Study guide · Calibration
How the difficulty and complexity measures are calculated
Every paper page in the library reports five mark-weighted measures. This page gives the rubric behind each band, the formula for each measure, and a complete recomputation of one real paper so the numbers can be checked line by line.
Core finding
Every paper page in the library reports five mark-weighted measures built from part-level tags. Difficulty uses Easy 0.20, Medium 0.45 and Hard 0.75; algebraic complexity and text density and modelling each use Low 0.20, Medium 0.45 and High 0.75. A Hard part worth four or more marks is down-weighted to marks0.75, so accessible opening steps cannot inflate the result. WPH11/01 October 2019 is recomputed below from 32 parts worth 80 marks, giving a Difficulty Measure of 0.41 and a Deviation of 0.15.
What each measure means
These five values appear on every Edexcel IAL Physics paper page. A paper page repeats the formulas next to its own numbers; the definitions and band rubrics live here.
| Measure | Scale | What it means | Formula |
|---|---|---|---|
| Difficulty Measure | 0.20–0.75 | Mark-weighted average difficulty of the parts. Higher values mean the paper carries more of its marks in demanding parts. | Σ(di × wi) / Σwi, where d is Easy 0.20, Medium 0.45 or Hard 0.75, and w is the part marks — or marks0.75 for a Hard part worth 4 or more marks. |
| Difficulty Deviation | 0 or more | Mark-weighted spread of part difficulty around the paper mean. 0 means every part has the same tag; larger values mean a more mixed paper. | √(Σwi(di − μ)2 / Σwi), using the same weights w as the Difficulty Measure and its mean μ. |
| Difficulty Ratio | three shares, 100% | Share of the paper’s marks attached to Easy, Medium and Hard parts, in that order. The three printed shares sum to 100.0%. | marks tagged to a band / all marks carrying a difficulty tag. Each part is counted once; no mark falls in two bands. |
| Algebraic Complexity Measure | 0.20–0.75 | Mark-weighted algebraic demand. Higher values mean more symbolic manipulation, multi-step rearrangement or algebra-heavy working. | Σ(ci × marksi) / Σmarksi, where c is Low 0.20, Medium 0.45 or High 0.75. Raw part marks are used as weights. |
| Text Density and Modelling Measure | 0.20–0.75 | Mark-weighted reading and modelling demand. Higher values mean longer prose, more context to extract or more model construction. | Σ(ti × marksi) / Σmarksi, where t is Low 0.20, Medium 0.45 or High 0.75. Raw part marks are used as weights. |
Difficulty bands
Each part is tagged Easy, Medium or Hard. The band contributes an anchor value of 0.20, 0.45 or 0.75 to the Difficulty Measure; the definition below is the rubric the tags follow.
| Band | Anchor value | Definition | Mathematics example | Physics example |
|---|---|---|---|---|
| Easy | 0.20 | Direct application of a formula or definition. One or two routine steps, with no chaining of ideas. | Solve . | Substitute into to find after 3 s when and . |
| Medium | 0.45 | Requires understanding of the concept and a multi-step calculation, linking two or more ideas with standard methods. | Find the first three terms of . | Use conservation of momentum and then energy to find the speed of a joined trolley. |
| Hard | 0.75 | Comprehensive application across several knowledge points. Non-routine reasoning, proof, or a model that has to be built before any calculation. | Prove . | Derive the minimum coefficient of friction for a rod resting on rough ground against a smooth wall. |
Algebraic complexity bands
Algebraic complexity measures the manipulation workload on its own, independent of how hard the idea is. It contributes 0.20, 0.45 or 0.75 to the Algebraic Complexity Measure.
| Band | Anchor value | Definition | Mathematics example | Physics example |
|---|---|---|---|---|
| Low | 0.20 | One or two standard manipulation steps. No nested operations and no simultaneous equations. | Differentiate . | Rearrange to make the subject. |
| Medium | 0.45 | Multi-step manipulation, negative or fractional indices, or a standard pair of simultaneous equations. | Solve and simultaneously. | Eliminate between two equations of motion to obtain an expression for . |
| High | 0.75 | Heavy algebraic-fraction manipulation, trigonometric identity proofs, or non-linear systems that need boundary or extraneous-root checks. | Express in partial fractions. | Solve the non-linear system from energy and momentum conservation, then reject the root that has no physical meaning. |
Text density and modelling bands
This measures the reading and modelling load: how much prose has to be decoded before any mathematics can start. It contributes 0.20, 0.45 or 0.75 to the Text Density and Modelling Measure.
| Band | Anchor value | Definition | Mathematics example | Physics example |
|---|---|---|---|---|
| Low | 0.20 | A bare equation or a standard command. No context to decode. | Evaluate . | Differentiate with respect to . |
| Medium | 0.45 | A short word problem that translates into one standard model, with the variables easy to identify. | The second term of a geometric progression is 24 and the fifth term is 3. Find the sum to infinity. | A particle has displacement . Find the time at which it is at rest. |
| High | 0.75 | A long context paragraph that requires a model to be built, assumptions identified and variables defined before any calculation. | A uniform rod rests with one end on rough ground and the other against a smooth wall, with a particle attached partway along. Find the minimum coefficient of friction for equilibrium. | A block is released from rest on a rough incline and later hits a spring. Derive the maximum compression, stating what is neglected. |
Worked example: recompute a whole paper
WPH11/01 October 2019 has 32 parts worth 80 marks, all tagged. 2 of them are Hard parts worth 4 or more marks, so their weight drops below the raw mark value (5 marks: 3.34 instead of 5; 4 marks: 2.83 instead of 4). Every other row uses its marks as the weight.
| Part | Marks | Difficulty tag | d | Weight w | d × w |
|---|---|---|---|---|---|
| Q1 | 1 | Easy | 0.20 | 1.00 | 0.20 |
| Q2 | 1 | Easy | 0.20 | 1.00 | 0.20 |
| Q3 | 1 | Medium | 0.45 | 1.00 | 0.45 |
| Q4 | 1 | Easy | 0.20 | 1.00 | 0.20 |
| Q5 | 1 | Easy | 0.20 | 1.00 | 0.20 |
| Q6 | 1 | Medium | 0.45 | 1.00 | 0.45 |
| Q7 | 1 | Medium | 0.45 | 1.00 | 0.45 |
| Q8 | 1 | Medium | 0.45 | 1.00 | 0.45 |
| Q9 | 1 | Medium | 0.45 | 1.00 | 0.45 |
| Q10 | 1 | Easy | 0.20 | 1.00 | 0.20 |
| Q11 | 3 | Medium | 0.45 | 3.00 | 1.35 |
| Q12(a) | 2 | Medium | 0.45 | 2.00 | 0.90 |
| Q12(b) | 4 | Medium | 0.45 | 4.00 | 1.80 |
| Q13(a) | 5 | Hard | 0.75 | 3.34 | 2.51 |
| Q13(b) | 6 | Medium | 0.45 | 6.00 | 2.70 |
| Q14(a)(i) | 2 | Easy | 0.20 | 2.00 | 0.40 |
| Q14(a)(ii) | 3 | Medium | 0.45 | 3.00 | 1.35 |
| Q14(b)(i) | 4 | Medium | 0.45 | 4.00 | 1.80 |
| Q14(b)(ii) | 2 | Easy | 0.20 | 2.00 | 0.40 |
| Q15(a)(i) | 5 | Medium | 0.45 | 5.00 | 2.25 |
| Q15(a)(ii) | 4 | Medium | 0.45 | 4.00 | 1.80 |
| Q15(b)(i) | 3 | Easy | 0.20 | 3.00 | 0.60 |
| Q15(b)(ii) | 4 | Medium | 0.45 | 4.00 | 1.80 |
| Q16(a) | 2 | Easy | 0.20 | 2.00 | 0.40 |
| Q16(b) | 3 | Medium | 0.45 | 3.00 | 1.35 |
| Q16(c)(i) | 4 | Medium | 0.45 | 4.00 | 1.80 |
| Q16(c)(ii) | 2 | Medium | 0.45 | 2.00 | 0.90 |
| Q17(a)(i) | 1 | Easy | 0.20 | 1.00 | 0.20 |
| Q17(a)(ii) | 2 | Easy | 0.20 | 2.00 | 0.40 |
| Q17(a)(iii) | 2 | Easy | 0.20 | 2.00 | 0.40 |
| Q17(b)(i) | 4 | Hard | 0.75 | 2.83 | 2.12 |
| Q17(b)(ii) | 3 | Medium | 0.45 | 3.00 | 1.35 |
| Σ over 32 parts | 80 | 77.17 | 31.83 | ||
| Difficulty Measure = Σ(d × w) / Σw | 0.41 | ||||
Difficulty Measure = 31.8291 / 77.1721 = 0.41 on the 0.20–0.75 scale.
Difficulty Deviation = √(Σw(d − μ)2 / Σw) = 0.15, using the mean μ above and the same weights.
Algebraic Complexity Measure = 0.26 and Text Density and Modelling Measure = 0.37, both mark-weighted with the raw part marks and no decay.
How the Difficulty Ratio is built
| Band | Marks in that band | Share of tagged marks |
|---|---|---|
| Easy | 19 | 23.8% |
| Medium | 52 | 65.0% |
| Hard | 9 | 11.2% |
| Total tagged marks | 80 | 100.0% |
Ratio = Easy 23.8% / Medium 65.0% / Hard 11.2%, which is the value printed on the WPH11/01 October 2019 paper page.
Questions about the measures
- Are Easy, Medium and Hard official exam-board difficulty ratings?
- No. They are internal editorial tags applied part by part, using the rubric above. They are not published by Pearson or Cambridge, and no candidate results, grade boundaries or examiner statistics go into the calculation. Treat the measures as a description of question design, not as a prediction of how students will score.
- Why is a Hard part worth 4 or more marks given a smaller weight?
- A long structured question usually opens with accessible steps before the demanding part, so its full mark value overstates how hard the part is. The rule reduces the weight to marks0.75 only when both conditions hold: the tag is Hard and the part is worth at least 4 marks. On WPH11/01 October 2019 this affects 2 parts (5 marks: 3.34 instead of 5; 4 marks: 2.83 instead of 4); a Hard part worth 3 marks keeps its raw weight.
- Why does the Difficulty Ratio use marks instead of question counts?
- Because a paper is marked out of its total marks, so marks are the only unit that matches how the paper is scored. Counting questions would give a 10-mark Hard question the same weight as a 1-mark Easy multiple-choice item. The ratio is a share of tagged marks, the three shares sum to 100% before rounding, and no mark is counted in two bands.
- Why are the anchors 0.20, 0.45 and 0.75 not evenly spaced?
- The anchors are an ordinal scale, not a linear measurement. 0.45 marks the middle band and sits slightly below the midpoint of 0.20 and 0.75, because the middle band covers the largest share of parts. Use the values to compare papers and to track change over time; do not read a difference of 0.05 as a fixed percentage change in difficulty.
- What counts as one part?
- A part is the smallest unit that carries its own marks: a labelled sub-question such as (a), (b)(ii), or a single multiple-choice item. All three per-question measures on a paper page aggregate that question’s parts with the same weights as the paper profile, so a question value and the paper value are always computed the same way.
- How can I recompute a paper myself?
- Use the five columns on the paper page, or the worked table above. Multiply each part’s anchor d by its weight w, add the products, and divide by the sum of the weights. For WPH11/01 October 2019 that is 31.8291 / 77.1721 = 0.41.
See the measures on a paper
Every paper page in the library reports all five values and repeats the three per-question measures row by row.
Open WPH11/01 October 2019