Geometry & Measures – AQA GCSE Maths (8300)

Key Concepts

• Angles: interior, exterior, vertically opposite, complementary, supplementary
• Triangles, quadrilaterals, polygons, and their properties
• Circles: radius, diameter, circumference, area, arcs, sectors
• Perimeter, area, and volume of 2D and 3D shapes
• Pythagoras’ theorem and trigonometry
• Transformations: translations, rotations, reflections, enlargements
• Coordinate geometry
• Units of measurement, conversions, scale diagrams, bearings

Definitions & Examples

• Interior Angle: The angle inside a polygon.
• Exterior Angle: Angle formed outside a polygon adjacent to interior angle.
• Pythagoras’ Theorem: In a right-angled triangle, a² + b² = c².
• Trigonometry: sin, cos, tan ratios to find missing sides/angles.
• Transformation: Moving or resizing shapes (translation, rotation, reflection, enlargement).

Methods

• Calculate missing angles using sum of angles in polygons
• Use Pythagoras and trigonometric ratios to solve problems
• Find perimeter, area, and volume using formulas
• Apply transformations using coordinates or geometrically
• Convert between units (length, area, volume, time)
• Draw and interpret scale diagrams and bearings

Advantages & Disadvantages

• Advantages: Develops spatial awareness, useful in real-life contexts such as construction, navigation, and engineering.
• Disadvantages: Requires careful diagram drawing, mistakes in units can cause errors, trigonometry can be challenging for some students.

Practice Questions

• Find the missing angle in a triangle with angles 50° and 60°.
• Calculate the area of a circle with radius 5 cm.
• Use Pythagoras’ theorem to find the hypotenuse of a right triangle with sides 6 cm and 8 cm.
• Find sin, cos, and tan for a right triangle with sides 3, 4, 5.
• Translate a triangle 3 units right and 2 units down on a coordinate grid.
• Convert 2500 m² to hectares.
• Calculate the volume of a cylinder with radius 4 cm and height 10 cm.