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Led by Archimedes Simulacrum
The seventh module of the OCR GCSE Mathematics course — congruence, similarity, perimeter, area, volume, Pythagoras, trigonometry and vectors. Hosted by Archimedes Simulacrum.
Led by Archimedes Simulacrum
The question
Congruent triangles (SSS, SAS, ASA, RHS conditions), similar shapes and scale factors, the effect of enlargement on areas (k²) and volumes (k³), and formal geometric proofs using congruence and similarity at Higher tier.
Outcome
The student can apply congruence and similarity conditions and calculate the effect of enlargement on area and volume. (Shape relationships)
Sub-units
Led by Archimedes Simulacrum
The question
Formulae for all standard 2D shapes (rectangle, triangle, parallelogram, trapezium, circle), compound shapes, arc length and sector area, and 3D shapes (cuboid, prism, cylinder, cone, sphere, pyramid). Plans and elevations. Unit conversions for area and volume.
Outcome
The student can calculate perimeter, area and volume for standard and compound shapes and convert between units. (Mensuration)
Sub-units
Led by Archimedes Simulacrum
The question
Pythagoras' theorem in 2D and 3D, the trigonometric ratios (SOH CAH TOA), exact values for standard angles, and at Higher tier the sine rule, cosine rule, area = ½ab sin C for non-right-angled triangles, and 3D trigonometry.
Outcome
The student can apply Pythagoras and trigonometry to find unknown sides and angles, and use sine/cosine rules for general triangles at Higher. (Triangle calculation)
Sub-units
Led by Archimedes Simulacrum
The question
Column vectors, addition, subtraction and scalar multiplication, describing translations, magnitude, parallel vectors, and at Higher tier using vectors to construct geometric proofs involving midpoints, parallel lines and collinearity.
Outcome
The student can perform vector operations and use vectors to prove geometric results. (Vector algebra and proof)
Sub-units