LEARN · EXPLAIN · REVISE
Selective compulsory volume 1
Read the idea, work independently, then explain what changed.
Each section contains concept explanations, three worked examples, ten graded exercises and teacher preparation.
Space vectors and their operations
Add, scale and multiply space vectors; distinguish scalar and vector results.
1.2The fundamental theorem of space vectors
Recognise a basis and use unique vector coordinates and affine combinations.
1.3Coordinate representation of space vectors
Calculate spatial lengths, angles, projections and perpendicular directions from coordinates.
1.4Applications of space vectors
Use direction and normal vectors to establish angles, distances and spatial relations.
2.1Inclination and slope of a line
Connect slope, inclination and parallel/perpendicular directions, including vertical lines.
2.2Equations of a line
Choose point-slope, two-point, intercept or general form without losing exceptional lines.
2.3Intersections and distance formulas
Solve intersections and calculate point-line and parallel-line distances with geometric checks.
2.4Equations of a circle
Construct circle equations from centers, radii, diameters and point constraints.
2.5Relations between lines and circles
Classify intersection and tangency using distances, discriminants and common chords.
3.1Ellipse
Use the focal definition, standard equation and geometric properties of an ellipse.
3.2Hyperbola
Use the distance-difference definition, asymptotes and branch restrictions.
3.3Parabola
Relate focus, directrix and vertex, and retain conditions in line-parabola intersections.