TMUA Preview
Links to Examples are in blue
General Notes
About the TMUA paper (2 pages; 18/9/24)
TMUA - Exam Technique (10 pages; 17/9/25)
TMUA - Useful material outside syllabus (2 pages; 6/10/24)
TMUA - Index of Questions (20 pages; 14/12/24)
TMUA Topics (5 pages; 14/12/24)
Important Ideas (17 pages; 28/9/21)
Basic Ideas & Exs (20 pages; 18/11/24)
TMUA Methods - Ideas & Exs (51 pages; 10/1/25)
TMUA & MAT Recommended Q'ns (with sol'ns)(50 pages; 10/1/25)
Topics
Algebra: Ideas & Exs (12 pages; 21/12/24)
Suggested q'ns:
2023/p2/Q6 (eq'ns)
2023/P2/Q12 (number of sol'ns of eq'n)
2021/P2/Q16 (sol'n of eq'n)
2018/P2/Q20 (spurious solutions)
Counting Exs (20 pages; 5/11/22)
Cubics (5 pages; 5/6/23)
Cubics Exs [3 pages, 29/7/16] Sol'ns (10 pages, 29/7/16)
Suggested q'ns:
2023/P1/Q14 (cubic)
2020/P1/Q20 (cubic)
2020/P2/Q18 (cubic)
Spec/P2/Q19 (cubic)
Curve Sketching (5 pages; 6/10/24)
Curve Sketching Ideas & Exs (23 pages; 22/12/24)
Suggested q'n:
2022/P1/Q20 (curve sketching)
2018/P2/Q15 (curve sketching)
Differentiation Exs (2 pages; 5/11/22)
Turning points & Points of inflexion (FM) (7 pages; 5/6/23)
Functions
Suggested q'ns:
2023/P1/Q2 (intersection of curves)
2023/P1/Q20 (functions)
2023/P2/Q19 (functions)
2023/P2/Q20 (functions; integral)
2022/P2/Q14 (modulus function; inequalities)
2021/P1/Q12 (functions)
2021/P1/Q18 (rotation of curve)
2018/P2/Q18 (convex function)
Geometry Exs (2 pages; 5/11/22)
Suggested q'ns:
2023/P1/Q16 (right-angled triangle)
2023/P2/Q9 (pentagon)
2023/P2/Q14 (parallel & perp. lines)
2022/P2/Q19 (polygon)
2021/P1/Q1 (circles)
2021/P1/Q8 (geometry)
2021/P1/Q20 (geometry)
2021/P2/Q7 (geometry)
2021/P2/Q18 (geometry)
2020/P1/Q16 (geometry)
2022/P1/Q17 (triangle)
2022/P1/Q19 (circles)
Practice(aka 2016)/P1/Q20 (pyramid)
Practice(aka 2016)/P2/Q8 (geometry)
Practice(aka 2016)/P2/Q16 (geometry; trapezium)
Inequalities
Inequalities - Notes (3 pages; 29/12/24)
Inequalities - Ideas & Exs (20 pages; 29/12/24)
Inequalities: Further Exs (8 pages; 22/4/25)
Integers Exs (10 pages; 10/10/24)
Integration Exs (2 pages; 5/11/22)
Suggested q'n:
2021/P1/Q7 (integration)
2021/P1/Q15 (integration)
2020/P2/Q16 (Fundamental Theorem of Calculus)
Logarithms: Ideas & Exs (10 pages; 14/12/24)
Suggested q'n:
Practice(aka 2016)/P2/Q7
Logic
True or False problems: Ideas & Exs (6 pages; 17/12/24)
Suggested q'ns:
2018/P2/Q12** (negation)
2016/P2/Q4 (true or false; urns)
2022/P2/Q16 (true or false; sequence)
2020/P2/Q19 (true or false)
2020/P2/Q20 (true or false)
Spec/P2/Q20 (true or false)
Polynomials Exs (8 pages; 3/9/24)
Suggested q'n:
2022/P1/Q18 (intersection of polynomial functions)
Probability
Probability Methods (17 pages; 17/12/25)
Suggested q'n:
Practice(aka 2016)/P1/Q7 (conditional probability)
Proof
Necessary & sufficient conditions: Ideas & Exs (12 pages; 24/12/24)
Errors in reasoning - common q'n types (10 pages; 27/12/24)
Suggested q'ns:
2016/P2/Q10 (necessary & sufficient conditions)
2023/P2/Q7 (necessary & sufficient conditions)
2023/P2/Q9 (necessary & sufficient conditions)
2022/P2/Q7 (error in proof)
2021/P2/Q6 (necessary & sufficient conditions)
2021/P2/Q8 (necessary & sufficient conditions)
2021/P2/Q15 (necessary & sufficient conditions)
Practice(aka 2016)/P2/Q10 (necessary & sufficient conditions)
Quadratics (4 pages; 10/10/24)
Suggested q'n:
2020/P1/Q19 (quadratic)
Recurrence relations Exs (10 pages; 5/11/22)
Suggested q'n:
2023/P2/Q16 (recurrence relation)
2021/P2/Q20 (recurrence relation)
Sequences
Suggested q'n:
2018/P2/Q7 (sequences)
Series: Ideas & Exs (3 pages; 27/12/24)
Statistics
Suggested q'ns:
2020/P2/Q17 (mean & median)
Spec/P2/Q18 (mean & median)
2018/P2/Q16 (median)
Transformations of Functions: Ideas & Exs (8 pages; 28/12/24)
Transformations of Functions: Further Exs (10 pages; 28/12/24)
Suggested q'n:
Practice(aka 2016)/P1/Q9 (transformations)
Trigonometry: Ideas & Exs (15 pages; 11/10/24)
Trigonometry: Further Exs (10 pages; 11/10/24)
Suggested q'ns:
2023/P1/Q9 (Trig.)
2023/P1/Q12 (Trig.)
2022/P2/Q18 (Trig.)
2021/P1/Q19 (Trig.)
Practice(aka 2016)/P1/Q8 (Trig.)
Miscellaneous
Suggested q'n:
2022/P2/Q8 (arithmetic sequence)
2018/P2/Q3 (average speed)
Themes
Exam technique
Practice(aka 2016)/P2/Q19 (ambiguity)
Case by case
2021/P2/Q20
Practice(aka 2016)/P2/Q4
Matching graphs to function
2021/P1/Q17
Number of solutions
2021/P1/Q14
2020/P1/Q12
Past Papers & Official Solutions etc
Specimen P1 Solns; P2 Solns; Answers (P1&P2)
Practice (aka 2016) P1 Solns; P2 Solns; Answers (P1&P2)
2017 P1 Solns; P2 Solns; Answers (P1&P2)
2018 P1 Solns; P2 Solns; Answers (P1&P2)
2019 P1 Solns; P2 Solns; Answers (P1&P2)
2020 (same as computer-based demo) P1 Solns; P2 Solns; Answers (P1&P2)
2021 P1 Solns; P2 Solns; Answers (P1&P2)
2022 P1 Solns; P2 Solns; Answers (P1&P2)
2023 P1 Solns; P2 Solns; Answers (P1&P2)
(2024+ not available)
My solutions for Past Papers (with q'ns)
Practice (aka 2016) P1 P2
2018 P2
2020 [also used for Computer-based Demo] P1 P2
2021 P1 P2
2022 P1 P2
2023 P1 P2
MAT Past Papers & Official Solutions
(the multiple choice questions may be of interest for TMUA)
1996 Paper MC Answer Key
1997 Paper MC Answer Key
1998 Paper MC Answer Key
1999 not available
2000 Paper MC Answer Key
2001 not available
2002 not available
2003 Paper MC Answer Key
2004 Paper MC Answer Key
2005 Paper MC Answer Key
2006 Paper MC Answer Key
2007 Paper Sol'ns
2008 Paper Sol'ns
2009 Paper Sol'ns
2010 Paper Sol'ns
2011 Paper Sol'ns
2012 Paper Sol'ns
2013 Paper Sol'ns
2014 Paper Sol'ns
2015 Paper Sol'ns
2016 Paper Sol'ns
2017 Paper Sol'ns
2018 Paper Sol'ns
2019 Paper Sol'ns
2020 Paper Sol'ns
2021 Paper Sol'ns
2022 Paper Sol'ns
2023 Paper Sol'ns
2024 (MC not available)
My Solutions for MAT Multiple Choice questions
Specimen 1: MC
Specimen 2: MC
2005: MC (with q'ns)
2006: MC (with q'ns)
2007: MC (with q'ns)
2008: MC (with q'ns)
2009: MC (with q'ns)
2010: MC (with q'ns)
2011: MC (with q'ns)
2012: MC (with q'ns)
2013: MC
2014: MC
2015: MC
2016: MC
2017: MC
2018: MC
2019: MC
2020: MC
2021: MC
2022: MC
2023: MC
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