STEP 2020

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

Pure15
Mechanics4
Statistics4

Chapter mix · 2020

Integration4
Mechanics4
Probability & Statistics4
Complex Numbers2
Differential Equations2
Functions & Curve Sketching2
Proof & Number Theory2
Vectors & Matrices2
Sequences & Series1

Methods triggered this session

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

1
Find a locus of $w = f (z)$ by substituting $z = x + i y$ or by tracking modulus and argument
Complex Numbers
×1
2
Rotation as multiplication: encode equilateral triangles and right angles by a fixed unimodular factor
Complex Numbers
×1
3
Degree-zero homogeneous ODE: substitute $y = xu$ to separate variables
Differential Equations
×1
4
Eliminate one unknown from simultaneous ODEs to get a single higher-order equation
Differential Equations
×1
5
Range of a rational or quadratic-in-disguise function via the discriminant of an auxiliary quadratic
Functions & Curve Sketching
×1
6
Build a new sketch from a known one by acting on $x$ or $y$ (squaring, modulus, replacing $x$ by $x^{2}$ )
Functions & Curve Sketching
×1
7
Weierstrass and structured substitutions to rationalise trig/surd integrands
Integration
×1
8
Reflect the interval onto itself: $x \mapsto a + b - x$ , then add the two copies
Integration
×1
9
Generate a reduction relation, then telescope or solve the recurrence
Integration
×1
10
Recognise the integrand as an exact derivative and reverse-engineer by differentiating a template
Integration
×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