TMUA 2023

Glossary

Curated question: — Past-paper question with a worked solution and a tagged method.
Method: — Portable technique that pops up across years.
Worked solution: — Step-by-step solution written by us in our voice.
Past paper: — Official exam session published by the board.

These pages only count the curated set: questions with both a worked solution and at least one tagged method. Bulk past papers without that treatment are hidden.

Session overview

Questions

Worked

100%

Methods triggered

Papers

Theme mix

Pure27
Reasoning4

Chapter mix · 2023

Integration6
Logic & Proof4
Sequences & Series4
Algebra & Inequalities3
Coordinate Geometry & Circles3
Differentiation3
Functions & Graphs2
Proof & Number Theory2
Trigonometry2
Combinatorics & Binomial1
Exponentials & Logarithms1

Methods triggered this session

Each method that at least one question in this session hits.

1
Recognise a disguised geometric series, extract its first term and ratio, then apply $\frac{a}{1 - r}$
Sequences & Series
×3
2
Turn a question about the nature or count of roots into a discriminant condition
Algebra & Inequalities
×2
3
When asked for 'all possible', the sum/difference, 'two values', or the largest, enumerate every configuration first
Coordinate Geometry & Circles
×2
4
Connect roots to stationary points structurally: stationary values straddle the axis, discriminant counts, Rolle bridges $f$ and $f^{'}$
Differentiation
×2
5
Complete the square to read off the vertex, the axis of symmetry, the optimum and tangency in one move
Functions & Graphs
×2
6
Integral-defined sequences and sums: find the inner integral in closed form, then collapse the sum
Integration
×2
7
Mind the direction of an implication: the contrapositive keeps the truth value, the converse and inverse do not
Logic & Proof
×2
8
For a linear-quadratic system, substitute the linear equation into the quadratic at once
Algebra & Inequalities
×1
9
Tame surds by clearing fractions or recognising a perfect-square radicand, then check validity
Algebra & Inequalities
×1
10
Spot the hidden quadratic and substitute to expose it
Algebra & Inequalities
×1

Try a method on a real paper

Open the TMUA methods app to see worked examples, linked questions and the 3-panel revision view.

Open TMUA methods