Features

What's inside.

Plotter, diagram builder, marking schemes, past-paper index, worksheets. The figures on this page are the same ones the product renders into a paper.

Function plotter

Every curve from its equation.

Type the equation. The plot comes out at print quality, with roots and turning points correctly placed.

Fig 1 · f(x) = ln(x − 1), with its vertical asymptote and x-intercept

Every function class on the LC syllabus.

Linear, quadratic, cubic, higher-degree polynomial, rational, trigonometric, exponential, logarithmic, surd, and absolute-value. Nested expressions like sin(2x) + x/3 are handled.

Line weight, grid spacing, and ink colour match the SEC papers.

  • DomainChosen automatically, or set by you
  • RangeScaled so roots and turning points are visible
  • LabelsRoots, turning points, asymptotes, holes on request
  • OutputSVG on screen, PDF on export. No raster.
Diagram builder

Diagrams built from the numbers you give.

Lengths, angles, and constraints from the question end up in the figure.

Fig 2 · Triangle inscribed in a circle, diameter |AB|, right-angle at P

Coordinates come from the description.

Write “triangle inscribed in a circle, diameter AB, P on the circle”. The right angle at P and the vertex labels follow from there.

When more than one layout is valid, the one that prints cleanly is picked.

  • ShapesPoint, line, segment, circle, arc, angle, polygon, locus
  • ConstraintsLength, angle, tangency, perpendicularity, on-circle, equal-to
  • LabelsSerif italic vertices, mono units, auto-offset to avoid overlap
  • DeterminismThe same description produces the same figure, every time
Geometry, trig, 3D

Unit-circle proofs, cones, vector figures.

Drawn the way SEC papers draw them. The figures below come from the same engine as the figure studio.

ConeVolume / surface-area questions. Back ellipse dashed, slant edges drawn, height labelled.
Unit circle with rayscos(α − β) derivations, angle placement, trig identities. Arc between rays labels the difference.
ParallelogramVector-area questions. Opposite sides marked with matching tick counts, diagonals dashed.

The same engine powers unit-circle proofs, scene-3D flagpole and elevation-angle questions, triangle-rule derivations, and every other SEC-style scaffold in the studio.

Marking scheme

The marking scheme is built into the paper.

Each question carries its scheme in the file. The paper and the scheme print together.

Q3(b)10 marks
Differentiate f'(x) = 3x² − 32
Set f'(x) = 0, solve for x3
Evaluate f at x = ±12
Classify: (−1, 3) max, (1, −1) min2
Sketch with correct shape1
Total10
Scheme 1 · Auto-balanced, totals match the question header

Marks add up to the header total.

Each part has a mark allocation and an accepted solution. Part allocations sum into the question header.

SEC marking schemes already use this structure. Here it can be edited directly.

  • PartsParts (a), (b), sub-parts (i), (ii), renumber automatically
  • Solution setAccepted final answer plus accepted intermediate forms
  • TotalsPart allocations sum into the question header
  • ExportSeparate PDF, same layout as the paper, answer key column on the right
SEC-indexed library

Past questions, indexed by what they test.

Every Leaving Certificate maths paper since 2017, indexed by topic and sub-part.

Topic: exponential growth · HL47 questions
YearPaperQMarksSub-topic
2023P1Q625continuous compound
2022P1Q520half-life
2021P1Q730continuous compound
2019P1Q525doubling time
2018P1Q630population model
2016P1Q520half-life
Index 1 · Exponential-growth questions across the SEC archive

Drop a question in, the scheme follows.

When a past question is dropped into a new paper, the original wording and marking scheme stay attached.

  • CoverageEvery SEC paper, 2017 to present
  • GranularityIndexed by question, part, and sub-part
  • SearchBy topic, year, mark allocation, difficulty
  • AdaptChange numbers or context, the figure and scheme re-solve
Worksheets & notes

Worksheets, warm-ups, class notes.

Shorter formats than a full paper, written with the same authoring tools.

5th year, differentiation · warm-up

Differentiation, ten minutes

  1. Differentiate f(x) = 3x² − 5x + 2.
  2. Find dy/dx where y = (2x + 1)³.
  3. For g(x) = x² ex, find g'(x).
  4. A particle moves with s(t) = t³ − 6t² + 9t. Find the time(s) when velocity is zero.
Sheet 1 · Ten-minute class warm-up, 5th year higher

What changes is the layout.

A worksheet is a paper without the cover page. Class notes are a paper with the answers shown inline alongside the questions.

  • Warm-upsFive questions, ten minutes, one topic
  • WorksheetsTopic-scoped practice, with or without a marking scheme
  • NotesWorked examples, rendered inline, ready to hand out
  • Class testsUnder an hour, custom mark totals, shareable answer key
Demo

See SmarTest on one of your topics.