Choose the destination. Build only the mathematics that gets you there.

1. Stage 1

   Coordinate and practical geometry

   Connect equations and measurements to points, lengths, areas and volumes.

   Why it is here: It supplies a prerequisite used later on the route to Vectors and linear algebra.

   Open 15 lessons

   Readiness: Understand basic algebra and square roots.

   SlopeCalculate the slope of the line through two coordinate points.MidpointFind the point exactly halfway between two coordinates.Distance between pointsCalculate straight-line distance between two coordinates.RectangleCalculate area, perimeter and diagonal from length and width.Triangle areaCalculate triangle area from a base and perpendicular height.CircleCalculate a circle's diameter, circumference and area from its radius.Trapezoid areaFind trapezoid area from the two parallel base lengths and perpendicular height.EllipseCalculate ellipse area and an accurate perimeter approximation from its semi-axes.Pythagorean theoremFind the hypotenuse of a right triangle from its two legs.Cube dimensionsCalculate a cube's volume, surface area and space diagonal from its side length.Rectangular prismCalculate volume, surface area and space diagonal from length, width and height.CylinderCalculate cylinder volume and surface area from radius and height.Cone volumeCalculate the volume and base area of a circular cone from radius and height.SphereCalculate sphere volume and surface area from radius.Square pyramidCalculate volume, slant height and total surface area from base side and vertical height.
2. Stage 2

   Angles and trigonometry

   Move between angle systems and solve right-triangle relationships.

   Why it is here: It supplies a prerequisite used later on the route to Vectors and linear algebra.

   Open 5 lessons

   Readiness: Understand similar triangles, algebra and the Pythagorean theorem.

   Degrees and radiansConvert an angle entered in degrees to radians and common turn measures.Right triangleSolve a right triangle from its two perpendicular legs.Unit circleConvert an angle into its unit-circle coordinates, sine, cosine and reference angle.Inverse trig functionsCalculate arcsine, arccosine and arctangent for a real ratio and show their principal angles.Trig identityEvaluate sine, cosine and the identity sin²θ+cos²θ=1 at any angle.
3. Stage 3

   Linear algebra

   Work with vectors and matrices, then understand determinants, inverses and eigenvalues.

   Why it is here: This is your selected destination.

   Open 8 lessons

   Readiness: Understand algebra, coordinate geometry, trigonometry and functions.

   Vector magnitudeCalculate the length of a three-dimensional vector from its components.Vector additionAdd two three-dimensional vectors component by component.Dot productCalculate the scalar dot product of two three-dimensional vectors.Cross productCalculate the three-dimensional vector perpendicular to two input vectors.Angle between vectorsFind the angle between two three-dimensional vectors using their dot product.2×2 determinantCalculate the determinant of a 2×2 matrix and identify whether it is invertible.2×2 matrix inverseInvert a nonsingular 2×2 matrix and display all four inverse entries.2×2 eigenvaluesCalculate the real eigenvalues of a 2×2 matrix from its trace and determinant.

This is a recommendation, not a mastery decision. Nothing is marked complete until you choose to record progress. Future EII-learning adaptation will use evidence and remain advisory.