TMUA 2022

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
Reasoning7

Chapter mix · 2022

Logic & Proof7
Functions & Graphs6
Trigonometry5
Differentiation3
Integration3
Proof & Number Theory3
Algebra & Inequalities2
Coordinate Geometry & Circles2
Combinatorics & Binomial1
Exponentials & Logarithms1
Sequences & Series1

Methods triggered this session

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

1
Quantifier order and scope: 'for all $x$ there exists $y$ ' is weaker than 'there exists $y$ for all $x$ ', so reduce to a function and push the variable to extremes
Logic & Proof
×3
2
Complete the square to read a circle's centre and radius (or a parabola's vertex)
Coordinate Geometry & Circles
×2
3
Test special, extreme and boundary values to settle possible / impossible / complete-list questions
Functions & Graphs
×2
4
Mind the direction of an implication: the contrapositive keeps the truth value, the converse and inverse do not
Logic & Proof
×2
5
Reduce a mixed $sin$ / $cos$ equation to a polynomial in one ratio via $sin^{2} + cos^{2} = 1$
Trigonometry
×2
6
Turn triangle and sector data into the standard formulae, then solve the resulting algebra
Trigonometry
×2
7
Spot the hidden quadratic and substitute to expose it
Algebra & Inequalities
×1
8
Read an absolute value as a distance, then bound or use the midpoint
Algebra & Inequalities
×1
9
The coefficient in a product or a sum of expansions is the sum of every contributing piece
Combinatorics & Binomial
×1
10
Turn a tangency, a single-intersection, or an existence statement into a discriminant or a distance-equals-radius condition
Coordinate Geometry & Circles
×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