STEP Preview

Links to Examples are in blue

 

Key:

- suggested questions: * = recommended; ** = strongly recommended

- FM = repeat of document on FM pages

 

General 

About the STEP paper (9 pages; 17/7/25)

STEP - Preparation (6 pages; 15/7/25) 

STEP - Methods (9 pages; 17/9/25) 

STEP - Exam Technique (10 pages; 9/1/25) 

Index of q'ns: Pure (47 pages; 29/8/25)

Index of q'ns: Mechanics (18 pages; 29/8/25)

Index of q'ns: Probability & Statistics (15 pages; 29/8/25)

Reference (9 pages; 4/7/25)

Introductory Ideas & Exs (20 pages; 4/7/25)

 

 

Themes

 

Rearrangements - Ideas & Exs (13 pages; 4/7/25)

 

MAT: 2023/Q2** (q'n & sol'n) (polynomials; rearrangements; iff)

 

Symmetry

Suggested question:

2004/P1/Q14** (q'n & sol'n) (probability; counting)

 

Using an earlier part of the question (3 pages; 20/6/25)

Suggested questions:

2023/P3/Q5** (q'n & sol'n) (prime numbers)

2019/P2/Q3* (q'n & sol'n) (polynomials; integer roots)

2023/P2/Q4* (q'n & sol'n) (polynomials; integer coeffs)

2023/P2/Q6* (q'n & sol'n) (matrices)

2008/P1/Q1 (q'n & sol'n) (irrational numbers)

2011/P2/Q1** (q'n & sol'n) (curve sketching)

2017/P1/Q1* (q'n & sol'n) (integration; substitution) 

2021/P3/Q3* (q'n & sol'n) (integration; recurrence relation)

2022/P2/Q10* (q'n & sol'n) (projectiles)

2023/P3/Q7* (integration)

 

Algebra: Ideas & Exs (19 pages; 22/7/25)

Algebra: Further Exs (6 pages; 21/12/24)

 

 

Proof   

   Necessary & Sufficient Conditions - Ideas & Exs (14 pages; 13/8/25)

   Proof - Exs (12 pages; 3/7/25)

   Proof - Further Exs (11 pages; 18/5/25)

   Induction (2 pages; 2/7/25)

   Suggested questions:

   2001/P1/Q2* (q'n & sol'n)(necessary & sufficient conditions)

   2006/P1/Q3* (q'n & sol'n)(proof; quadratic)

   2024/P3/Q8* (q'n & sol'n)('if and only if'; sol'ns of quartic)

   2008/P1/Q1 (q'n & sol'n) (proof; irrational numbers)

   2007/P2/Q4* (q'n & sol'n) (proof)

   2001/P2/Q11* (q'n & sol'n) (proof; inequalities [2nd part of q'n])

 

 

[Links for the following items appear in the password protected pages]

 

Pure Topics

 

 

Complex Numbers

 

   Complex Numbers: Ideas & Exs (17 pages; 1/5/25)

 

   Complex Number Methods (9 pages; 28/2/15) 

 

   Complex Numbers - Further Exs (FM) (10 pages; 22/3/25) 

 

   Suggested questions:

 

   2009/P3/Q6* (q'n & sol'n)

 

   2013/P3/Q6* (q'n & sol'n)

 

   2011/P3/Q8* (q'n & sol'n)   

 

   2012/P3/Q6* (q'n & sol'n)   

 

   2013/P3/Q8* (q'n & sol'n) 

 

   2023/P2/Q7  (q'n & sol'n) 

 

 

 

 

Conics

 

 Conics (FM)(4 pages; 17/8/19)

 

 Parabolas (FM) (10 pages; 16/7/19)

 

 Parabolas Exs (FM) (13 pages; 21/3/25)

 

 Ellipses (FM) (7 pages; 18/8/19)

 

 Ellipses Exs (FM) (6 pages; 21/3/25)

 

 Hyperbolas (FM) (13 pages; 11/9/19)

 

 Hyperbolas Exs (FM) (14 pages; 21/3/25)

 

 Suggested question:

 

 2013/P3/Q8* (q'n & sol'n) (parabola)

 

 

 

 

 

 

 

Counting

 

  Suggested questions

 

  2005/P1/Q1* (q'n & sol'n) (counting)  

 

  Specimen/P1/Q5* (q'n & sol'n) (counting)

 

 

 

 

 

 

 

Cubics

 

   Cubics (5 pages; 5/6/23)

 

   Cubics Exs [3 pages, 29/7/16] Sol'ns (10 pages, 29/7/16) 

 

   Suggested questions:

 

   2006/P1/Q3* (q'n & sol'n) (quadratics & cubics)

 

   2007/P2/Q2* (q'n & sol'n) (cubic)

 

   2018/P1/Q7* (q'n & sol'n) (cubic)

 

   2008/P2/Q3* (q'n & sol'n) (cubic)

 

   2007/P1/Q4*  (q'n & sol'n) (cubic)

 

 

 

 

 

 

 

Curve Sketching  (see also Functions & Differentiation)

 

   Curve Sketching: Ideas & Exs (20 pages; 25/3/25)

 

   Functions & Curve Sketching (5 pages; 22/11/24)

 

   Mappings & functions (FM) (3 pages; 2/6/23) 

 

   Curve Sketching - Further Exs (23 pages; 23/7/25)

 

   Curve Sketching (Transformations) - Exs (17 pages; 25/3/25)

 

   Suggested questions:

 

   2011/P2/Q1** (q'n & sol'n) (curve sketching)

 

   2008/P1/Q6* (q'n & sol'n) (curve sketching)

 

   2010/P1/Q2* (q'n & sol'n) (curve sketching)

 

   2013/P2/Q1* (q'n & sol'n) (curve sketching)

 

   2014/P1/Q2* (q'n & sol'n) (curve sketching; ln)   

 

   2003/P2/Q6* (q'n & sol'n) (curve sketching; modulus function)

 

   

 

   

 

Differential Eq'ns

 

   2nd order DEs - Ideas & Exs (FM) (17 pages; 4/3/25)

 

   Differential Equations - Ideas & Exs (10 pages; 12/4/24)   

 

   Differential Equations - Further Exs (12 pages; 4/3/25)   

 

   Suggested questions:

 

   2024/P3/Q6** (q'n & sol'n) (systems of DEs) 

 

   2008/P2/Q7* (q'n & sol'n) (DEs)

 

   Specimen/P3/Q7* (q'n & sol'n) (DEs)

 

   2007/P2/Q6* (q'n & sol'n) (DEs)

 

   2013/P3/Q7 (q'n & sol'n) (DEs)

 

 

 

 

 

 

 

Differentiation

 

   Turning points & Points of inflexion (FM) (7 pages; 5/6/23)

 

   Differentiation: Ideas & Exs (13 pages; 3/7/25)

 

   Differentiation: Further Exs (6 pages; 3/7/25)

 

   Suggested questions:

 

   Specimen/P1/Q2* (q'n & sol'n) (differentiation)

 

   2014/P1/Q4* (q'n & sol'n) (differentiation)

 

 

 

 

Functions

 

   Modulus Function (FM) (2 pages; 2/6/23)

 

   Convex & Concave functions (FM) (2 pages; 2/6/23)

 

   Inverse functions (FM) (3 pages; 2/6/23)

 

   Rational Functions (FM) (5 pages; 12/7/24)

 

   y^2=f(x) (FM) (2 pages; 2/6/23)

 

  Suggested questions:

 

   2008/P1/Q6* (q'n & sol'n) (inverse function)

 

   2003/P2/Q6* (q'n & sol'n) (modulus function) 

 

 

 

 

 

 

 

Geometry

 

   Shortest distance from Origin to line (FM) (7 pages; 6/3/25)

 

   Geometry Exs (FM)(12 pages; 6/3/25)

 

   Geometry Exs (STEP)(5 pages; 6/3/25)

 

   Suggested questions:

 

   2006/P1/Q2* (q'n & sol'n) (geometry; goat problem)

 

   2023/P2/Q8* (q'n & sol'n) (isosceles tetrahedron)

 

   2013/P3/Q8* (q'n & sol'n) (geometry)

 

 

 

 

 

 

 

Hyperbolic Functions 

 

   Hyperbolic Functions [FM] (10 pages; 26/7/16)   

 

   Hyperbolic Functions Exs [FM] (43 pages; 11/3/25)

 

   Suggested questions:

 

   Specimen/P2/Q4* (q'n & sol'n) (hyperbolic fns; curve sketching)

 

   2020/P3/Q2* (q'n & sol'n) (curve sketching; hyperbolic functions)

 

 

 

 

 

 

 

Inequalities

 

   Inequalities - Notes (3 pages; 29/12/24)

 

   Inequalities: Ideas & Exs (24 pages; 3/7/25) 

 

   Inequalities: Further Exs (23 pages; 22/4/25) 

 

   Suggested questions: 

 

   2001/P1/Q2* (q'n & sol'n)(inequalities; necessary & sufficient conditions)

 

   2020/P2/Q4* (q'n & sol'n) (inequalities; triangles)

 

   1987/P3/Q3*(i) (q'n & sol'n) (inequalities)

 

   2001/P2/Q11* (q'n & sol'n) (inequalities proof - 2nd part of q'n)

 

   2008/P2/Q5* (q'n & sol'n) (inequalities - 2nd part of q'n)

 

   

 

Integers

 

   Integers - Ideas & Exs (19 pages; 3/7/25)

 

   Suggested questions:

 

   2023/P3/Q5** (q'n & sol'n) (prime numbers)

 

   2020/P2/Q5** (q'n & sol'n) (divisibility)

 

   2024/P2/Q5* (q'n & sol'n) (integers)

 

   2005/P1/Q1* (q'n & sol'n) (digits)

 

   2006/P1/Q1* (q'n & sol'n) (integers; perfect squares)

 

 

 

 

 

 

 

Integration

 

   Integration - Ideas & Exs (27 pages; 13/1/25)

 

   Integration Methods (FM) (11 pages; 15/6/24)

 

   Further Integration Methods (STEP) (8 pages; 20/6/24)    

 

   Suggested questions:

 

   2017/P1/Q1* (q'n & sol'n) (integration; substitution) 

 

   Specimen/P1/Q4* (q'n & sol'n) (integration; substitution) 

 

   2023/P2/Q1** (q'n & sol'n) (integration; substitution)

 

   2019/P1/Q3* (q'n & sol'n) (integration)

 

   2011/P1/Q2* (q'n & sol'n) (integration)

 

   2010/P2/Q4** (q'n & sol'n) (integration)

 

   2016/P2/Q7* (q'n & sol'n) (integration)

 

   2014/P3/Q2* (q'n & sol'n) (integration)

 

   1987/P1/Q5* (q'n & sol'n) (integration; substitution)

 

   2007/P1/Q3* (q'n & sol'n) (integration)

 

   2007/P2/Q3* (q'n & sol'n) (integration; substitution)

 

   2008/P2/Q5* (q'n & sol'n) (integration)

 

   Further questions:

 

   2012/P1/Q5* (q'n & sol'n) (integration)

 

   2014/P2/Q4* (q'n & sol'n) (integration)

 

   2020/P2/Q1* (q'n & sol'n) (integration)

 

   2019/P3/Q5* (q'n & sol'n) (integration)

 

   1987/P1/Q8* (q'n & sol'n) (integration; substitution)

 

   1987/P2/Q6** (q'n & sol'n) (integration; trigonometry)   

 

   2005/P1/Q5* (q'n & sol'n) (integration)

 

   2006/P2/Q4* (q'n & sol'n) (integration; substitution)

 

   2007/P3/Q7* (q'n & sol'n) (integration)

 

   2008/P1/Q6* (q'n & sol'n) (integration)

 

   2011/P2/Q6* (q'n & sol'n) (integration)

 

   2012/P2/Q3* (q'n & sol'n) (integration)

 

   2019/P2/Q2* (q'n & sol'n) (integration)

 

   2021/P3/Q3* (q'n & sol'n) (integration; recurrence relation)

 

   2022/P3/Q5* (q'n & sol'n) (integration; hyperbolic fns)

 

  

 

 

 

 

Logarithms

 

   Logarithms - Ideas & Exs (11 pages; 14/12/24)

 

   Logarithms - Further Exs (11 pages; 16/12/24)  

 

   Suggested questions:

 

   2018/P1/Q2** (q'n & sol'n) (logarithms)

 

   1987/P1/Q4** (q'n & sol'n) (logarithms)

 

   2013/P2/Q1* (q'n & sol'n) (logarithms)

 

 

 

 

Matrices (See FM Pure for theory & exercises)

 

   Matrices - Ideas & Exs (20 pages; 14/7/24)

 

   Suggested questions:

 

   2023/P2/Q6* (q'n & sol'n) (matrices)

 

   2019/P3/Q3* (q'n & sol'n) (matrices; invariant points & lines)

 

   2021/P2/Q7* (q'n & sol'n) (matrices; rotations)

 

 

 

 

 

 

 

Polar Curves

 

  Polar Curves (FM)(30 pages; 25/2/25)

 

  Polar Lines (14 pages; 10/4/25)

 

 Suggested questions:

 

  1989/P3/Q6** (q'n & sol'n) (polar curves; conics; lines)

 

 

 

 

Polynomials (see also Quadratics & Cubics)

 

   Polynomials - Ideas & Exs (7 pages; 13/3/25)

 

   Polynomials - Exs (STEP) (18 pages; 5/4/25) 

 

   Suggested questions:    

 

   2002/P1/Q5* (q'n & sol'n) (polynomials; integer roots)

 

   2023/P2/Q4* (q'n & sol'n) (polynomials; integer coeffs)

 

   2019/P2/Q3* (q'n & sol'n) (polynomials; integer roots)

 

   2007/P2/Q2* (q'n & sol'n) (polynomials)

 

   2019/P2/Q1* (q'n & sol'n) (polynomials)

 

 

 

 

 

 

 

 Quadratics

 

   Suggested question:

 

   2006/P1/Q3* (q'n & sol'n) (quadratic; cubic) 

 

 

 

 

Sequences & Series

 

   Sequences & Series: Ideas & Exs (4 pages; 28/4/25)

 

   Sequences & Series - Further Exs (8 pages; 27/12/24)

 

   Maclaurin Series (FM) (7 pages; 23/7/21)

 

   Maclaurin Series Exs (FM) (12 pages; 13/3/25)

 

   Recurrence relations (FM)(16 pages; 29/4/25)

 

   Recurrence relations - Ideas & Exs (6 pages; 29/4/25)

 

   Suggested questions:

 

   1989/P3/Q9** (q'n & sol'n) (Series)

 

   2010/P1/Q5* (q'n & sol'n) (Binomial)

 

   2005/P2/Q6* (q'n & sol'n) (Binomial)

 

   2013/P3/Q2* (q'n & sol'n) (Maclaurin)

 

   2007/P2/Q1* (q'n & sol'n) (Binomial)

 

   2022/P2/Q2 (q'n & sol'n) (Recurrence relations)

 

 

 

 

Transformations

 

   Transformations of Functions - Ideas & Exs (10 pages; 25/2/25) 

 

   Transformations of Functions - Further Exs (10 pages; 28/12/24)

 

 

 

 

 

 

 

Trigonometry

 

   Trigonometry - Ideas & Exs (10 pages; 11/4/25)

 

   Trigonometry - Important Ideas (5 pages; 15/4/21)

 

   Trigonometry - Further Exs (28 pages; 11/4/25)

 

   Suggested question:

 

   2005/P2/Q4 (q'n & sol'n) (arctan)

 

   

 

 

 

 

Vectors

 

   Ideas & Exs (9 pages; 18/1/25)

 

   Further Exs  (21 pages; 18/1/25)  

 

   Suggested questions:

 

  Specimen/P2/Q9* (q'n & sol'n) (vectors)

 

  2019/P2/Q7* (q'n & sol'n) (vectors)

 

  2007/P1/Q7* (q'n & sol'n) (vectors)

 

  2014/P3/Q7* (q'n & sol'n) (vectors; cyclic quadrilateral)

 

  2023/P2/Q8** (q'n & sol'n) (isosceles tetrahedron)  

 

  2022/P3/Q7** (q'n & sol'n) (vector triple product)

 

 

 

 

 

 

 

 

 

 

Mechanics Topics

 

Mechanics - Ideas & Exs (20 pages; 15/4/25)

 

Mechanics Notes (4 pages; 20/7/23) 

 

 

 

 

Centre of Mass

 

Suggested question:

 

2010/P1/Q9* (sol'n) (centre of mass)

 

 

 

 

Circular Motion

 

Circular Motion - Constant Speed (FM) (9 pages; 25/10/20)

 

Circular Motion - Variable Speed (FM) (13 pages; 30/9/15)

 

Suggested questions:

 

2018/P3/Q11* (q'n & sol'n) (circular motion, projectiles)  

 

2020/P2/Q10* (q'n & sol'n) (circular motion/energy)

 

 

 

 

Collisions

 

Collisions - Important Ideas (FM) (4 pages; 22/4/21)

 

Collisions - reversal of direction (FM) (6 pages; 24/6/20) 

 

Oblique impacts (FM) (4 pages; 23/8/18)

 

Impulses & connected particles (FM) (13 pages; 28/8/18) 

 

Collisions - Exs (25 pages; 16/4/25)

 

Suggested questions:

 

2006/P2/Q10* (q'n & sol'n) (collisions)

 

2016/P2/Q9* (q'n & sol'n) (collisions)

 

2008/P2/Q10* (q'n & sol'n) (collisions)

 

2009/P2/Q10* (q'n & sol'n) (collisions)

 

2011/P1/Q10* (q'n & sol'n) (collisions)

 

2011/P2/Q9* (q'n & sol'n) (collisions)

 

Further questions:

 

2013/P1/Q10* (q'n & sol'n) (collisions)

 

2015/P2/Q11* (q'n & sol'n) (collisions)

 

2021/P3/Q9* (q'n & sol'n) (collisions)

 

2022/P3/Q9* (q'n & sol'n) (collisions)

 

 

 

 

Differential Eq'ns

 

Suggested questions:

 

2007/P3/Q9** (q'n & sol'n) (oscillations; spring on hoop)

 

2013/P3/Q9* (q'n & sol'n) (differential eq'ns)

 

2020/P3/Q10* (q'n & sol'n) (oscillations) 

 

 

 

Forces / Equilibrium / Friction 

 

Friction(FM)(5 pages; 1/6/24)

 

Forces - Exs (FM) (33 pages; 25/3/25)

 

Forces - Exs (STEP) (16 pages; 25/3/25)

 

Suggested questions - 'basic':

 

2023/P3/Q10** (q'n & sol'n) (equilibrium; algebra)

 

2014/P1/Q11* (q'n & sol'n) (forces)

 

2018/P1/Q10* (q'n & sol'n) (forces)

 

2016/P1/Q9* (q'n & sol'n) (friction)

 

2015/P2/Q10* (q'n & sol'n) (forces)

 

2005/P2/Q11* (q'n & sol'n) (forces) 

 

2023/P2/Q9** (q'n & sol'n) (forces)

 

Suggested questions - more advanced:

 

2021/P2/Q10** (q'n & sol'n) (constrained motion)

 

2021/P3/Q10** (q'n & sol'n) (constrained motion)  

 

Further questions:

 

2014/P2/Q11* (q'n & sol'n) (forces)

 

2020/P3/Q9* (q'n & sol'n) (equilibrium, friction)

 

2021/P2/Q9* (q'n & sol'n) (equilibrium)

 

2022/P2/Q9* (q'n & sol'n) (equilibrium)

 

 

 

 

 

 

 

Hooke's Law

 

Hooke's Law: Ideas & Exs (FM)(15 pages; 5/2/25)

 

Hooke's Law: Further Exs (FM) (10 pages; 5/2/25)

 

Suggested questions:

 

2014/P3/Q10* (q'n & sol'n) (Hooke's law)

 

2015/P3/Q9* (q'n & sol'n) (Hooke's law)

 

2017/P3/Q9* (q'n & sol'n) (Hooke's law)

 

 

 

 

 

 

 

Kinematics

 

Suggested questions:

 

2015/P1/Q10* (q'n & sol'n) (kinematics)

 

2019/P3/Q9* (q'n & sol'n) (kinematics)

 

2021/P2/Q10 (q'n & sol'n) (kinematics)

 

   

 

Projectiles

 

Suggested questions:

 

2005/P2/Q10* (q'n & sol'n) (projectiles)

 

2012/P1/Q9* (q'n & sol'n) (projectiles)

 

Specimen/P2/Q11* (q'n & sol'n) (projectiles)

 

2006/P1/Q10* (q'n & sol'n) (projectiles)

 

2009/P1/Q9* (q'n & sol'n) (projectiles)

 

2011/P1/Q9* (q'n & sol'n) (projectiles)

 

Further questions:

 

2018/P3/Q11* (q'n & sol'n) (circular motion, projectiles)  

 

2020/P2/Q9* (q'n & sol'n) (projectiles)

 

2022/P2/Q10* (q'n & sol'n) (projectiles)

 

 

 

 

Rotating Bodies

 

Rotating Bodies - Examples (6 pages; 16/3/18) 

 

Suggested questions:

 

Specimen/P2/Q14* (q'n & sol'n) (rotation)

 

Specimen/P3/Q14* (q'n & sol'n) (rotation)

 

2008/P1/Q9* (q'n & sol'n) (rolling)

 

 

 

 

Vectors

 

Suggested question:

 

2019/P3/Q9* (q'n & sol'n) (hemisphere)

 

  

 

Work, Energy & Power

 

Suggested questions:

 

1990/P1/Q10* (q'n & sol'n) (power)

 

Specimen/P1/Q10* (q'n & sol'n) (power)

 

2016/P3/Q11* (q'n & sol'n) (power)

 

2020/P2/Q10* (q'n & sol'n) (circular motion/energy)

 

 

 

 

    

 

Probability & Statistics Topics

 

 

 

 

  Probability

 

  Probability & Counting Approaches (FM) (12 pages; 21/3/24)  

 

  Selections (FM) (6 pages; 15/3/24)

 

  Selections: Ideas & Exs (11 pages; 13/2/25) 

 

  Combinatorics: Ideas & Exs (10 pages; 13/2/25) 

 

  Counting - Exs (32 pages; 19/4/25)

 

  Probability Methods: Ideas & Exs (17 pages; 23/4/25)

 

  Probability - Exs (12 pages; 21/4/25) 

 

 

 

 

  Suggested questions - Counting:

 

  2004/P1/Q14** (q'n & sol'n) (Probability; Combinatorics)

 

  2013/P1/Q13* (q'n & sol'n) (Counting)

 

  2012/P1/Q13* (q'n & sol'n) (Counting)

 

  2023/P3/Q12** (q'n & sol'n) (Combinatorics)

 

  Specimen/P3/Q16** (q'n & sol'n) (Combinatorics)

 

 

 

 

  Suggested questions - Probability:

 

  2009/P1/Q13** (q'n & sol'n) (Probability)

 

  2021/P2/Q12** (q'n & sol'n) (Probability)

 

  2000/P1/Q12* (q'n & sol'n) (Probability)

 

  2015/P2/Q12* (q'n & sol'n) (Probability)

 

  2015/P1/Q13* (q'n & sol'n) (Probability)

 

  2020/P2/Q11** (q'n & sol'n) (Probability)

 

  

 

 

 

 

  Further questions - Probability:

 

  2005/P3/Q13* (q'n & sol'n) (Probability)

 

  Specimen/P2/Q16** (q'n & sol'n) (Probability)

 

  Specimen/P3/Q15** (q'n & sol'n) (Probability)

 

  2006/P1/Q14* (q'n & sol'n) (Probability)

 

  2013/P1/Q12* (q'n & sol'n) (Probability) 

 

  2017/P1/Q13* (q'n & sol'n) (Probability; recurrence relations)

 

  2019/P1/Q11* (q'n & sol'n) (Probability)  

 

  2019/P2/Q11* (q'n & sol'n) (Probability)

 

  2019/P3/Q12* (q'n & sol'n) (Probability)

 

  2020/P2/Q12* (q'n & sol'n) (Probability)

 

 

 

 

  Suggested questions - Conditional Probability:

 

  1987/P2/Q16* (q'n & sol'n) (Conditional probability; Bayesian estimate)  

 

  1987/P1/Q14** (q'n & sol'n) (Conditional probability)

 

  1987/P1/Q16** (q'n & sol'n) (Conditional probability)

 

    

 

Distributions / Random Variables

 

  Distributions (STEP): Ideas & Exs

 

  Discrete Distributions (STEP): Ideas & Exs

 

  Geometric & Negative Binomial distributions (FM) (5 pages; 11/2/25)

 

  Continuous Distributions (STEP): Ideas & Exs (7 pages; 24/4/25)

 

 

 

 

  Suggested questions - Poisson:

 

  2023/P3/Q11* (q'n & sol'n) (Poisson)

 

  2015/P1/Q12* (q'n & sol'n) (Poisson)

 

  2017/P2/Q12* (q'n & sol'n) (Poisson)

 

  2006/P2/Q12* (q'n & sol'n) (Poisson)

 

  2006/P1/Q13* (q'n & sol'n) (Poisson)

 

  2019/P3/Q11* (q'n & sol'n) (Poisson)

 

  Further questions - Poisson:

 

  2012/P2/Q13* (q'n & sol'n) (Poisson)  

 

  Suggested questions - Distributions/RVs:

 

  2015/P3/Q13* (q'n & sol'n) (Distributions/RVs)

 

  2010/P2/Q12* (q'n & sol'n) (Distributions/RVs)   

 

  2005/P1/Q14* (q'n & sol'n) (Distributions/RVs)  

 

  2007/P3/Q12* (q'n & sol'n) (Distributions/RVs) 

 

  2012/P1/Q13* (q'n & sol'n) (Distributions/RVs) 

 

  2014/P2/Q12* (q'n & sol'n) (Distributions/RVs)

 

  Further questions - Distributions/RVs:

 

  2021/P3/Q12** (q'n & sol'n) (Distributions/RVs;Variance)

 

  2023/P2/Q11* (q'n & sol'n) (conditional RVs)

 

  2023/P2/Q12* (q'n & sol'n) (Distributions/RVs)  

 

  2022/P3/Q11* (q'n &sol'n) (Distributions/RVs)

 

  2017/P3/Q13* (q'n & sol'n) (Distributions/RVs; Uniform)

 

  2013/P1/Q13* (q'n & sol'n) (Distributions/RVs)

 

  2006/P3/Q12* (q'n & sol'n) (Normal)   

 

   2008/P3/Q13* (q'n & sol'n) (Distributions/RVs)   

 

  2010/P3/Q12* (q'n & sol'n) (Distributions/RVs) 

 

  

 

 

 

 

 

 

 

Past Papers & Official Sol'ns etc

 

 

 

 

Individual questions for 1986 (Specimen) to 2018 can be found at https://stepdatabase.maths.org/database (you can also search by keyword); or in the book "STEP Mathematics - All exams from 1986 to 2018" by T.K. Finchley (tkfinchley.com). (Official sol'ns prior to 2005 are not readily available though.)

 

 

 

 

 

 

 

2005  Paper 1  Paper 2  Paper 3  Hints & Answers

 

2006  Paper 1  Paper 2  Paper 3  Hints & Answers

 

2007  Paper 1  Paper 2  Paper 3  Sol'ns  Examiners' Report

 

2008  Paper 1  Paper 2  Paper 3  Sol'ns  Examiners' Report

 

2009  Paper 1  Paper 2  Paper 3  Sol'ns  Examiners' Report

 

2010  Paper 1  Paper 2  Paper 3  Sol'ns  Examiners' Report

 

2011  Paper 1  Paper 2  Paper 3  Sol'ns  Examiners' Report

 

2012  Paper 1  Paper 2  Paper 3  Sol'ns  Examiners' Report

 

2013  Paper 1 Paper 2  Paper 3  Sol'ns Examiners' Report

 

2014  Paper 1 Paper 2  Paper 3  Sol'ns Examiners' Report

 

2015  Paper 1 Paper 2  Paper 3  Sol'ns Mark Scheme Examiners' Report

 

2016  Paper 1 Paper 2  Paper 3  Sol'ns Mark Scheme Examiners' Report

 

2017  Paper 1 Paper 2  Paper 3  Mark Scheme 

 

2018  Paper 1 Paper 2  Paper 3  Sol'ns+MS+ER

 

2019  Paper 1 Paper 2  Paper 3  Sol'ns+MS+ER

 

2020  Paper 2 ER+Sol'ns Paper 3 ER+Sol'ns

 

2021  Paper 2 ER+Sol'ns Paper 3 ER+Sol'ns

 

2022  Paper 2 ER+Sol'ns Paper 3 ER+Sol'ns

 

2023  Paper 2 ER+Sol'ns Paper 3 ER+Sol'ns

 

2024  Paper 2 ER+Sol'ns Paper 3 ER+Sol'ns

 

 

 

 

 

 

 

My solutions

 

Specimen (1986) Paper 1: 2 4 5 9 10

 

Specimen (1986) Paper 2: 3 4 7 9 10 11 14 16

 

Specimen (1986) Paper 3: 7 14 15 16

 

1987, Paper 1: 4 5 8 14 16

 

1987, Paper 2: 6 16

 

1987, Paper 3: 3

 

1989, Paper 3: 6 9

 

1990, Paper 1: 10

 

2000, Paper 1: 12

 

2001, Paper 1: 2

 

2001, Paper 2: 11

 

2002, Paper 1: 5

 

2003, Paper 2: 1 2 3 6 7 8 10

 

2003, Paper 3: 4

 

2004, Paper 1: 12 14

 

2005, Paper 1: 1  3  4  5  11  12  13  14

 

2005, Paper 2: 1  4  6  10  11

 

2005, Paper 3: 2  3  7 8 13

 

2006, Paper 1: 1  2  3  4  5  6  7  8  9  10  11  12  13  14

 

2006, Paper 2: 2  4  6  10 12   

 

2006, Paper 3: 2 3  4  10  11  12  13  

 

2007, Paper 1: 1  2  3  4  5  7  12  13

 

2007, Paper 2: 1  2  3  4  5 6

 

2007, Paper 3: 1  2  3  7 9 12

 

2008, Paper 1: 1  2  6  9  13  

 

2008, Paper 2: 1  3  4  5  6  7  10  

 

2008, Paper 3: 1  2  5  8  13  

 

2009, Paper 1: 1  2  9  12  13

 

2009, Paper 2: 5  8  10  11  13

 

2009, Paper 3: 1  4  6  7  8  11  

 

2010, Paper 1: 1  2  3  5  9  

 

2010, Paper 2: 4  5  7  12  13

 

2010, Paper 3: 2  3  8  9 12 

 

2011, Paper 1: 1  2  6  9  10

 

2011, Paper 2: 1  2  5  6  9  11  12

 

2011, Paper 3: 1  2  3  4  5  6  7  8  9  10  11  12  13

 

2012, Paper 1: 2  5  8  9  11  13

 

2012, Paper 2: 3  5  7  9  10  11  12  13

 

2012, Paper 3: 1  6  7  9  10  11  12  13

 

2013, Paper 1: 1 4 10 12 13

 

2013, Paper 2: 1 2 11 12 13

 

2013, Paper 3: 1 2 6 7 8 9

 

2014, Paper 1: 2 3 4 9 11

 

2014, Paper 2: 4 5 9 11 12

 

2014, Paper 3: 2 7 9 10 13

 

2015, Paper 1: 3 9 10 12 13

 

2015, Paper 2: 2 6 10 11 12

 

2015, Paper 3: 1 6 9 12 13

 

2016, Paper 1: 2 9 10 11 12 13

 

2016, Paper 2: 3 6 7 9 13

 

2016, Paper 3: 1 2 3 8 11

 

2017, Paper 1: 1 2 10 12 13

 

2017, Paper 2: 1 9 10 12 13

 

2017, Paper 3: 3 4 9 12 13

 

2018, Paper 1: 2 7 9 10 12 13

 

2018, Paper 2: 2 6 8 10 11 13

 

2018, Paper 3: 1 2 3 5 8 11

 

2019, Paper 1: 3 4 9 10 11

 

2019, Paper 2: 1 2 3 7 10 11

 

2019, Paper 3: 3 5 9 11 12

 

2020, Paper 2: 1 4 5 6 9 10 11 12

 

2020, Paper 3: 1 2 7 9 10 11 12

 

2021, Paper 2: 2 7 8 9 10 11 12

 

2021, Paper 3: 3 4 9 10 11 12

 

2022, Paper 2: 1 2 8 9 10 12

 

2022, Paper 3: 5 7 8 9 10 11

 

2023, Paper 2: 1 4 6 7 8 9 11 12

 

2023, Paper 3: 5 6 7 10 11 12

 

2024, Paper 2: 1 5 6

 

2024, Paper 3: 5 6 8