Mark like an examiner.

The most likely paper

Section A frequencies, Section B templates

Every past Paper 2, ranked

Scored on four factors — topic-mix match to the forecast, coverage of the high-value genres, recency, and a small TZ2 nudge. The top 3 are your priority; the balanced five (top 3 plus May 2025 TZ3 and Nov 2025 TZ1) cover both ways Q9 could go.

We tested whether your Paper 1 predicts Paper 2

What Paper 2 actually is

Format

90 minutes, 80 marks, GDC required. Formula booklet provided. Same two-section shape as P1: Section A ~six short questions, Section B three extended questions (Q7–Q9).

What changes

The numbers go deliberately ugly — the calculator is meant to absorb them. The work moves to the two ends: setting up and interpreting. The calculator owns the middle.

Topic emphasis (avg of 15 sittings)

The hierarchy inverts vs Paper 1 — Statistics dominates, Functions is marginal:

NA · 10m F · 8m GT · 17m SP · 24m C · 20m

Exact form

Mostly stops being the demand. Default is a 3 s.f. decimal unless a question explicitly says "exact". Precision is still carried — but inside calculator memory, not as surds on the page.

Weighting

Paper 2 is 40% of your SL maths grade — the same as Paper 1.

Three real shifts: questions lean into computation, modelling, and "set up then interpret"; the topic emphasis tilts hard toward stats, normal/binomial, regression and finance (the topics that need a machine); and the failure modes change — mode errors, premature rounding, and bare answers replace algebra slips.

The operations you must be fluent in

You do not have time to work out how to make the calculator do something — the sequences must be reflexes. Keystrokes differ between a Casio fx-CG50 and a TI-84/Nspire; the operation is identical, so learn the operation and know where it lives on your machine.

Solving & graphing

• Solve a single equation — any equation in one unknown. Type the whole thing including = 0; restrict the domain to filter unwanted roots.
• Solve simultaneous equations — the Equation menu; choose the number of unknowns, type the coefficients.
• Roots of a polynomial — Polynomial mode returns every root at once.
• Intersection of two graphs — plot both, or plot the difference y = f(x) − g(x) and find its roots.
• Read a function value / solve f(x) = k graphically — the y-calc / x-calc tools; also how you read an inverse value off a graph.

Calculus

• Numeric derivative at a point — f′(a) as a number. For "gradient at x = …" and "rate of change when …".
• Definite integral — the ∫dx template, between two limits. Area, displacement from velocity, total change from a rate.
• Area between curves — integrate the absolute value, or split at the roots; a plain integral and the area differ where the curve dips below the axis.
• Max / min from a graph — the technology route to optimisation, without differentiating by hand.

Statistics & probability

• One-variable statistics — mean, standard deviation, Q1/median/Q3, min/max in one step.
• Linear regression — returns the line y = ax + b and the correlation coefficient r.
• Normal — probabilities (normalcdf / Ncd) — P(a < X < b) from bounds, μ, σ. One-sided tail: use ±1×10⁹ as the open bound.
• Normal — inverse (invNorm / InvN) — given a probability, returns the value of x that cuts it off.
• Binomial — binompdf for P(X = x); binomcdf for a range ("at most", "at least", "fewer than").
• Finance / TVM solver — N, I%, PV, PMT, FV, P/Y, C/Y; leave the unknown blank and solve. Money in vs money out carry opposite signs.

If any of these still needs a menu-hunt, that is the single most valuable hour of practice left to you.

The patterns in the corpus

Section A — the recurring six

Section A is remarkably stable. The same handful of genres fill the six short slots; frequency out of 15 papers:

A regression question, a normal-distribution question and a kinematics question are very nearly guaranteed to be three of the six.

Section B — the chain templates

Every Section B question fits one of a small set of multi-part shapes. Recognising the template tells you what the later parts demand before you finish part (a).

The three Section B slots are most often: one Statistics chain (frequently the closer), one modelling/kinematics chain, and a rotating third — finance or geometry/optimisation.

The cardinal rule: show your setup

The examiner cannot see your calculator screen. All they have is your page. So if your page says only x = 4.73, no method has been shown — even if the answer is perfect. A bare answer on Paper 2 routinely scores 1 out of 3, or zero, because the M mark has nothing to attach to, and the A marks gated behind it fall too.

What "showing your setup" means, concretely

• Solving an equation — write the equation you solved before the value.
• A definite integral — write the integral with its limits before the answer.
• Normal — write X ~ N(μ, σ²) and the probability statement, or normalcdf with named arguments.
• Binomial — write X ~ B(n, p) and P(X ≥ 5) before the number.
• Regression — write the line y = ax + b before you use it to predict.
• Finance — write the N, I%, PV, PMT, FV entries before the result. Those entries are the method.

Also verbatim from the schemes: "do not accept final answers written using calculator notation" — an unevaluated normalcdf(...) or ∫ can earn intermediate credit but never the final A. And: with no working shown, examiners will not infer a misread — a bare wrong answer is simply wrong, no mitigation.

Traps the calculator creates

Almost every Paper-2-specific mark-loss is a presentation failure, an accuracy failure, or a mode failure — not a mathematics failure. The top 15, in priority order:

1. Premature rounding propagating through a multi-step calculation. The #1 P2 trap. Carry full precision; round once, at the end.
2. Bare answers with no setup. Wrong bare answer = zero; wrong answer with method = partial credit.
3. Radian / degree mode error. Silently corrupts every trig answer in a question. No recoverable method.
4. Calculator notation as the final answer. Always finish with an evaluated number.
5. normalcdf vs invNorm. Given a probability → invNorm. Given values → normalcdf.
6. Regressing the wrong variable. y-on-x to predict y; x-on-y to predict x. Wrong line = explicit M0A0, no follow-through.
7. GDC returns one solution when the domain wants several. Graph over the whole domain, count, solve each.
8. Trusting a root outside the valid domain. A negative length or time is a real root, not a valid answer.
9. Finance solver: P/Y vs C/Y, sign convention, or time units. Write the inputs as a labelled list first.
10. "Show that" / "Hence" answered with the calculator. Loses both the M and the AG. Pen, not machine.
11. Displacement vs distance — ∫v dt is signed displacement; distance needs ∫|v| dt.
12. Optimisation: stopping at the input x instead of substituting back for the value asked.
13. Sequence inequality: reporting the GDC's non-integer instead of rounding to the correct integer (round up to exceed a target).
14. Extrapolation not flagged when predicting outside the data range — a whole R mark.
15. Exact value demanded but a decimal given — e.g. k = ln a left as 0.0998.

Three or four of these will be your recurring habits. On the calculator paper the habits are almost never mathematical — they are mode, rounding, and showing setup. Fixing those three is worth more than any new technique.

The seven keystone habits for Paper 2

1. Write down what you typed into the calculator. The equation, the integral with limits, the named distribution, the TVM entries. Protects the M mark — and the A behind it — on almost every question.
2. Check the angle mode before any trigonometry. Radians unless told otherwise. A five-second glance at the start of the paper, and again whenever a trig answer looks wrong.
3. Store intermediate results in memory; recall at full precision. Never re-type a rounded number into the next part. Show 3 s.f. on the page; carry every digit in the machine.
4. Round only the final answer, to 3 s.f. unless told otherwise. Watch for money (2 d.p.) and explicit instructions.
5. Match the route to the command term. When it invites technology, use it confidently; when it says "show that" or "hence", do the written work anyway.
6. Name the distribution, label the sketch, state the interpretation. X ~ N(μ, σ²) before any probability; features marked with values on any sketch; a sentence on any "comment" or "interpret" part.
7. In Section B, attempt every (a) and (b) before any (d) or (e). ~60% of a chain's marks live in its first half.

The deepest finding about Paper 2 is the same boring truth as Paper 1: there is no trick. The calculator moves the difficulty to the setting-up and the interpreting. Show your setup — everything else is bookkeeping.