Work through long contextual Paper 2 questions part by part, use "hence" and given answers to keep going after a lost part, and interpret every result in its context.
Paper 2 is a set of compulsory extended-response questions. Each question follows one real-world context through many parts, and the parts build on one another: a value found early is used later, a model fitted in one part is tested or applied in the next, and the final parts ask what the results mean. Paper 1 covers the breadth of the course; Paper 2 assesses it in depth, with reasoning sustained across a long question.
The skills that matter most are therefore about the structure of a question as well as technique. They include reading a long stem that adds information as it goes, seeing how the parts connect, using "hence" and given answers, recovering when one part goes wrong, and writing interpretations that earn their reasoning marks. The GDC is available throughout, as on every paper of the course.
In the SL Paper 2s of 2021 and 2022, every paper had five questions worth between 13 and 20 marks each. HL Paper 2 has about seven questions of 12 to 21 marks, and its opening questions are often shared with SL. Each question has 5 to 10 parts, usually on one context, and mixes two to four subtopics. A single question on daylight hours, for example, moved from a scatter diagram to a criticism of a quadratic model, then to a sinusoidal model and its parameters, then to solving an equation with the model and finally to a percentage error.
Questions follow an incline of difficulty. The first parts are routine (write down a value from a graph, calculate a mean, find a regression line), the middle parts apply the course's techniques to the context, and the last parts need more thought: an optimisation, an interpretation, a criticism of the model, or a calculation that combines several earlier results. The last two or three parts of each question are where the highest grades are decided.
Stage of a question | Typical command terms | What the marks reward |
|---|---|---|
Opening parts | write down, calculate, find | Reading values correctly; a routine GDC calculation |
Middle parts | find, show that, hence, use … to | Applying a model; setting up equations, integrals or tests |
Final parts | hence, determine, justify, explain, comment, interpret | Combining results; reasoning; interpretation in context; criticism of the model |
The range of topics on Paper 2 can be narrower than on Paper 1, but individual questions can draw on more than one topic. Statistics, sequences and finance, functions and modelling, trigonometry and calculus all appear as main themes, and they are often combined: a probability question with an expected-profit calculation, or a trigonometry question that ends with a rate of change.
A Paper 2 stem is often several paragraphs long, and it does not give all its information at the start. New information appears between parts, introduced by sentences such as "The company decides to change its price" or "Further data are collected". That new information applies to the parts that follow it, not to the earlier ones. Many lost marks come from using a value from the wrong stage of the question or from missing a condition stated halfway through.
Reading the stem actively prevents most of these errors. Underline each quantity with its units, write the variable names the question uses, and note any domain or condition ("for ", "until the tank is empty", "the first year of the model"). When a diagram is given, add values to it as they are found. When new information arrives mid-question, draw a line across the page so that the change is visible.
Before answering, it helps to spend 30 seconds seeing which parts depend on which. A quick map such as "(c) uses (b); (e) uses the model from (d); (f) is separate" shows where an early error would spread and where a given answer allows a fresh start. It also shows which later parts can be answered even if an earlier one fails. Parts that open with "hence" or "use your answer to" depend on an earlier result; parts that introduce new information often stand alone.
A long question is designed as a path. Each part usually gives exactly what the next one needs, and an approach that ignores the path is almost always longer and riskier. Questions signal the path in several ways.
"Hence" means the previous result must be used. An answer reached by a different method may earn nothing.
"Hence or otherwise" suggests the previous result, but any correct method is credited.
"Use your answer to part (b) to …" is a direct instruction, marked like "hence".
A value given in the question ("it can be shown that ", or the answer to a "show that") is to be used in the parts that follow, even if your own value was different.
The structure also tells you when a result should be simple. If part (a) asks for the value of a parameter and part (b) uses it, a surprising value in (a) is a warning sign. Checking the size of an answer against the context (a price of $7.50 for renting a bicycle is plausible; $750 is not) catches errors before they travel through the rest of the question.
Being stuck on one part of a 16-mark question does not mean losing the rest. Paper 2 is written so that a candidate who cannot do one part can usually still do the next, and the marking supports this in two ways: given answers and follow-through.
When a part says "show that the angle is 44.0°, correct to three significant figures", the answer is printed in the question so that everyone can use it later. If the "show that" cannot be done, skip it and use the given value in the following parts. Those later parts are marked as normal, so a candidate who scores nothing on the "show that" can still earn every later mark.
Two points about "show that" parts are easy to miss. First, the given answer must be reached by working forwards from the information in the question; substituting into the cosine rule and checking that the sides come out right earns nothing. Second, when the given value is rounded, a more accurate value (here 44.0486…) must appear before the rounded one, to show the result was calculated and not copied.
The second safety net is follow-through. If part (c) is wrong, part (d) is marked using the candidate's own answer to (c), and correct working from that wrong value earns the marks in (d).
Follow-through only works when the examiner can see what was used. A wrong regression equation followed by a prediction with no working gives the examiner no way to check that the prediction came from that equation, so the follow-through mark cannot be given. Markschemes often add limits, such as "do not FT if working is not shown" or no follow-through when the earlier error makes the later part much simpler or leads to an impossible value (a probability above 1, a negative length).
The last parts of a Paper 2 question often ask what a result means. The command terms are interpret, comment, explain and justify, and the marks are usually a reasoning mark (R1) for a valid reason and an answer mark (A1) for the conclusion. A conclusion with no valid reason earns nothing, because markschemes routinely say "do not award R0A1".
An interpretation in context names the real quantities, gives units and refers to the situation. "The gradient is 13.3" only states a value, and "as the temperature increases, the rentals increase" describes only the sign. A full interpretation of the gradient of is: each additional degree Celsius of maximum temperature is associated with about 13 more bicycle rentals per day.
Weak answer | Why it fails | Stronger answer |
|---|---|---|
"The model is not good." | No reason | "The model predicts a negative number of rentals when , which is impossible." |
"The sample is too small." | Vague; not linked to the question | "Only 8 days were recorded, all between 12 °C and 31 °C, so a prediction at 38 °C is outside the data." |
"There is strong correlation." | Strength without direction or context | " shows a strong positive linear correlation between temperature and daily rentals." |
"The y-intercept is 54.6." | States, does not interpret | "At 0 °C the model predicts about 55 rentals, but 0 °C is outside the data, so this has little meaning." |
Criticising a model is part of interpretation. Good criticisms point to a specific feature: a prediction that becomes impossible (negative, larger than the population, beyond 100%), a pattern that does not continue (daylight hours repeat each year, a quadratic does not), extrapolation outside the data, or an assumption that the context breaks. Vague comments such as "real life is more complicated" are not accepted.
The question that follows is written in the style of SL Paper 2. It moves from statistics to a model of revenue, with a "show that" in the middle to allow re-entry and a "hence" that sets the method. The data are hypothetical.
Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
Maximum temperature (°C) | 12 | 15 | 17 | 20 | 23 | 25 | 28 | 31 |
Bicycles rented | 210 | 260 | 275 | 330 | 365 | 390 | 420 | 470 |
Several features of the markscheme are typical. In part (c) each coefficient earns its own mark, and an answer written with and loses one. Part (d) is marked A1FT, so a candidate with a wrong line in (c) can still earn both marks in (d) by substituting into it. Part (f) is a one-mark "show that" whose main purpose is to give everyone the revenue function for (g) to (i). In part (h) "hence" fixes the method: the mark is for setting the derivative from (g) equal to zero, not for reading the maximum off a graph.
Premature rounding is one of the most frequently reported causes of lost marks on Paper 2, because values travel through so many parts. A value from part (b), rounded to 3 significant figures and then used in parts (d), (f) and (h), can drift far enough to cost the final accuracy marks. Store each value in the GDC at full accuracy and recall it when needed; write the 3 s.f. value on the page, but calculate with the stored one.
The final common loss is leaving later parts blank after an earlier failure. A part that uses a given answer, a "show that" result or a new piece of information in the stem can usually be done even when everything before it went wrong.
Write each part's answer clearly, with its label, and keep the working for one part together. When an answer from an earlier part is reused, quote it with its label, as in "using from (a)". This makes follow-through easy to award and shows the examiner exactly where each value came from.
Paper 2 has long contextual questions (five of 13–20 marks at SL; about seven of 12–21 marks at HL), each rising from routine opening parts to demanding final parts.
Read the stem actively: underline quantities and units, use the question's variables, and note new information when it appears between parts.
"Hence" requires the previous result; "hence or otherwise" allows any method; given values must be used in later parts.
A "show that" part gives the answer so you can continue; skip it if necessary and use the given value.
Follow-through lets correct work from a wrong earlier answer earn marks, but only when the working is shown.
Interpretations need a reason and a conclusion in the words of the context; a conclusion with no reason scores nothing.
Criticise a model with a specific reason: an impossible value, extrapolation, a pattern that will not continue.
Keep full accuracy in the GDC across parts; round only the answers you write down.
I can map how the parts of a long question depend on one another.
I can spot new information in a stem and apply it only to the parts that follow it.
I can use a given "show that" result to continue after a part I could not do.
I can explain what follow-through is and why it needs working to be shown.
I can tell the difference between "hence" and "hence or otherwise" and answer each correctly.
I can interpret a gradient, an intercept and a correlation coefficient in context, with units.
I can give a specific criticism of a model, such as extrapolation or an impossible prediction.
I can budget about 1.1 minutes per mark and move on from a question that overruns.
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