STEP   

(recently added material is in green)

General Notes

STEP Exams - Tips (3 pages; 14/2/21)

STEP Exams - Preparation (3 pages; 4/6/20) 

STEP Exams - Methods (9 pages; 14/3/24) 

STEP Exams - Technique (7 pages; 4/6/20) 

Index of q'ns: Pure (25 pages; 6/2/24)

Index of q'ns: Mechanics (10 pages; 6/2/24)

Index of q'ns: Probability & Statistics (7 pages; 14/7/23)

Topics (with recommended q'ns)

Algebra

  Algebra (5 pages; 23/1/18)

  Exercises: Algebra 1 2 3 4 5

Proof

   Ideas & Exercises

   Proofs: If and Only If (6 pages; 18/5/23)

   Exercises: Induction 1

   2008/P1/Q1 (sol'n) [irrational numbers]

   2006/P1/Q3 (sol'n) [quadratic]

Curve Sketching

    Ideas & Exercises

   Functions & Curve Sketching (5 pages; 2/6/23)

   Cubics (4 pages; 11/12/19)

   Transformations  (6 pages; 29/2/24)

   Exercises: Curve sketching 1 2 3 4 5 6

   Exercises: Transformations 1 2 3 4 5

   2007/P2/Q2 (sol'n) [cubic]

   2011/P2/Q1 (sol'n) [square roots]

Geometry

   Exercises: Geometry 1

Integers

   Exercises: Integers 1 2 3 4 5 6 7 8

Logarithms

   Logarithms (2 pages; 14/7/21)

   Exercises: Logarithms 1 2 3 4

Inequalities

   Exercises: Inequalities 1 2 3 4 5 6 7 8 9 10 11

Polynomials

   Exercises: Polynomials 1 2 3 4 5 6 7 8

Trigonometry

    Ideas & Exercises

   Trigonometry (5 pages; 15/4/21)

   Exercises: Trigonometry 1 2 3 4 5 6 7 8 9 10 11 12 13

   2005/P2/Q4 (sol'n) [arctan]

Hyperbolic Functions

    Ideas & Exercises

   Exercises: Hyperbolic Functions 1 2 3 4

   2020/P3/Q2 (sol'n) [curve sketching]

Differentiation

    Ideas & Exercises

   Exercises: Differentiation 1 2 3 4 5 6 7

Integration

   Ideas & Exercises

   Integration Ideas (5 pages; 17/7/23)

   Exercises: Integration 1 2 3 4 5 6 7 8 9 10

   2011/P1/Q2 (sol'n) [E&e]

   2008/P2/Q5 (sol'n) [Binomial expansion]

Series

    Ideas & Exercises

   Exercises: Sequences & Series 1 2 3 4 5 

   Exercises: Recurrence relations (10 pages, 6/11/22)

   2005/P2/Q6 (sol'n)

Matrices

    Ideas & Exercises

   2021/P2/Q7 (sol'n)

Vectors

    Ideas & Exercises

   Vector Methods (5 pages; 26/3/21)

   Exercises: Vectors 1 2 3 4 5 6 7 8 9

   2014/P3/Q7 (sol'n)

Complex Numbers

    Ideas & Exercises 

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

   Exercises: Complex Numbers 1 2 

   2009/P3/Q6 (sol'n)

Differential Eq'ns

    Ideas & Exercises

   Differential Equations (6 pages; 21/4/23)

   Exercises: Differential equations 1 2 3 4

   2008/P2/Q7 (sol'n)

Miscellaneous Pure

   Misc. Topic Notes (6 pages; 2/6/23)

   Exercises: General 1 2 3 4   

Mechanics - General

   Slides 

   Mechanics Notes  (4 pages; 20/7/23)

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

   2005/P2/Q10 (sol'n) [missiles]

   2018/P3/Q11 (sol'n) [circular motion]

   2021/P2/Q10 (sol'n) [bead on train]

Forces

   Exs: Forces 1 2 3 4 5 6 7

  2018/P1/Q10 (sol'n) [engines & carriages]

Collisions

   Exs: Collisions 1 2 3 4 5 6 7 8 9 10

Probability

  Slides [Probability Methods]

  Exs: Probability 1 2 3 4 5

  2009/P1/Q13 (sol'n)

Counting

  Slides [Selections]

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

  Selections (6 pages; 15/3/24)

  Exs: Counting 1 2 3 4 5 6 7 8 9 10 11

Expectation & Variance

  SlidesContinuous Distributions

  Slides

  2010/P2/Q12 (sol'n)

Statistical Distributions

  Slides

  Distributions (STEP) (1 page; 6/7/23)

   Exs: Statistics 1 

  2017/P2/Q12 (sol'n) [Poisson]

Probability Generating Functions

  Slides

  2011/P3/Q12 (sol'n)

Past Papers & Official Sol'ns etc

[Earlier papers (back to 1994) can be found on the MyMathsCloud website.]

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

Past Paper Solutions

[See also Peter Mitchell's site] 

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 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 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 8 11