Which courses does AscentIQ cover?

IB Mathematics: Analysis and Approaches SL, Applications and Interpretation SL, and Applications and Interpretation HL — exercises generated for each course's syllabus and marked against the IB mark scheme. Analysis and Approaches HL isn't available yet; it's on our roadmap. We add courses one at a time rather than several superficially.

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?

A tablet with a stylus is the best experience — the whiteboard is built for it. A laptop or desktop works fully too. We wouldn't recommend a phone: the whiteboard needs more room than a phone screen gives it.

Seven days of full access — every chapter of your course, unlimited generated exercises, and per-mark feedback on the work you write out. No card required to start.

What happens when the trial ends?

If you'd like to continue afterwards, leave your details at ascentiq.io/continue or write to renzo@ascentiq.io, and you'll hear back by email — including about the asynchronous tutoring we're building on top of your results.

What is the asynchronous tutoring?

It's a tutoring method built on your results in the exercise mode — where your marks are lost, which topics are slipping, what to work on next — followed up at your own pace, without having to coordinate a live session. It's still in development, so there's no fixed format yet. If you'd like to hear how it will work, write to renzo@ascentiq.io.

← IB Math AA SL

IB Math AA SL · Topic 2

Functions

The topic that every other topic borrows from. A function is a rule with a domain and a range, and most of the course is that rule seen three ways — as an equation, as a graph and as a model. Here the work is knowing which representation answers the question, and writing the features you found in the form the mark scheme asks for.

What the syllabus covers

Eleven assessed sections, SL 2.1 to 2.11 — from straight lines to the transformation of graphs.

SL 2.1Equations of a straight lineThe different forms of a line, gradient and intercepts, and the conditions for parallel and perpendicular lines.

SL 2.2Functions: domain, range, graph and inverseFunction notation, the idea of a function as a model, and the inverse as a reflection in y = x.

SL 2.3The graph of a functionSketching from given information or a context, including transferring a graph from the screen to paper.

SL 2.4Key features and intersectionsIntercepts, vertices, asymptotes and symmetry from a graph; intersections of curves found with technology.

SL 2.5Composite and inverse functionsComposite functions, the identity function, and finding f⁻¹(x).

SL 2.6Quadratic functionsThe standard, factored and vertex forms, and what each one shows at a glance: y-intercept, roots, vertex.

SL 2.7Quadratic equations and inequalitiesFactorising, completing the square and the quadratic formula; the discriminant and the nature of the roots.

SL 2.8Reciprocal and rational functionsThe graph of 1/x and its self-inverse nature; rational functions of the form (ax + b)/(cx + d) and their asymptotes.

SL 2.9Exponential and logarithmic functionsThe graphs of aˣ, eˣ, logₐ x and ln x, and the way they mirror each other.

SL 2.10Solving equations graphically and analyticallyUsing technology where no analytic route exists, and applying both approaches to real-life situations.

SL 2.11Transformations of graphsTranslations, reflections, vertical and horizontal stretches, and the composition of several transformations.

How it is examined

Functions questions are rarely about a single skill. They chain two or three, and the marks follow the chain.

Paper 1 (no calculator) solves by hand: factorising, completing the square, the quadratic formula, exact asymptotes, composite and inverse functions with exact values. Paper 2 (technology) hands the intersection or the maximum to the GDC and marks how you set the problem up.
Sketches are marked on features, not on artistry: the intercepts, the asymptotes and the vertex have to be present and labelled with their coordinates or equations, and the shape has to behave near them.
'Find the values of k for which the equation has two distinct real roots' is the discriminant in disguise. It needs Δ > 0, a strict inequality, and a conclusion about k — not just a value of Δ.
Asymptotes are equations. A vertical asymptote is x = −2, not −2; a horizontal one is y = 3, not 3.
Transformations are described in words, one at a time and completely: the type, the direction and the size. 'Moved by 3' is not a description; 'a translation of 3 units to the right' is.
Domain and range are statements about x and y, usually as inequalities, and for an inverse they swap: the range of f becomes the domain of f⁻¹.

A marked question, mark by mark

A discriminant question where the method is right and the condition is not stated — exactly the shape of most lost marks in this topic.

Practise the whole chain, on fresh exercises

From SL 2.1 lines to SL 2.11 transformations, every generated exercise comes back with each mark awarded or withheld and a reason — including the labels and conditions that are easy to forget.

Start your trial

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

The discriminant · SL 2.7

Seed 7P14

Consider the equation x² + 6x + k = 0, where k is a constant.

(a)Find the values of k for which the equation has two distinct real roots, stating the condition you use.

Your work

Δ = 6² − 4(1)(k) = 36 − 4k

Δ ≥ 0, so k ≤ 9

Marks awarded

M1Mark awarded. Discriminant Δ = b² − 4ac written and evaluated correctly: 36 − 4k.
A1Mark not awarded. k ≤ 9 includes k = 9, where the roots coincide. 'Two distinct' needs the strict k < 9.
R1Mark not awarded. The condition for two distinct real roots, Δ > 0, was never stated; Δ ≥ 0 is the condition for real roots.

Where marks are actually lost

The calculation is usually fine. The marks are lost in how the answer is written down.

Giving an asymptote as a number — '−2' — instead of as an equation, x = −2.

CostThe answer mark is for the equation. A number alone does not say whether the asymptote is vertical or horizontal.

Sketching a graph without labelling the intercepts, asymptotes and vertex.

CostSketch marks are awarded for each key feature shown with its coordinates or equation; an unlabelled curve earns the shape and little else.

Composing functions in the wrong order — (f ∘ g)(x) written as g(f(x)).

CostEverything downstream is built on the wrong function. Follow-through can rescue later marks, but the composition mark itself is gone.

Describing a transformation incompletely, or two transformations in one phrase.

CostEach transformation is marked separately on its type, direction and size; a vague description scores none of them.