STEP 2009

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
Mechanics5
Statistics3

Chapter mix · 2009

Mechanics5
Integration3
Probability & Statistics3
Coordinate Geometry & Conics2
Differential Equations2
Functions & Curve Sketching2
Sequences & Series2
Complex Numbers1
Proof & Number Theory1
Trigonometry1
Vectors & Matrices1

Methods triggered this session

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

1
Differentiate to convert acceleration: use $v d v / d x$ for speed-versus-position, $d v / d t$ for speed-versus-time
Mechanics
×2
2
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
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
Two points on a curve: carry $s + t$ and $s t$ (sum and product of parameters) as the variables
Coordinate Geometry & Conics
×1
5
In "show that ... hence ...", the first part is the tool you must reuse
Proof & Number Theory
×1
6
Differentiate the defining relation repeatedly (Leibniz) to manufacture a recurrence in $y^{(n)}$ , then read off the Maclaurin series
Differential Equations
×1
7
Logarithmic derivative to handle products and quotients of many factors
Functions & Curve Sketching
×1
8
Prove a sign or inequality by anchoring at a point and reading the sign of the derivative
Functions & Curve Sketching
×1
9
Exploit a built-in symmetry of the function to pin turning points and fold the sketch
Functions & Curve Sketching
×1
10
Weierstrass and structured substitutions to rationalise trig/surd integrands
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