STEP 2021

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

Pure10
Mechanics4
Statistics4

Chapter mix · 2021

Mechanics4
Probability & Statistics4
Vectors & Matrices3
Complex Numbers2
Coordinate Geometry & Conics1
Differential Equations1
Functions & Curve Sketching1
Integration1
Trigonometry1

Methods triggered this session

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

1
Energy first for $v^{2}$ at a position, Newton along the normal for the reaction
Mechanics
×2
2
Condition on the first step to get a self-referential equation
Probability & Statistics
×2
3
Pin down a complex root through its symmetric functions and the conjugate-root reflex
Complex Numbers
×1
4
On a circle centred at the origin, eliminate conjugates via $z^{*} = a^{2} / z$
Complex Numbers
×1
5
Half-angle factorisation: split $e^{i β} - e^{i α}$ into modulus $2 sin \frac{β - α}{2}$ and argument $\frac{α + β}{2} + \frac{π}{2}$
Complex Numbers
×1
6
In polar coordinates, build gradient and cutting-angle from $\frac{d r}{d θ}$
Coordinate Geometry & Conics
×1
7
Read the qualitative solution straight from the gradient: stationary points, asymptotes and sketch without solving
Differential Equations
×1
8
Count roots by sketching one side and sweeping a horizontal or moving line across it
Functions & Curve Sketching
×1
9
Recognise the integrand as an exact derivative and reverse-engineer by differentiating a template
Integration
×1
10
Resolve at the junction: write the unit vector along each string, multiply by tension, add weight, set to zero
Mechanics
×1

Try a method on a real paper

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

Open STEP methods