Interactive Math Tools
Free, hands-on visualisations for O-Level and JC math — drag, play and explore the concepts that are hard to see on paper.
Trigonometric Graphs Explorer
Type your own a, b and c into y = a sin bx + c — cos and tan too. Every repeat is drawn in its own colour and numbered, the period and the a are marked on the curve, and you can put two graphs on the same axes.
OpenGraph Transformations
Translations, stretches and reflections in real time — plus the JC set: |f(x)|, f(|x|), 1/f(x) and f′(x). Type your own y = f(x), or snap a photo of a printed graph and transform that.
OpenCurve Sketching Pad
Sketch polynomials and rational curves; find the turning points, asymptotes and intercepts.
OpenArgand Diagram & Complex Numbers
Plot complex numbers, add and multiply them, and watch modulus–argument geometry come alive.
Open3D Vector & Plane Visualiser
Rotate vectors, lines and planes in 3D to build intuition for H2 vectors.
OpenCalculus Drill
Rapid-fire differentiation and integration practice with instant feedback.
OpenMental Math Sprint
Timed arithmetic drills to sharpen speed and accuracy.
OpenRatio of Areas
Same height ⇒ areas follow the bases; similar figures ⇒ k, k², k³. Drag the figures and watch the exam ratios — including the trapezium-diagonals classic — hold live.
OpenLinear Law
Why plot lg y against x? Watch a curve straighten under the right axes, then recover a and b from the gradient and intercept. Snap a photo of the question’s data table and it reads, fits and solves it for you.
OpenAnimated Worked Solutions
Watch an equation solve itself one operation at a time — each step glows with what was done to both sides, including the ± everyone forgets.
OpenDifferentiation from First Principles
A guided animated lesson: the secant line visibly swings into the tangent as h shrinks to 0 — then the algebra says the same thing.
OpenCompleting the Square, with Actual Squares
A guided animated lesson: x² + 8x drawn as real squares and rectangles that split, wrap and patch into (x + 4)² − 16 — then straight to the turning point.
OpenThe R-Formula — Two Waves Become One
A guided animated lesson: a sin θ + b cos θ visibly collapses into one wave R sin(θ + α), with the 3-4-5 triangle showing where R and α come from. Sliders included.
OpenTriangle Solver & the Ambiguous Case
Give it any three parts (SSS, SAS, ASA, SSA) — see the triangle drawn to scale, which rule applies, and BOTH triangles when sine gives two answers.
OpenCircle Geometry Theorem Explorer
Drag points around a circle and watch angle-at-centre, same-segment, semicircle, cyclic quad, tangent and alternate-segment theorems hold live.
OpenBite-size Video Clips
Narrated 20-second explainers made for WhatsApp — watch once, remember the idea. First up: why tan blows up at 90°.
OpenUnit Circle → Sine, Cosine & Tangent
The unit circle with the classic tangent-line construction, tracing all three graphs live beside it — drag the dot, jump to special angles, see exact values and why tan blows up at 90°. 3D unwrap view included.
OpenSpot the Error
Real exam working with exactly one illegal line hidden inside — tap it, then see why. Trained on the slips that actually cost marks: signs, logs, illegal cancelling, the forgotten ±.
OpenProbability Tree Builder
Fill in every branch, then multiply along the path and add across paths — with and without replacement, plus the trees where the second branch depends on the first.
OpenDraw the Line
The classic "add a suitable straight line to solve…" question, live: work out the line, drag it onto the drawn curve, read the roots off the graph like the real paper.
OpenInequalities: the Sign Test
Critical values → signs → answer. Solve quadratic, rational and modulus inequalities the systematic way — including the denominator values you must never include.
OpenHypothesis Tests: the Conclusion Mark
Every H2 test ends with one sentence worth one mark. Assemble it — the comparison, the decision, the strength, the claim in context — and never say "accept H₀".
OpenProve It: Trig Identities
Proving is choosing the right next move. Build ten proofs line by line and learn the five moves that crack almost every identity — Pythagoras in disguise, the conjugate, and friends.
OpenTrig Identities: Why Each Step
The companion to the trainer: a proof unfolds line by line, and each line tells you what you spotted, which identity you used and what it bought you. Read the plan before writing anything.
OpenSpeed-Time Graphs
The whole topic is two facts: gradient is acceleration, area is distance. Draw the journey from the story, then make the graph pay — trapezium areas, unknown times and all.
OpenBar Model Builder
Draw the problem before you solve it: units, stubs and brackets for ratio, percentage and before-after problems — then see the algebra your bars secretly were. Sec 1–2, and the PSLE bridge.
OpenConstructions, Drawn For You
Watch the compass actually swing: the perpendicular bisector and the angle bisector built arc by arc, like a video you can pause and scrub. Then drag the points and it rebuilds on your figure — plus the loci question where you shade the region.
OpenRatio of Areas — Endless Practice
A fresh figure every time with the ratios marked: key in the area ratio, and the working builds itself step by step over the diagram. Every family that shows up in E-Math vectors, congruence and similarity.
OpenExponential & Logarithmic Graphs
Every one of these graphs is one of four shapes, flipped. Watch a curve flip in each axis, then sketch y = ln(2 − x) the exam way — asymptote, shape, draw, intercepts. Build your own, then drill the shape ID.
OpenAdding Algebraic Fractions
Why you can’t add across, shown with bars — then every common-denominator move, one line at a time: cross-multiplying, the minus that bites, factorising first, and the 6 − 5y swap. Sec 2 algebra.
OpenQuadratic Graphs — the Three Forms
y = x² − 6x + 5, y = (x − 1)(x − 5) and y = (x − 3)² − 4 are the same parabola. See what each form hands you for free — roots, turning point, y-intercept — then drag a, b and c and watch all three rewrite.
OpenGraphs of Functions — the Seven Shapes
Every E-Math sketching question is one of seven shapes: y = xⁿ for n = −2 to 3, and y = aˣ. Learn the gallery, see what a minus does, then slide them up and down and find the intercepts.
OpenMultiplying Matrices
Check the sizes, then build the answer one entry at a time with the row and column lit up — 2×2, 2×3 with 3×2, and the pair that shows why order matters: 1×3 with 3×1 gives a number, 3×1 with 1×3 gives a 3×3.
OpenMatrix Multiplier — Your Own Numbers
Type any two matrices and step through the product entry by entry, with the row, the column and the full working shown. Tells you when the multiplication is impossible, and why.
OpenCircle Proofs — Statement and Reason
The eight theorems as a toolkit, then real proofs built one line at a time — each line lights up the part of the figure it is about and names the reason that earns the mark. Ends with a name-the-reason drill.
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