CONTENTS (@18/7/21) [See Complex Numbers & Counting for examples]

 

Question Bank - Pure (with worked sol'ns)

Types: Exam-style / Practice / Problem

[E=easier; M=moderate; H=harder]

 

Misc. Problems 1

Tests 1 

Algebra 1 2

Arithmetic Series 1 2 3 4

Complex Numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Counting 1 2 3 4 5 6 7

Cubics Qns [3 pages] Sol'ns [10 pages]

Differential Eq'ns 1 

Differentiation 1 2 3 4 5 6

Ellipses 1 2 3

Geometry 1 2 3 4 5 6

Graphs

  Sketches 1 2 3 4 7 8 12

  Transformations 5 6 9 10 11

Groups 1 2 3 4

Hyperbolas 1 2 4 5

Hyperbolic Functions 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Induction [3 pages] Sol'ns [23 pages]

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

Integers 1 2 3 4 5

Integration - P1 (E)(1 page; 7/11/17); Sol'ns (8 pages; 7/11/17)

Integration - P2 (H)(3 pages; 6/4/21); Sol'ns (23 pages; 6/4/21)

Integration - P3 (Hyperbolic)(2 pages; 6/2/18); Sol'ns (12 pages; 17/4/20)

Integration 2 5 6

   Improper Integrals 1  

   Volume of Revolution / Surface Area 3 4 7  

Linear Interpolation 1

Logarithms 1 2 3 4 5 6 7 8 9    

Maclaurin Series 1 2 3 4 5 6  

Matrices

  General 16 21 25

  Determinants 18 23 24 26

  Eigenvectors 4 5 6 7 8 9 10 11 12 13 14 15 47 48

  Invariant Points & Lines 27 28 29 30 42 43 45 46 49

  Inverses 19 22

  Shears 31 32 33 34

  Simultaneous Eq'ns 3 35 36 37 38 39

  Transformations 1 2 17 40 41 44 50

Numerical Methods

  Convergence 2

  Integration 3 4 5 6 7

  Sol'n of Eq'ns 1

Parabolas 1 2 3 4 5

Parametric Eq'ns 1

Partial Fractions 1

Polar Curves 1 2 3 4

Polynomials 4 5

   Factorisations 1 2 3

   Relations between roots 6 7 8 9 10 11 12

Quadratics 1 2 3 4 5

Recurrence relations 1

Series 5 6 7

   Method of Differences 1 2 3 4

Surds 1 2

Trigonometry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Vectors 2 4 14 16 21 24 25 26 27

   Lines 5 6

   Planes 7 9 11 15

   Lines & Planes 1 8 10 17 20 23

   Shortest Distance 3 12 13 18 19 22

 

 

Question Bank - Mechanics (with worked sol'ns)

 Types: Exam-style / Practice / Problem

[E=easier; M=moderate; H=harder]

 

Centre of Mass 1 2 3 4 5  

Circular Motion 1 2

Forces 1 2 3 4 5 6 7 8 9 10 11 

Friction 1 2 3 4

Hooke's Law 1 2 3 4

Impulse & Momentum 1 2 3 4 5 6 7 8 9 10 11 12 

   Oblique impact with plane Exs

Kinematics 1 2

Oscillations 1 2 3 4

Rotating Bodies 1

Work & Energy 1 2 3 4

 

  

Question Bank - Probability & Statistics (with worked sol'ns)

Types: Exam-style / Practice / Problem

[E=easier; M=moderate; H=harder]

 

Chi-Squared

  Contingency Tables 2a 2b

  Goodness of Fit 1

Correlation 1 2

Discrete Random Variables 1 2 3 4

Geometric Distribution 1 2

Normal Distribution 1 2

Poisson Distribution 1 2 3 4

Probability 1 2 3 4 5 6 7

Probability Generating Function 1 2

Uniform Distribution (Discrete) 1

 

Question Bank - Discrete (with worked sol'ns)

Types: Exam-style / Practice / Problem

[E=easier; M=moderate; H=harder]

 

Algorithms 1 7

   Bin Packing 3 5 6

   Sorting 2 4    

Critical Path Analysis 1a 1b 2

Dijkstra's algorithm 1

Floyd's Algorithm  1 2

Game Theory  1 2 3

Graphs 2

   Kuratowski's Thm 1

Linear Programming 1 2a 2b

   Formulate as LP problem 3 4 5 6 7

   Simplex 2c 8 9a 9b

Minimum Connector 1 2

Planarity algorithm 1

Route Inspection 1 2

Travelling Salesman problem 1

 

STEP   

General Notes

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

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

STEP Exams - Methods (8 pages; 4/6/20)

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

Index of q'ns: Pure (24 pages; 2/9/20)

Index of q'ns: Mechanics (9 pages; 2/9/20)

Index of q'ns: Probability & Statistics (7 pages; 2/9/20)

 

Topic Notes & Exercises

Miscellaneous (5 pages; 14/7/21)

Algebra Methods 5 pages; 23/1/18)

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

Cubics (4 pages; 11/12/19)

Curve Sketching (12 pages; 14/7/21)

Differential Equations (5 pages; 18/11/18)

Inequalities (2 pages; 14/7/21)

Integration Ideas (4 pages; 14/4/21)

Logarithms (2 pages; 14/7/21)

Probability & Counting Approaches (12 pages; 14/7/21)

Transformations (6 pages; 12/12/19)

Trigonometry (5 pages; 15/4/21)

Vector Methods (5 pages; 26/3/21)

STEP Exercises (5 pages; 2/12/20); Sol'ns (24 pages; 2/12/20)

 

Solutions for Past Papers

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: 3  4  10  11  12  13 

2007, Paper 1: 1  2  3  4  5  7  12 

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

 

MAT

 

General Notes

MAT Exam Tips (3 pages; 14/2/21)

Notes on MAT paper (3 pages; 6/8/20)

MAT Exam Technique (12 pages; 4/9/20)

MAT - Index of Q'ns (14 pages; 4/11/20)

  

Topic Notes & Exercises

Important Ideas (17 pages; 15/2/20)

MAT Exercises (3 pages; 2/12/20); Sol'ns (12 pages; 2/12/20)

 

Solutions for Past Papers

Specimen 1: MC 3 4 5

Specimen 2: MC 2 4

2007: MC 4 5

2008: MC 2 3 5

2009: MC 2

2010: MC 3

2011: MC 2

2012: MC 5

2013: MC 2 3 4 5

2014: MC 2 3 4 5

2015: MC 2 3 4 5

2016: MC

2017: MC 2

2018: MC

2019: MC 2 3

2020: MC