STEP 2013

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
Mechanics6
Statistics3

Chapter mix · 2013

Mechanics6
Functions & Curve Sketching4
Probability & Statistics3
Complex Numbers2
Differential Equations2
Integration2
Proof & Number Theory2
Coordinate Geometry & Conics1
Sequences & Series1
Vectors & Matrices1

Methods triggered this session

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

1
Count roots by sketching one side and sweeping a horizontal or moving line across it
Functions & Curve Sketching
×2
2
Roots of unity: factor $z^{n} - 1 = \prod (z - ω^{k})$ and feed in a clever value of $z$
Complex Numbers
×1
3
Modulus inequalities: bound a sum below or above to force existence or impossibility
Complex Numbers
×1
4
Use the focus-directrix polar form $\frac{ℓ}{r} = 1 + e cos θ$ as the master conic equation
Coordinate Geometry & Conics
×1
5
Differentiate the defining relation repeatedly (Leibniz) to manufacture a recurrence in $y^{(n)}$ , then read off the Maclaurin series
Differential Equations
×1
6
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
7
Exploit a built-in symmetry of the function to pin turning points and fold the sketch
Functions & Curve Sketching
×1
8
Use a sketch as the actual proof of an inequality
Functions & Curve Sketching
×1
9
Generate a reduction relation, then telescope or solve the recurrence
Integration
×1
10
Turn the integral into algebra: introduce an auxiliary unknown integral and solve a linear system
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