STEP 2015

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
Mechanics3
Statistics3

Chapter mix · 2015

Integration3
Mechanics3
Probability & Statistics3
Proof & Number Theory3
Sequences & Series3
Complex Numbers1
Coordinate Geometry & Conics1
Differential Equations1
Functions & Curve Sketching1
Trigonometry1
Vectors & Matrices1

Methods triggered this session

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

1
Guess the closed form, prove it by induction, and carry an invariant through the step
Proof & Number Theory
×3
2
Pin down a complex root through its symmetric functions and the conjugate-root reflex
Complex Numbers
×1
3
Read centre and radius off a second-degree equation by completing the square
Coordinate Geometry & Conics
×1
4
Reduce a chord/tangent/intersection condition to a quadratic and steer its discriminant
Coordinate Geometry & Conics
×1
5
Express a squared geometric quantity as $A^{2} - B^{2}$ and factor (or expand) to reach a clean closed form
Coordinate Geometry & Conics
×1
6
Change variable to convert a variable-coefficient ODE into a constant-coefficient one
Differential Equations
×1
7
Degree-zero homogeneous ODE: substitute $y = xu$ to separate variables
Differential Equations
×1
8
Exploit a built-in symmetry of the function to pin turning points and fold the sketch
Functions & Curve Sketching
×1
9
Reflect the interval onto itself: $x \mapsto a + b - x$ , then add the two copies
Integration
×1
10
Fold a tail onto a finite piece with $x \mapsto k / x$ (and exploit interval-preserving maps)
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