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# STEP Questions Database

## 2018

### Step: 1

Question: 1 Area between curve and line (18-S1-Q1)
Question: 2 Logarithms (18-S1-Q2)
Question: 3 Hyperbola (18-S1-Q3)
Question: 4 Sketching an integral function (18-S1-Q4)
Question: 5 Polynomials at integer points (18-S1-Q5)
Question: 6 Numerical integration (18-S1-Q6)
Question: 7 Solving the cubic (18-S1-Q7)
Question: 8 Coupled differential equations (18-S1-Q8)
Question: 9 Motion on two inclined roads (18-S1-Q9)
Question: 10 Tension in train coupling (18-S1-Q10)
Question: 11 Pulley and rough inclined plane (18-S1-Q11)
Question: 12 Coin tosses (18-S1-Q12)
Question: 13 Multiple choice questions (18-S1-Q13)

### Step: 2

Question: 1 Quartic repeated roots (18-S2-Q1)
Question: 2 Concave functions (18-S2-Q2)
Question: 3 Tan integral (18-S2-Q3)
Question: 4 Trigonometric equations (18-S2-Q4)
Question: 5 Integration of series (18-S2-Q5)
Question: 6 Factorial equations (18-S2-Q6)
Question: 7 Triangle intersection (18-S2-Q7)
Question: 8 Differential equations (18-S2-Q8)
Question: 9 Beads on wire (18-S2-Q9)
Question: 10 Ant on elastic string (18-S2-Q10)
Question: 11 Motorbike slipping (18-S2-Q11)
Question: 12 Coin toss game (18-S2-Q12)
Question: 13 Pass the parcel (18-S2-Q13)

### Step: 3

Question: 1 Quadratic roots inequalities (18-S3-Q1)
Question: 2 Hermite polynomials (18-S3-Q2)
Question: 3 Second order differential equation (18-S3-Q3)
Question: 4 Tangent to hyperbola (18-S3-Q4)
Question: 5 Arithmetic mean - geometric mean (18-S3-Q5)
Question: 6 Complex geometry (18-S3-Q6)
Question: 7 Basel series (18-S3-Q7)
Question: 8 Integrating fractional part (18-S3-Q8)
Question: 9 Particle bouncing (18-S3-Q9)
Question: 10 Oscillating disc with point mass (18-S3-Q10)
Question: 11 Slack pendulum (18-S3-Q11)
Question: 12 Ordering samples (18-S3-Q12)
Question: 13 Poisson distribution (18-S3-Q13)

## 2017

### Step: 1

Question: 1 Integration by substitution (17-S1-Q1)
Question: 2 Inequlaities (17-S1-Q2)
Question: 3 Parabola (17-S1-Q3)
Question: 4 Geometric progression (17-S1-Q4)
Question: 5 Area of rectangle in circle segment (17-S1-Q5)
Question: 6 Integration (17-S1-Q6)
Question: 7 Triangles (17-S1-Q7)
Question: 8 Sequence (17-S1-Q8)
Question: 9 Projectile motion (17-S1-Q9)
Question: 10 Colliding particles (17-S1-Q10)
Question: 11 Box on inclined plane (17-S1-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)

OCR: Exam board information about STEP (external link)

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