Mathematics: Analysis and Approaches HL

Geometry and trigonometry

Higher-level trigonometric identities, extended equations, and vector geometry.

Calculate reciprocal trigonometric ratios Develop calculate reciprocal trigonometric ratios through finite, exact AA HL practice aligned to current syllabus point AHL 3.9. Use compound-angle identities Develop use compound-angle identities through finite, exact AA HL practice aligned to current syllabus point AHL 3.10. Use double-angle identities Develop use double-angle identities through finite, exact AA HL practice aligned to current syllabus point AHL 3.10. Use trigonometric symmetry identities Develop use trigonometric symmetry identities through finite, exact AA HL practice aligned to current syllabus point AHL 3.11. Evaluate vector equations of lines Develop evaluate vector equations of lines through finite, exact AA HL practice aligned to current syllabus point AHL 3.14. Calculate scalar products and vector angles Develop calculate scalar products and vector angles through finite, exact AA HL practice aligned to current syllabus point AHL 3.13. Determine relationships between vector lines Develop determine relationships between vector lines through finite, exact AA HL practice aligned to current syllabus point AHL 3.15. Form Cartesian equations of planes Develop form cartesian equations of planes through finite, exact AA HL practice aligned to current syllabus point AHL 3.17. Find line and plane intersections Develop find line and plane intersections through finite, exact AA HL practice aligned to current syllabus point AHL 3.18. Add vectors and calculate magnitudes Develop add vectors and calculate magnitudes through finite, exact AA HL practice aligned to current syllabus point AHL 3.12. Prove parallelogram properties using vectors Develop prove parallelogram properties using vectors through finite, exact AA HL practice aligned to current syllabus point AHL 3.12. Apply exact trigonometric difference identities Develop apply exact trigonometric difference identities through finite, exact AA HL practice aligned to current syllabus point AHL 3.10. Distinguish parallel, intersecting and skew lines Develop distinguish parallel, intersecting and skew lines through finite, exact AA HL practice aligned to current syllabus point AHL 3.15. Calculate displacement vectors between points Develop calculate displacement vectors between points through finite, exact AA HL practice aligned to current syllabus point AHL 3.12. Calculate vector products Develop calculate vector products through finite, exact AA HL practice aligned to current syllabus point AHL 3.16. Find angles between planes Develop find angles between planes through finite, exact AA HL practice aligned to current syllabus point AHL 3.18. Find areas using vector products Develop find areas using vector products through finite, exact AA HL practice aligned to current syllabus point AHL 3.16. Solve trigonometric equations using symmetry Develop solve trigonometric equations using symmetry through finite, exact AA HL practice aligned to current syllabus point AHL 3.11. Find unit normal vectors using cross products Develop find unit normal vectors using cross products through finite, exact AA HL practice aligned to current syllabus point AHL 3.16. Test vector parallelism using cross products Develop test vector parallelism using cross products through finite, exact AA HL practice aligned to current syllabus point AHL 3.16. Find intersections of vector lines Develop find intersections of vector lines through finite, exact AA HL practice aligned to current syllabus point AHL 3.15. Prove parallelograms using opposite side vectors Develop prove parallelograms using opposite side vectors through finite, exact AA HL practice aligned to current syllabus point AHL 3.12. Apply negative-angle trigonometric symmetries Develop apply negative-angle trigonometric symmetries through finite, exact AA HL practice aligned to current syllabus point AHL 3.11. Solve tangent equations on finite intervals Develop solve tangent equations on finite intervals through finite, exact AA HL practice aligned to current syllabus point AHL 3.11. Test vector perpendicularity using scalar products Develop test vector perpendicularity using scalar products through finite, exact AA HL practice aligned to current syllabus point AHL 3.13. Find angles between planes and coordinate planes Develop find angles between planes and coordinate planes through finite, exact AA HL practice aligned to current syllabus point AHL 3.18. Form vector lines through two points Develop form vector lines through two points through finite, exact AA HL practice aligned to current syllabus point AHL 3.14. Find angles between lines and planes Develop find angles between lines and planes through finite, exact AA HL practice aligned to current syllabus point AHL 3.18. Recover trigonometric ratios from reciprocal ratios Develop recover trigonometric ratios from reciprocal ratios through finite, exact AA HL practice aligned to current syllabus point AHL 3.9. Recover component angles from compound-angle values Develop recover component angles from compound-angle values through finite, exact AA HL practice aligned to current syllabus point AHL 3.10. Calculate unit direction vectors Develop calculate unit direction vectors through finite, exact AA HL practice aligned to current syllabus point AHL 3.12. Find intersections of three planes Develop find intersections of three planes through finite, exact AA HL practice aligned to current syllabus point AHL 3.18. Prove collinearity using vectors Develop prove collinearity using vectors through finite, exact AA HL practice aligned to current syllabus point AHL 3.12. Model three-dimensional motion with vectors Develop model three-dimensional motion with vectors through finite, exact AA HL practice aligned to current syllabus point AHL 3.14. Calculate compound-angle tangent values Develop calculate compound-angle tangent values through finite, exact AA HL practice aligned to current syllabus point AHL 3.10. State inverse trigonometric domains and ranges Develop state inverse trigonometric domains and ranges through finite, exact AA HL practice aligned to current syllabus point AHL 3.9. Form planes from direction vectors Develop form planes from direction vectors through finite, exact AA HL practice aligned to current syllabus point AHL 3.17. Classify relationships between two planes Develop classify relationships between two planes through finite, exact AA HL practice aligned to current syllabus point AHL 3.18. Find endpoints from displacement vectors Develop find endpoints from displacement vectors through finite, exact AA HL practice aligned to current syllabus point AHL 3.12. Analyse periodic trigonometric solutions Develop analyse periodic trigonometric solutions through finite, exact AA HL practice aligned to current syllabus point AHL 3.11. Apply the tangent double-angle identity Develop apply the tangent double-angle identity through finite, exact AA HL practice aligned to current syllabus point AHL 3.10. Recover parameters from points on vector lines Develop recover parameters from points on vector lines through finite, exact AA HL practice aligned to current syllabus point AHL 3.14.