STEP Preview (Examples are in blue)
Key:
- recently added material is in green (where changes are significant)
- suggested questions: * = recommended; ** = strongly recommended
- FM = repeat of document on FM pages
General
Notes on STEP (3 pages; 2/12/24)
STEP - Preparation (3 pages; 9/1/25)
STEP - Methods (12 pages; 9/1/25)
STEP - Exam Technique (10 pages; 9/1/25)
Index of q'ns: Pure (26 pages; 7/12/24)
Index of q'ns: Mechanics (10 pages; 25/7/24)
Index of q'ns: Probability & Statistics (7 pages; 7/12/24)
Possible topics to specialise in (12 pages; 14/12/24)
Important Ideas (6 pages; 12/7/24)
Basic Ideas & Exercises (20 pages; 18/11/24)
Pure
Algebra
Ideas & Exs (17 pages; 21/12/24)
Further Exs (6 pages; 21/12/24)
Complex Numbers
Ideas & Exs (14 pages; 12/4/24)
Complex Number Methods (9 pages; 28/2/15)
2009/P3/Q6* (sol'n)
2011/P3/Q8* (sol'n)
2012/P3/Q6* (sol'n)
2013/P3/Q6* (sol'n)
2013/P3/Q8* (sol'n)
Cubics
Cubics (5 pages; 5/6/23)
Cubics Exs [3 pages, 29/7/16] Sol'ns (10 pages, 29/7/16)
2006/P1/Q3* (sol'n) (quadratics & cubics)
2007/P2/Q2 (sol'n) (cubic)
2008/P2/Q3* (sol'n) (cubic)
2018/P1/Q7* (sol'n) (cubic)
Curve Sketching (see also Functions & Differentiation)
Curve Sketching: Ideas & Exs (22 pages; 12/4/24)
Functions & Curve Sketching (5 pages; 22/11/24)
Mappings & functions (FM) (3 pages; 2/6/23)
Exs: Curve sketching 1 2 3 4 5 6
2007/P2/Q2* (sol'n) (curve sketching)
2008/P1/Q6* (sol'n) (curve sketching)
2010/P1/Q2* (sol'n) (curve sketching)
2011/P2/Q1** (sol'n) (curve sketching)
2013/P2/Q1* (sol'n) (curve sketching)
2014/P1/Q2* (sol'n) (curve sketching; ln)
2020/P3/Q2* (sol'n) (curve sketching; hyperbolic functions)
Differential Eq'ns
Differential Equations: Ideas & Exs (10 pages; 12/4/24)
Differential Equations (6 pages; 21/4/23)
Exs: Differential equations 1 2 3 4
2008/P2/Q7*(sol'n) (DEs)
Differentiation
Turning points & Points of inflexion (FM) (7 pages; 5/6/23)
Differentiation: Ideas & Exs (11 pages; 26/11/24)
Exs: Differentiation 1 2 3 4 5 6 7
Specimen/P1/Q2* (q'n & sol'n) (differentiation)
2014/P1/Q4* (sol'n)
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)
2008/P1/Q6* (sol'n) (inverse function)
2003/P2/Q6** (sol'n) (modulus function)
Geometry
Exs: Geometry 1 2
2006/P1/Q2* (sol'n) (geometry)
2023/P2/Q8** (sol'n) (isosceles tetrahedron)
2013/P3/Q8* (sol'n) (geometry)
Hyperbolic Functions
Ideas & Exs (4 pages; 12/4/24)
Exs: Hyperbolic Functions 1 2 3 4
Specimen/P2/Q4* (q'n & sol'n) (hyperbolic fns; curve sketching)
Inequalities
Notes (3 pages; 29/12/24)
Ideas & Exs (20 pages; 29/12/24)
Further Exs (15 pages; 29/12/24)
2008/P2/Q5* (sol'n) (inequalities)
Integers
Exs: Integers 1 2 3 4 5 6 7 8
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)
Specimen/P1/Q4* (q'n & sol'n) (integration; substitution)
2005/P1/Q5* (sol'n) (integration)
2006/P2/Q4* (sol'n) (integration; substitution)
2007/P1/Q3* (sol'n) (integration)
2007/P2/Q3* (sol'n) (integration; substitution)
2007/P3/Q7* (sol'n) (integration)
2008/P1/Q6* (sol'n) (integration)
2008/P2/Q5* (sol'n) (integration)
2010/P2/Q4* (sol'n) (integration)
2011/P1/Q2* (sol'n) (integration)
2011/P2/Q6* (sol'n) (integration)
2012/P1/Q5* (sol'n) (integration)
2012/P2/Q3* (sol'n) (integration)
2014/P2/Q4* (sol'n) (integration)
2014/P3/Q2* (sol'n) (integration)
2016/P2/Q7* (sol'n) (integration)
2019/P1/Q3* (sol'n) (integration)
2019/P2/Q2* (sol'n) (integration)
2019/P3/Q5* (sol'n) (integration)
2020/P2/Q1* (sol'n) (integration)
2021/P3/Q3* (sol'n) (integration; recurrence relation)
2022/P3/Q5* (sol'n) (integration; hyperbolic fns)
2023/P2/Q1** (sol'n) (integration; substitution)
Logarithms
Ideas & Exs (11 pages; 14/12/24)
Further Exs (11 pages; 16/12/24)
2013/P2/Q1* (sol'n) (logarithms)
Matrices
Ideas & Exs (20 pages; 14/7/24)
2019/P3/Q3* (sol'n) (matrices)
2021/P2/Q7* (sol'n) (matrices)
Polynomials
Ideas & Exercises (6 pages; 8/11/24)
Exs: Polynomials 1 2 3 4 5 6 7 8 9
2007/P2/Q2* (sol'n) (polynomials)
2019/P2/Q1* (sol'n) (polynomials)
Proof
Necessary & Sufficient Conditions - Ideas & Exs (12 pages; 24/12/24)
Exs: Proof 1 2 3 4 5 6 7 8 9
Exs: Induction 1
2008/P1/Q1 (sol'n) (irrational numbers)
2006/P1/Q3 (sol'n) (quadratic)
Sequences & Series
Ideas & Exs (3 pages; 27/12/24)
Further Exs (8 pages; 27/12/24)
Recurrence relations (FM)(16 pages; 5/9/18)
Exs: Recurrence relations (10 pages, 6/11/22)
2005/P2/Q6* (sol'n)
2007/P2/Q1* (sol'n) (Binomial expansion)
2010/P1/Q5* (sol'n) (Binomial expansion)
Transformations
Transformations of Functions - Ideas & Exs (8 pages; 28/12/24)
Transformations of Functions - Further Exs (10 pages; 28/12/24)
Trigonometry
Ideas & Exs
Trigonometry (5 pages; 15/4/21)
Exs: Trigonometry 1 2 3 4 5 6 7 8 9 10 11 12 13 14
2005/P2/Q4 (sol'n) (arctan)
Vectors
Ideas & Exs (9 pages; 18/1/25)
Further Exs (21 pages; 18/1/25)
Specimen/P2/Q9* (q'n & sol'n) (vectors)
2014/P3/Q7* (sol'n) (vectors; cyclic quadrilateral)
2019/P2/Q7* (sol'n) (vectors)
2022/P3/Q7** (sol'n) (vector triple product)
2023/P2/Q8** (sol'n) (isosceles tetrahedron)
Miscellaneous Pure
Exs: General 1 2 3 4
2005/P1/Q1* (sol'n) (digits)
Mechanics
Ideas & Exs
Mechanics Notes (4 pages; 20/7/23)
Centre of Mass
2010/P1/Q9* (sol'n) (centre of mass)
Circular Motion
2018/P3/Q11* (sol'n) (circular motion, projectiles)
2020/P2/Q10* (sol'n) (circular motion/energy)
Collisions
Exs: Collisions 1 2 3 4 5 6 7 8 9 10
2006/P2/Q10* (sol'n) (collisions)
2008/P2/Q10* (sol'n) (collisions)
2009/P2/Q10* (sol'n) (collisions)
2011/P1/Q10* (sol'n) (collisions)
2011/P2/Q9* (sol'n) (collisions)
2013/P1/Q10* (sol'n) (collisions)
2015/P2/Q11* (sol'n) (collisions)
2016/P2/Q9* (sol'n) (collisions)
2021/P3/Q9* (sol'n) (collisions)
2022/P3/Q9* (sol'n) (collisions)
Differential Eq'ns
2013/P3/Q9* (sol'n) (differential eq'ns)
Forces / Equilibrium / Friction / Hooke's Law
Friction(FM)(5 pages; 1/6/24)
Exs: Forces 1 2 3 4 5 6 7
2005/P2/Q11* (sol'n) (forces)
2014/P1/Q11* (sol'n) (forces)
2014/P2/Q11* (sol'n) (forces)
2014/P3/Q10* (sol'n) (Hooke's law)
2015/P2/Q10* (sol'n) (forces)
2015/P3/Q9* (sol'n) (Hooke's law)
2016/P1/Q9* (sol'n) (friction)
2017/P3/Q9* (sol'n) (Hooke's law)
2018/P1/Q10* (sol'n) (forces)
2020/P3/Q9* (sol'n) (equilibrium, friction)
2021/P2/Q9* (sol'n) (equilibrium)
2022/P2/Q9* (sol'n) (equilibrium)
2023/P2/Q9** (sol'n) (forces)
Kinematics
2015/P1/Q10* (sol'n) (kinematics)
Projectiles
Specimen/P2/Q11* (sol'n) (projectiles)
2005/P2/Q10* (sol'n) (projectiles)
2006/P1/Q10* (sol'n) (projectiles)
2009/P1/Q9* (sol'n) (projectiles)
2011/P1/Q9* (sol'n) (projectiles)
2012/P1/Q9* (sol'n) (projectiles)
2018/P3/Q11* (sol'n) (circular motion, projectiles)
2020/P2/Q9* (sol'n) (projectiles)
2022/P2/Q10* (sol'n) (projectiles)
Rotating Bodies
Rotating Bodies - Examples (6 pages; 16/3/18)
Specimen/P2/Q14* (sol'n) (rotation)
2008/P1/Q9* (sol'n) (rolling)
Work, Energy & Power
2016/P3/Q11* (sol'n) (power)
2020/P2/Q10* (sol'n) (circular motion/energy)
Miscellaneous
2019/P3/Q9* (sol'n) (vectors)
2020/P3/Q10* (sol'n) (oscillations)
2021/P2/Q10** (sol'n) (constrained motion)
2021/P3/Q10** (sol'n) (constrained motion)
Probability & Statistics
Counting
Probability & Counting Approaches (FM) (12 pages; 21/3/24)
Selections (FM) (6 pages; 15/3/24)
Selections: Ideas & Exs (13 pages; 8/7/24)
Counting Exs 1 2 3 4 5 6 7 8 9 10 11
Specimen/P1/Q5* (q'n & sol'n) (counting)
2005/P1/Q1* (sol'n) (counting)
Distributions
Distributions (STEP): Ideas & Exs
Discrete Distributions (STEP): Ideas & Exs
Continuous Distributions (STEP): Ideas & Exs
2010/P2/Q12 (sol'n)
Statistics Exs 1
2017/P2/Q12 (sol'n) (Poisson)
Probability Generating Functions: Ideas & Exs
2006/P1/Q13* (sol'n) (Poisson)
2006/P2/Q12* (sol'n) (Poisson)
2006/P3/Q12* (sol'n) (Normal)
2011/P3/Q12 (sol'n)
2012/P2/Q13* (sol'n) (Poisson)
2017/P2/Q12* (sol'n) (Poisson)
2019/P3/Q11* (sol'n) (Poisson)
Probability
Probability Methods: Ideas & Exs (8 pages; 2/4/24)
Probability Exs 1 2 3 4 5
Specimen P2, Q16** (q'n & sol'n) (Probability: Tennis tournament)
2009/P1/Q13** (sol'n) (Probability)
2013/P1/Q12* (sol'n) (Probability)
2013/P1/Q13* (sol'n) (Probability)
2015/P1/Q13* (sol'n) (Probability)
2015/P2/Q12* (sol'n) (Probability)
2017/P1/Q13* (sol'n) (Probability; recurrence relations)
2019/P1/Q11* (sol'n) (Probability)
2019/P2/Q11* (sol'n) (Probability)
2020/P2/Q11** (sol'n) (Probability)
2020/P2/Q12* (sol'n) (Probability)
2021/P2/Q12** (sol'n) (Probability)
Past Papers & Official Sol'ns etc
Individual questions for 1986 (Specimen) to 2018 can be found at https://stepdatabase.maths.org/database ; 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
My solutions
Specimen (1986) Paper 1 (with q'ns): 2 4 5
Specimen (1986) Paper 2 (with q'ns): 3 4 7 9 10 11 14 16
2003, Paper 2: 1 2 3 6 7 8 10
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
2007, Paper 3: 1 2 3 7 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 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: 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 7 10 11
2019, Paper 3: 3 5 9 11 12
2020, Paper 2: 1 6 9 10 11 12
2020, Paper 3: 1 2 7 9 10 11 12
2021, Paper 2: 2 7 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 7 8 9 12
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