Mathematics: Analysis and Approaches HL
Geometry and trigonometry
Higher-level trigonometric identities, extended equations, and vector geometry.
Use reciprocal and Pythagorean identities
Simplify expressions and solve equations using core trigonometric identities.
Use compound angle formulae
Apply compound angle identities to exact values and trigonometric expressions.
Use double angle formulae
Use double angle identities to simplify, solve, and interpret trigonometric expressions.
Solve extended trigonometric equations
Solve trigonometric equations over extended intervals with exact or technology-supported reasoning.
Use vector equations of lines
Work with vector line equations, points, directions, and parameter values.
Use scalar product and vector angles
Calculate scalar products, angles, projections, and perpendicularity conditions.
Find intersections of vector lines
Solve parameter equations to decide whether vector lines intersect.
Use vector equations of planes
Interpret vector and Cartesian plane equations, normals, and points on planes.
Find angles between lines and planes
Use scalar products and normals to find angles involving lines and planes.
Use vector projection
Calculate scalar and vector projections and interpret components in a direction.
Prove geometric results with vectors
Use vectors to prove parallelism, perpendicularity, collinearity, and midpoint results.
Use advanced trigonometric proof
Prove identities using compound, double angle, reciprocal, and Pythagorean relationships.
Use 3D vector line intersections
Determine whether lines in three dimensions intersect, are parallel, or are skew.
Find distances from points to lines
Use vectors and projections to calculate point-to-line distances.
Find distances from points to planes
Use plane equations and normals to calculate perpendicular distance.
Find angles between planes
Use normal vectors and scalar products to determine angles between planes.
Use vector areas and volumes
Use cross products or scalar triple products to calculate areas and volumes.
Use trigonometric substitutions
Recognise and apply trigonometric substitutions in geometric or calculus contexts.
Use cross product for normals
Find normal vectors and plane equations using vector products.
Use scalar triple product
Calculate volume and coplanarity using scalar triple products.
Find shortest distance between skew lines
Use vector methods to find shortest distances between skew lines.
Use rotations in the plane
Apply rotation matrices and angle relationships to coordinate transformations.
Use complex numbers for transformations
Represent rotations and dilations using multiplication by complex numbers.
Prove trigonometric inequalities
Use identities and graph reasoning to justify trigonometric inequalities.
Use vector projection in 3D
Resolve vectors into projected components and interpret 3D geometry.
Find dihedral angles with normals
Use normal vectors to calculate and interpret dihedral angle relationships.
Use vector equations for reflections
Represent reflections in lines and planes using vector equations.
Analyse spherical trigonometry contexts
Interpret distances, bearings, and angles on spherical models.
Use reciprocal trigonometric identities
Apply reciprocal identities and restrictions in trigonometric equations.
Analyse phase and amplitude in compound trig models
Interpret amplitude, phase shift, period, and combined trigonometric models.
Use vector components along non-orthogonal directions
Resolve vectors in oblique directions and interpret component relationships.
Analyse intersections of three planes
Classify and solve systems representing intersections of three planes.
Use vector products in geometric proofs
Use dot and cross products to justify geometric relationships.
Model bearings with vectors
Represent bearings and navigation contexts using vectors.
Use compound angle identities in proof
Apply compound angle identities to prove and simplify trigonometric statements.
Analyse inverse trigonometric equation restrictions
Use ranges and restrictions to solve inverse trigonometric equations.
Use vector equations for projections onto planes
Project points and vectors onto planes using vector equations.
Find distances between parallel planes
Calculate distances between parallel planes using normal vectors.
Analyse loci with vectors
Represent loci and constraints using vector methods.
Use complex roots of unity geometrically
Interpret roots of unity and regular polygon geometry with complex numbers.
Prove identities with tangent half angle substitution
Use tangent half-angle substitution to prove and transform trigonometric expressions.
Analyse vector motion in three dimensions
Use vector functions to interpret position, velocity, and relative motion.