-Q1)
Question: 2 Trigonometry (15-S1-Q2)
Question: 3 Optimisation (15-S1-Q3)
Question: 4 Euclidean geometry (15-S1-Q4)
Question: 5 Curve sketeching (15-S1-Q5)
Question: 6 Euclidean geometry (15-S1-Q6)
Question: 7 Differentiation (15-S1-Q7)
Question: 8 Number theory (15-S1-Q8)
Question: 9 Projectile motion (15-S1-Q9)
Question: 10 Bus and rain (15-S1-Q10)
Question: 11 Friction (15-S1-Q11)
Question: 12 Poisson distribution (15-S1-Q12)
Question: 13 Dice (15-S1-Q13)

Step: 2

Question: 1 Analysis (15-S2-Q1)
Question: 2 Euclidean geometry (15-S2-Q2)
Question: 3 Proof by Induction (15-S2-Q3)
Question: 4 Curve sketching (15-S2-Q4)
Question: 5 Arctan sum (15-S2-Q5)
Question: 6 Integration (15-S2-Q6)
Question: 7 Coordinate geometry (15-S2-Q7)
Question: 8 Vector geometry (15-S2-Q8)
Question: 9 Rotating rods (15-S2-Q9)
Question: 10 Pulley (15-S2-Q10)
Question: 11 Collisions (15-S2-Q11)
Question: 12 Coin toss (15-S2-Q12)
Question: 13 Random variable (15-S2-Q13)

Step: 3

Question: 1 Integration (15-S3-Q1)
Question: 2 Analysis (15-S3-Q2)
Question: 3 Polar coordinates (15-S3-Q3)
Question: 4 Roots of polynomials (15-S3-Q4)
Question: 5 Number theory (15-S3-Q5)
Question: 6 Complex system (15-S3-Q6)
Question: 7 Differentiation (15-S3-Q7)
Question: 8 Differential equations (15-S3-Q8)
Question: 9 Elastic string (15-S3-Q9)

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)