This is the first post presenting my teacher’s notes of past UKMT papers, starting with JMC 2015.
The objective of these teacher’s notes is not to provide solutions — UKMT already provides an excellent Pdf of solutions and further investigations, which you can download here — but to provide insights to teachers as to how UKMT questions can be used in the classroom.
In other words, these teacher’s notes are about making the best of the educational value of UKMT questions. Which, by the way, extends the scope of UKMT questions beyond their target age group. For example, some JMC questions, although intended for Year 78 students, can be used for educational purposes up to GCSE, sometimes even with A level students with the addition of relevant extensions and investigations.
In order to help teachers, I have indexed each UKMT question by Maths skills and problemsolving skills.
With the Maths skills index (which will ultimately be laid out in an Excel file when more of these teacher’s notes have been published), a teacher can access all questions related to a particular topic (fractions, for example, or simultaneous equations, etc.).
With the problemsolving skills index, it is possible to select questions according to which specific key drivers you want students to learn in order to solve problems more efficiently, such as:
 Complete the grid
 Deduction
 Easy way out
 Economy
 Elimination
 Alternative strategies
 Name / Label
 Systematic list
 Tree
 Bar modelling
(NB: these problemsolving skills will be fully explained in my next post: Introducing some problemsolving skills)
The JMC 2015 paper can be downloaded here. We all have favourite questions. For me, the prize for JMC 2015 is Question 24, a highly educational problem on palindromic numbers.
Here is a recap table of JMC 2015 questions indexed by Maths skills and problemsolving skills, please click here to download the full PDF UKMT JMC 2015 (teacher’s notes).
JMC 2015 Teacher’s notes – Recap table
Competition  Year  Question  Skills  Problemsolving 
JMC  2015  1  · Number / Adding and subtracting integers
· Number / Negative numbers 
· Elimination
· Deduction · Alternative strategies 
JMC  2015  2  · Measuring / Time units  
JMC  2015  3  · Number / Estimating
· Number / Properties of number 
· Elimination
· Alternative strategies 
JMC  2015  4  · Number / Adding and subtracting integers
· Algebra / Forming and solving linear equations 
· Deduction
· Economy 
JMC  2015  5  · Fractions / Adding and subtracting fractions
· Algebra / Forming and solving linear equations 
· Name / Label
· Bar modelling

JMC  2015  6  · Geometry / Angles in a triangle  · Deduction 
JMC  2015  7  · Numbers / Factors and multiples  · Economy
· Deduction · Alternative strategies 
JMC  2015  8  · Numbers / Factors and multiples  · Elimination
· Deduction · Alternative strategies · Easy way out 
JMC  2015  9  · Number / Estimating  · Bar modelling 
JMC  2015  10  · Number / 4 operations on integers  
JMC  2015  11  · Number / Properties of numbers  · Systematic list 
JMC  2015  12  · Fractions / Adding and subtracting fractions
· Algebra / Forming and solving linear equations 
· Name / Label
· Bar modelling 
JMC  2015  13  · Number / Adding and subtracting integers
· Number / Factors and multiples 
· Systematic list 
JMC  2015  14  · Number / Properties of numbers  · Elimination 
JMC  2015  15  · Number / Factors and multiples  · Elimination
· Alternative strategies 
Competition  Year  Question  Skills  Problemsolving 
JMC  2015  16  · Geometry / Polygons / Angles in a triangle
· Algebra / simultaneous equations · Algebra / Rearranging formulae 
· Name / Label
· Alternative strategies 
JMC  2015  17  · Binary logic  · Tree
· Economy 
JMC  2015  18  · Fractions / Equivalent fractions  · Easy way out 
JMC  2015  19  · Number / Properties of numbers  · Systematic list
· Elimination 
JMC  2015  20  · Measuring / Area and Volume
· Algebra / Sequences 

JMC  2015  21  · Geometry / 2D shapes
· Algebra / Forming and solving linear equations 
· Name / Label

JMC  2015  22  · Geometry / 2D shapes
· Geometry / Symmetry · Fractions / Introducing fractions 
· Complete the grid
· Economy

JMC  2015  23  · Measuring / Area  · Deduction

JMC  2015  24  · Number / Place value
· Number / Factors and multiples 
· Deduction

JMC  2015  25  · Geometry / Angles in a triangle
· Algebra / Forming equations · Algebra / Rearranging formulae 
· Deduction
