Geometry and trigonometry strand

Students should be able to:

GT.1

Measurement

  • calculate, interpret, and apply units of measure;
  • calculate, interpret, and apply units of time.
GT.2

2D shapes and 3D solids

Working with diagrams

  • draw and interpret scaled diagrams;
  • draw and interpret nets of rectangular solids, prisms (polygonal bases), and cylinders.

Perimeter and area

  • find the perimeter and area of plane figures made from combinations of discs, triangles, and rectangles, including relevant operations involving pi.

Volume

  • find the volume of rectangular solids, cylinders, triangular-based prisms, spheres, and combinations of these, including relevant operations involving pi.

Surface area

  • find the surface area and curved surface area (as appropriate) of rectangular solids, cylinders, triangular-based prisms, spheres, and combinations of these.
GT.3

Geometry and proof

Investigate the concept of proof through engagement with geometry.

Constructions

  • perform constructions 1 to 15 in Geometry for Post-Primary School Mathematics (constructions 3 and 7 at HL only).

Axioms, theorems, and corollaries

  • recall and use axioms 1, 2, 3, 4, and 5;
  • recall and use theorems 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 15 and 11, 12, 19, and appropriate converses, including relevant operations involving square roots;
  • recall and use corollaries 3, 4 and 1, 2, 5, and appropriate converses.

Language and practice of proof

  • use and explain the terms: theorem, proof, axiom, corollary, converse, and implies;
  • create and evaluate proofs of geometrical propositions;
  • display understanding of the proofs of theorems 1, 2, 3, 4, 5, 6, 9, 10, 14, 15 and 13, 19, and of corollaries 3, 4, and 1, 2, 5 (full formal proofs are not examinable).
GT.4

Trigonometric ratios

  • evaluate and use trigonometric ratios (sin, cos, tan, defined in terms of right-angled triangles) and their inverses;
  • work with angles between 0° and 90° at integer values;
  • express answers in decimal form.
GT.5

Co-ordinate geometry of the line

Key measurements

  • find and interpret distance, midpoint, slope, point of intersection, and slopes of parallel and perpendicular lines.

Graphs

  • draw graphs of line segments and interpret such graphs in context, including discussion of the rate of change (slope) and the y-intercept.

Equations of a line

  • find and interpret the equation of a line in the forms y = mx + c, y − y1 = m(x − x1), and ax + by + c = 0 (for a, b, c, m, x1, y1 ∈ Q);
  • use these forms to find the slope, the y-intercept, and other points on the line.
GT.6

Transformations

Images of objects

  • recognise and draw the image of points and objects under translation, central symmetry, axial symmetry, and rotation.

Symmetry

  • draw the axes of symmetry in shapes.