High School 3 mathematics
High School 3 covers Calculus II and Geometry. Nine activities from this grade are translated into English so far, covering derivatives, integrals, 3D coordinates, vectors, and conic sections (ellipse, parabola, hyperbola) — more High School 3 topics are on the way.
📈 Functions & graphs
Derivatives of Various Functions
Compare the tangent line and derivative graph of sin, cos, eˣ, and ln x, and verify the formulas with a limit.
Open English lesson → 📐Parametric & Implicit Differentiation
Find a circle's tangent slope two different ways and confirm they always agree.
Open English lesson → 🔗Various Integration Techniques
Confirm the Fundamental Theorem of Calculus and explore the family of antiderivatives.
Open English lesson → 🔗Substitution & Integration by Parts
Verify antiderivatives found by substitution and integration by parts against a Riemann sum.
Open English lesson → 🌀Definite Integral Applications Lab (Volume, Speed & Distance)
Use definite integrals to find the volume of a solid of revolution and see directly how the area under a velocity graph gives displacement.
Open English lesson →📐 Shapes & geometry
Ellipse
The two-focus definition, eccentricity, the area formula (πab), planetary orbits, and whispering galleries.
Open English lesson → 📦3D Coordinates
Move a point along the x, y, and z axes and verify the distance formula in space.
Open English lesson → ➡️Vectors
Add vectors with the triangle rule and find the exact moment the dot product hits 0 (perpendicular).
Open English lesson → 🛰️Parabola
Confirm the focus-directrix definition with sliders, and see the reflection property behind satellite dishes and flashlights.
Open English lesson → 🌗Hyperbola
Confirm the two-focus definition and asymptotes with sliders, and see the navigation math behind LORAN and GPS.
Open English lesson → 🔺Conic Sections Lab
Adjust the cutting angle yourself and see how a cone can produce a circle, ellipse, parabola, or hyperbola depending on how it is sliced.
Open English lesson → ✖️Vector Cross Product Lab
Drag two vectors to create a parallelogram and verify that its area equals the magnitude of the cross product, while also seeing how the sign changes with the…
Open English lesson → 🪐Kepler’s Laws of Planetary Motion Simulation
Explore Kepler’s second law: a planet moves faster when it is closer to the Sun and slower when it is farther away, yet it always sweeps out the same area in the same amount of time.
Open English lesson →