STEP 2018

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

Pure16
Mechanics5
Statistics4

Chapter mix · 2018

Mechanics5
Probability & Statistics4
Integration3
Complex Numbers2
Coordinate Geometry & Conics2
Differential Equations2
Proof & Number Theory2
Algebra & Inequalities1
Differentiation1
Functions & Curve Sketching1
Sequences & Series1
Trigonometry1

Methods triggered this session

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

1
Halve the degree of a palindromic equation with $w = z \pm z^{- 1}$
Algebra & Inequalities
×1
2
On a circle centred at the origin, eliminate conjugates via $z^{*} = a^{2} / z$
Complex Numbers
×1
3
de Moivre expansion to turn a multiple-angle equation into a polynomial, then read roots by Vieta
Complex Numbers
×1
4
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
5
Affine ratios: write everything in position vectors to prove concurrency, collinearity and ratios
Coordinate Geometry & Conics
×1
6
Parametrise the conic, then run all tangent/normal/chord algebra in the parameter
Coordinate Geometry & Conics
×1
7
Express a squared geometric quantity as $A^{2} - B^{2}$ and factor (or expand) to reach a clean closed form
Coordinate Geometry & Conics
×1
8
Linearise a nonlinear first-order ODE by the right power/quotient substitution (Bernoulli and Riccati)
Differential Equations
×1
9
Read the qualitative solution straight from the gradient: stationary points, asymptotes and sketch without solving
Differential Equations
×1
10
Spot the left-hand side as a total derivative (or nested operator) and integrate the equation down
Differential Equations
×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