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 AI HL

IB Math AI HL · Topic 3

Geometry and trigonometry

The topic that changes most between SL and HL. At SL it is measurement — solids, triangles, Voronoi diagrams. At HL it becomes structure: radians, transformations by matrices, vectors in three dimensions, and graph theory — the networks, walks and optimal routes that turn up in the longest questions.

What the syllabus covers

Sixteen assessed sections: SL 3.1 to 3.6, shared with AI SL, and AHL 3.7 to 3.16, which are HL only.

SL 3.1Measurement in 2D and 3DDistance and midpoint in three dimensions; volume and surface area of right pyramids, cones, spheres, hemispheres and composite solids; angles between intersecting lines and between a line and a plane.

SL 3.2Triangle trigonometrySine, cosine and tangent ratios in right triangles; the sine rule and cosine rule for non-right triangles; area as ½ab·sinC.

SL 3.3ApplicationsAngles of elevation and depression, Pythagoras' theorem in context, and constructing labelled diagrams from written statements.

SL 3.4Arcs and sectorsLength of an arc and area of a sector, with the angle θ measured in degrees.

SL 3.5Perpendicular bisectorsEquations built from a midpoint and a negative-reciprocal gradient — the machinery behind Voronoi boundaries.

SL 3.6Voronoi diagramsSites, vertices, edges and cells; adding a site to an existing diagram; nearest-neighbour interpolation; the toxic-waste-dump problem.

AHL 3.7Radian measureThe radian, converting to and from degrees, and arc length and sector area in radians.

AHL 3.8The unit circle, identities and equationsSine and cosine on the unit circle, the Pythagorean and double angle identities, and equations built on them.

AHL 3.9Matrix transformationsReflections, stretches, enlargements and rotations as matrices; composite transformations; the determinant as an area scale factor.

AHL 3.10Vector conceptsPosition vectors, unit and base vectors, magnitude, and sums and multiples in two and three dimensions.

AHL 3.11The vector equation of a liner = a + λb in two and three dimensions; parallel, intersecting and skew lines; the angle between lines.

AHL 3.12Vectors and kinematicsMotion at constant velocity, and motion with a velocity that changes, found by differentiating and integrating a position vector.

AHL 3.13Scalar and vector productsThe angle between vectors, perpendicularity, and the area of a triangle or parallelogram.

AHL 3.14Graph theoryVertices, edges, degree, walks, paths and circuits; trees; weighted graphs; Eulerian and Hamiltonian graphs.

AHL 3.15Adjacency matrices, walks and transition matricesCounting walks of a given length with powers of the adjacency matrix, and random walks on a graph.

AHL 3.16Graph algorithmsKruskal's and Prim's algorithms, the route inspection (Chinese postman) problem, and bounds for the travelling salesman problem.

How it is examined

The HL sections are methods you can follow, and the marks follow the method stage by stage.

From AHL 3.7 the unit of an angle is radians unless the question says degrees. The calculator's angle mode is part of the answer.
Two lines in three dimensions can be parallel, intersect or be skew. 'Show that they do not intersect' needs a justification: parameters that satisfy some of the coordinate equations but not all of them.
The scalar product gives the angle between vectors and tests perpendicularity, a · b = 0. The vector product gives a vector perpendicular to both, and |a × b| is the area of the parallelogram they span.
Matrix transformations are read from the image of the unit square. The determinant is the area scale factor, and a composite transformation multiplies its matrices right to left.
Graph algorithms are marked as processes: the edges chosen in order for Kruskal or Prim, the tour and its length for nearest neighbour, the deleted-vertex lower bound. The total weight alone does not carry the marks.
Vector kinematics asks for position, velocity and speed at a time, and often for the closest approach of two moving objects — a distance minimised with calculus or technology.

A marked question, mark by mark

A scalar-product question where the angle is right, and the conclusion about perpendicularity is not justified.

Follow the whole method, on fresh exercises

From SL 3.1 to AHL 3.16, every generated exercise comes back mark by mark — and graph-theory questions are built so that only one answer is correct, so a different result is yours to explain.

Start your trial

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

Scalar product · AHL 3.13

Seed 6T27

Let a = (2, −1, 2) and b = (1, 2, 2).

(a)Find the angle between a and b, in radians, correct to three significant figures.
(b)State whether a and b are perpendicular, giving a reason.

Your work

a · b = 2(1) + (−1)(2) + 2(2) = 4

|a| = |b| = 3, so cos θ = 4/9

θ = 1.11 rad

They are not perpendicular.

Marks awarded

M1Mark awarded. Used cos θ = a · b / (|a||b|) with the scalar product and both magnitudes.
A1Mark awarded. θ = 1.11 radians, correct to three significant figures.
R1Mark not awarded. 'Not perpendicular' is stated without the reason: a · b = 4, which is not zero.

Where marks are actually lost

With vectors and graphs the method is long, and marks go where a stage is skipped or a unit is lost.

Calculating in degree mode when the question works in radians.

CostAngles, arc lengths and sector areas are all wrong together; the method marks may survive, the accuracy marks do not.

Deciding two lines intersect because two of the three coordinates agree.

CostAll three equations must hold for the same pair of parameters. Stopping early turns skew lines into an intersection.

Multiplying transformation matrices in the wrong order.

CostThe composite does the transformations in the opposite order. Every point, and every later answer, is then wrong.

Giving only the total weight of a spanning tree or route, without the edges chosen.

CostThe marks are for the algorithm's stages. A correct total with no working shows none of them.