Which course does AscentIQ cover?

IB Mathematics: Applications and Interpretation SL, completely — every topic in the syllabus, calibrated against real past papers and mark schemes. We cover one course properly rather than several superficially. Additional IB courses are on our roadmap; the Math AI SL depth is the standard we'll hold them to.

How does the marking actually work?

Your work is transcribed, then evaluated against the exercise's mark scheme one mark at a time. Each Method, Answer, and Reasoning mark is awarded or withheld with a written reason. Follow-through is applied, so an early error doesn't automatically cost you the marks that depend on it.

Can the AI get the maths wrong?

The maths isn't generated by AI. Every number in every exercise is computed deterministically before the AI is involved — the AI only writes the wording around values it's been given, and is blocked from producing numbers of its own.

Do I have to write by hand?

You don't have to, but the whiteboard is where the marking is worth most. Writing out formula, substitution, and answer lets each method mark be awarded or withheld on its own. Typing takes final answers only — quicker, but there's no working to mark, and nothing to review afterwards.

What do I need to use it?

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What's in the free trial?

Seven days of full access — every topic in the Math AI SL syllabus, unlimited generated exercises, and per-mark feedback on the work you write out. No card required to start — we'll ask for one on day 7 to continue.

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IB Math AI SL · Topic 5

Calculus

Applied, not abstract: differentiation finds best answers to word problems, integration measures areas under them, and the trapezoidal rule estimates what cannot be integrated neatly. The mathematics is short; the justification around it is everything.

What the syllabus covers

Eight assessed sections, SL 5.1 to 5.8.

SL 5.1Limits and the derivativeThe limit concept introduced informally; the derivative interpreted as a gradient function and as a rate of change.

SL 5.2Increasing and decreasingReading f′(x) > 0, f′(x) = 0 and f′(x) < 0 off a graph, and what each means for the function itself.

SL 5.3Differentiating polynomialsFunctions of the form f(x) = axⁿ + bxⁿ⁻¹ + …, where all exponents are integers.

SL 5.4Tangents and normalsTheir equations at a given point — gradient from the derivative, line through the point with substitution shown.

SL 5.5IntegrationAnti-differentiation of axⁿ-type functions (n ≠ −1); boundary conditions to pin down the constant; definite integrals by technology; area under a curve above the x-axis.

SL 5.6Stationary pointsSolving f′(x) = 0; identifying local maxima and minima among the solutions.

SL 5.7Optimisation in contextWord problems that run model → differentiate → solve → interpret, with units and a conclusion in terms of the scenario.

SL 5.8Trapezoidal ruleApproximating areas under curves when integration is not available — table of values, interval width h, weighted sum.

How it is examined

Optimisation word problems close Paper 2 modelling chains — the calculus is three lines, the framing and justification carry the rest.

Optimisation questions arrive fully dressed in context — maximum profit, minimum fencing — requiring a variable defined, a function constructed, and a stationary point found and classified.
Finding f′(x) = 0 earns method marks; asserting 'this is the maximum' without checking nature costs the reasoning mark.
Tangents and normals are examined as equations through a given point, with substitution shown.
Trapezoidal-rule questions provide tables of values; the interval width h is where silent errors live.
The booklet gives exactly three things here: the power rule for differentiating xⁿ, the power rule for integrating it, and the trapezoidal rule itself. Nothing about optimisation appears anywhere in it — the setup is entirely yours to construct.
The second-derivative test is not part of the SL syllabus, so a stationary point is classified by a sign-change argument around it — values of f′ either side, or the graph on your GDC.

A marked question, mark by mark

An optimisation chain showing where the justification mark separates complete answers from near-complete ones.

Get the justification habit, on fresh exercises

Unlimited generated optimisation, tangents and area questions across SL 5.1–5.8 — each returned mark by mark, so the missing classification or unit becomes visible immediately, not on results day.

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New to the codes? M1, A1, R1 explained →

Optimisation · SL 5.6 / 5.7

Seed 6A52

A farmer builds a rectangular enclosure against an existing wall using 60 m of fencing for the other three sides.

(a)Show that the area is A(x) = x(60 − 2x), where x is the depth.
(b)Find the dimensions that maximise the area, justifying that it is a maximum.

Your work

A(x) = x(60 − 2x)

A′(x) = 60 − 4x = 0 → x = 15

dimensions 15 m × 30 m, A = 450 m²

Marks awarded

M1Mark awarded. Differentiated and solved A′(x) = 0 correctly.
A1Mark awarded. x = 15 m, maximum area 450 m².
R1Mark not awarded. Maximum asserted, never justified — no second-derivative check or sign-change argument shown.

Where marks are actually lost

Calculus answers end with sentences, not numbers.

Stopping at the solution of f′(x) = 0 without classifying the stationary point.

CostThe reasoning mark exists precisely to distinguish maxima from minima — unearned by assertion.

Final answers without units or a closing sentence in the problem's terms.

Cost'x = 15' is a coordinate; 'the enclosure should be 15 m deep' is the answer the question asked for.

Setting the wrong interval width h in trapezoidal-rule approximations.

CostEvery ordinate is then weighted incorrectly and the estimate collapses.

Sign slips differentiating negative-coefficient polynomials.

CostFollow-through protects later marks only when the written method stays consistent and readable.