Senior Mathematical Challenge Past Papers 2012 2016 Pdf

The Zeta Club is an maths enrichment club for Tiffin students, with a particular focus on the Olympiads and Maths Challenges. Details are below.

Junior (Years 7-8)

Where: Room 56
Who with: Ms Bickerstaff
When: Wed at 1.05pm

Intermediate (Years 9-10)

Where: Room 57
Who with: Dr Frost
When: Wed/Thur at 1.05pm (pick either day)

UKMT Database

You can browse the UKMT database by topic here: https://www.drfrostmaths.com/browse.php?mode=ukmt and by paper here: https://www.drfrostmaths.com/worksheets.php?author=ukmt. Teacher accounts can export collections of these questions to Microsoft Word.

Junior Maths Challenge

All are harder questions from past JMCs, i.e. Q16-25, the point at which points are lost for incorrect answers. The topics for these questions are somewhat more evenly distributed than in the geometry-heavy IMC: within the 2004-2012 papers (Q16-25 on each paper), 14 were geometry, 22 number (ratios, time, numerical calculations, etc.), 5 number grids (filling numbers into structures according to some constraint), 23 on Number Theory (problems relating to integers: remainders, factors, digits, etc.), 20 on 'spatial reasoning', and 6 on non-applied algebra. These questions below are categorised according to these by topic to help you hone in on particular skills. Please contact me for answers.

Algebra
Geometry
Number (ratios, time, numerical calculations, etc.)
Number Grids (filling numbers in some grid/structure)
Number Theory (problems relating to integers: remainders, factors, digits, etc.)
Spatial Reasoning

Junior Maths Olympiad

Again, questions are categorised by topic, and 'fact sheets' provide key theory and tips for each of these topics. Section B advice I've written can be found here.

Sample student solutions can be found here.

JMO Geometry Questions

2 files16/05/2016

Junior Maths Olympiad Section B questions on the topic of Geometry. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards which I kept in a pack for use in lessons. 10 points corresponds to the first question, 15 points for the last.
JMO Miscellaneous Questions

2 files16/05/2016

Junior Maths Olympiad Section B questions. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards which I kept in a pack for use in lessons. 10 points corresponds to the first question, 15 points for the last.
JMO Number Grid Questions

3 files16/05/2016

Junior Maths Olympiad Section B questions on the topic of Number Grids. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards which I kept in a pack for use in lessons. 10 points corresponds to the first question, 15 points for the last.
JMO Number Theory Questions

3 files16/05/2016

Junior Maths Olympiad Section B questions on the topic of Number Theory. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards which I kept in a pack for use in lessons. 10 points corresponds to the first question, 15 points for the last.
JMO Sequences Questions

3 files16/05/2016

Junior Maths Olympiad Section B questions on the topic of Sequences. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards which I kept in a pack for use in lessons. 10 points corresponds to the first question, 15 points for the last.
JMO Spatial Reasoning Questions

3 files16/05/2016

Junior Maths Olympiad Section B questions on the topic of Spatial Reasoning. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards which I kept in a pack for use in lessons. 10 points corresponds to the first question, 15 points for the last.
JMO Speed Distance Time Questions

3 files16/05/2016

Junior Maths Olympiad Section B questions on the topic of Speed-Distance-Time. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards which I kept in a pack for use in lessons. 10 points corresponds to the first question, 15 points for the last.

Junior Mentoring sheets

You can find examples here: www.ukmt.org.uk/enrichment/mentoring-scheme. An index of these questions by topic can be found here.

Intermediate Maths Challenge

All are harder questions from past JMCs, i.e. Q16-25, the point at which points are lost for incorrect answers. I've categorised these by topic to hone in on particular skills. The ratio of (harder) question types for 2004-2012 is somewhat interesting: 38 were geometry, 16 were some kind of 'spatial reasoning' (paths through networks, rotating objects, etc.), 16 were general number problems (e.g. ratio, time, density, etc.), 14 'number theory' problems (involving integers, primes, digits, etc.) and just 6 non-applied algebra. As with the Olympiad, clearly the key to a high score is to master the geometry problems, many of which follow a similar approach. Please contact me for answers.

Algebra
Geometry
Number (ratios, time, numerical calculations, etc.)
Number Theory (problems relating to integers: remainders, factors, digits, etc.)
Sequences
Spatial Reasoning

Intermediate Maths Olympiad

Again, questions are categorised by topic, and 'fact sheets' provide key theory and tips for each of these topics.

The breakdown of questions across a 8 year period: 59 Geometry questions, 28 Number Theory, 25 (non-applied) Algebra, 13 Spatial Reasoning/Logic, 6 Number Grids, 5 Speed/Distance/Time questions, 4 Sequences and just 1 Probability. Obvious conclusion: concentrate preparation on Geometry!

Because of this, I've prepared an extra worksheet involving finding difficult areas and lengths: Geometry Challenge Worksheet.

IMO Algebra Questions

3 files17/05/2016

Intermediate Maths Olympiad question compilation on the topic of algebra. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards, which I kept in a pack for use in lessons. 10/13 points were for Cayley questions (Year 9 Olympiad), 15/18 for Hamilton (Year 10), 20/23 for Maclaurin (Year 11).
IMO Geometry Questions

3 files17/05/2016

Intermediate Maths Olympiad question compilation on the topic of geometry. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards, which I kept in a pack for use in lessons. 10/13 points were for Cayley questions (Year 9 Olympiad), 15/18 for Hamilton (Year 10), 20/23 for Maclaurin (Year 11).
IMO Logic, Combinatorics & Spatial Reasoning Questions

3 files17/05/2016

Intermediate Maths Olympiad question compilation on the topic of logic, combinatorics and spatial reasoning. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards, which I kept in a pack for use in lessons. 10/13 points were for Cayley questions (Year 9 Olympiad), 15/18 for Hamilton (Year 10), 20/23 for Maclaurin (Year 11).
IMO Number Grid Questions

3 files17/05/2016

Intermediate Maths Olympiad question compilation on the topic of number grids. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards, which I kept in a pack for use in lessons. 10/13 points were for Cayley questions (Year 9 Olympiad), 15/18 for Hamilton (Year 10), 20/23 for Maclaurin (Year 11).
IMO Number Theory Questions

3 files17/05/2016

Intermediate Maths Olympiad question compilation on the topic of number theory. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards, which I kept in a pack for use in lessons. 10/13 points were for Cayley questions (Year 9 Olympiad), 15/18 for Hamilton (Year 10), 20/23 for Maclaurin (Year 11).
IMO Sequences Questions

3 files17/05/2016

Intermediate Maths Olympiad question compilation on the topic of sequences. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards, which I kept in a pack for use in lessons. 10/13 points were for Cayley questions (Year 9 Olympiad), 15/18 for Hamilton (Year 10), 20/23 for Maclaurin (Year 11).
IMO Speed, Distance, Time Questions

3 files17/05/2016

Intermediate Maths Olympiad question compilation on the topic of speed, distance and time. Numerical solutions included. Note that the 'Puzz Points' were for when these were printed as laminated cards, which I kept in a pack for use in lessons. 10/13 points were for Cayley questions (Year 9 Olympiad), 15/18 for Hamilton (Year 10), 20/23 for Maclaurin (Year 11).

Intermediate Mentoring sheets

You can find samples here: ukmt.org.uk/enrichment/mentoring-scheme. An index of these questions by topic can be found here.