Co-ordinate geometry methods (internal)
Internal 2 credits Distance Midpoint Gradient Line equations Perpendicular CirclesAS 91256, 2 credits — the smallest maths internal. Distance, midpoint, gradient and the equation of a line, applied to a problem set in a real context. Small standard, so the context sentence matters proportionally more.
1 Reading the notation
A closed list of five method areas — know which of them your task draws on.📖 Terms the schedule grades you on
3 terms- Apply methods (Achieved)
- Select and use methods; demonstrate knowledge of geometric concepts and terms; communicate using appropriate representations.
- Named methods (note 4)
- Distance between points, midpoints, gradient, equation of a line, parallel/perpendicular/intersecting lines.
- Problem
- A situation, real-life or mathematical, giving an opportunity to apply the knowledge — the standard's own definition.
2 What the grades require
The same ladder every L2 maths internal uses.| Grade | What it takes | The half people drop |
|---|---|---|
| Achieved | Select and use methods; know the concepts and terms; communicate with appropriate representations | Showing no working — the method IS the evidence |
| Merit | A logical sequence of steps, connecting concepts, or forming and using a model | The "and also": relate findings back to the context |
| Excellence | Devise a strategy, build a chain of reasoning or a proof, or form a generalisation | The "and also": correct mathematical statements, or a stated insight |
Both Merit and Excellence are "one or more of … AND ALSO …". A perfect answer that never interprets its result in context cannot pass the Achieved ceiling.
3 The core formulas
Distance, midpoint, gradient, line — and the parallel/perpendicular test.The five to know cold
Distance d = √((x₂−x₁)² + (y₂−y₁)²) Order does not matter — it is squared Midpoint ((x₁+x₂)/2, (y₁+y₂)/2) The average of each coordinate Gradient m = (y₂−y₁)/(x₂−x₁) Rise over run; undefined for a vertical line Line (point-gradient) y − y₁ = m(x − x₁) The most useful form Circle (x−a)² + (y−b)² = r² Centre (a, b) — flip the signs when reading4 Circles, collinearity, and proving a shape
Gradient and distance are the two tools every proof here is built from. ✕Proving a shape with only ONE property
Showing one pair of sides is parallel does not prove a parallelogram — it could be a trapezium. State the FULL set of properties that specifically define the shape you are claiming (both pairs parallel, or equal diagonals, etc.), and show each one.Practice
Recall it first, then use it — testing yourself builds the memory, where rereading the notes above only feels easier.
Recall and application shuffled together — you have to work out what each item wants before you can answer it, which is the part the exam actually tests. Both kinds feed the same spacing schedule, so anything you miss comes back sooner.
Say the answer out loud before flipping — that attempt is where the learning happens, even when you get it wrong.
Exam-style only. Instant feedback, shuffled each attempt, best score saved on this device.