STEP 2012

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

Pure13
Mechanics6
Statistics3

Chapter mix · 2012

Mechanics6
Sequences & Series5
Probability & Statistics3
Differential Equations2
Functions & Curve Sketching2
Combinatorics & Binomial1
Coordinate Geometry & Conics1
Integration1
Vectors & Matrices1

Methods triggered this session

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

1
Telescope: write the general term as a difference $g (r) - g (r + 1)$ so the sum collapses
Sequences & Series
×2
2
Recognise a polynomial or rational expression as a known binomial or geometric series, then read off a coefficient
Combinatorics & Binomial
×1
3
Express a squared geometric quantity as $A^{2} - B^{2}$ and factor (or expand) to reach a clean closed form
Coordinate Geometry & Conics
×1
4
Build a first integral (energy): multiply by $y^{'}$ or use a given $E (x)$ to drop the order or bound the solution
Differential Equations
×1
5
Eliminate one unknown from simultaneous ODEs to get a single higher-order equation
Differential Equations
×1
6
Stitch a solution across intervals by matching value and gradient (piecewise / continuity conditions)
Differential Equations
×1
7
Exploit a built-in symmetry of the function to pin turning points and fold the sketch
Functions & Curve Sketching
×1
8
Tangency means a repeated root: convert touching, double zeros or tangent asymptotes into a discriminant or factor condition
Functions & Curve Sketching
×1
9
Fold a tail onto a finite piece with $x \mapsto k / x$ (and exploit interval-preserving maps)
Integration
×1
10
Treat the two horizontal coordinates of projectile motion separately, then eliminate the time
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