Graphical methods (internal)
Internal 4 credits Graph families Transformations Features Modelling Domain & rangeAS 91257, 4 credits — the largest Level 2 maths internal. Recognise, sketch and transform the graph families, identify their features, and fit a graph to a real situation. The modelling half is where relational and extended abstract thinking are easiest to earn.
1 Reading the notation
Four named method areas — the last one, connecting representations, is easy to forget to state explicitly.📖 Terms the schedule grades you on
2 terms- Apply methods (Achieved)
- Select and use methods; demonstrate knowledge of properties of functions and graphs; communicate using appropriate representations.
- Named methods (note 4)
- Graphs and their equations; transformations; connecting different representations; properties of functions (domain/range).
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 Graph families and their features
Recognising the family from the equation is the first decision every question turns on.What every sketch needs
- x- and y-intercepts.
- Vertex or turning points, where relevant.
- Asymptotes, named and drawn as dashed lines.
- Axes labelled and sensibly scaled.
4 Transformations
Four transformations, applied in order.| Form | Effect | Watch for |
|---|---|---|
| f(x) + d | Shifts up d (down if negative) | Moves the horizontal asymptote too |
| f(x − c) | Shifts RIGHT c | Counter-intuitive sign — minus means right |
| a·f(x) | Vertical stretch by a | a < 0 also reflects in the x-axis |
| f(−x) | Reflects in the y-axis | Distinct from −f(x) |
Identify the family first, then apply transformations in order. Doing them in the wrong order on a combined transformation gives a different graph.
5 Fitting a model to real data
The modelling half is where relational and extended abstract thinking are easiest to earn. Internal-style A population is 120, then 180, then 270 in successive years Which family, and what is the model? Differences: +60, +90 — not constant, so not linear. Ratios: 180/120 = 1.5, 270/180 = 1.5 — constant, so EXPONENTIAL. Model: P = 120 × 1.5ᵗ with t in years from the first count. CONTEXT: the population is growing 50% a year — but say the domain over which that is credible, because unbounded exponential growth is not physically possible. ✓ Constant ratio → exponential. The final sentence is the "and also relating findings to a context" clause both Merit and Excellence require.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.