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Maths · Geometry and Measures

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Maths · AQA Paper 2

Geometry and Measures

Angles in Parallel Lines and Polygons

Angle facts, angles in parallel lines, and the interior and exterior angles of polygons.

  • Transversal A line that crosses two or more other lines.
  • Parallel lines Lines that stay the same distance apart and never meet, marked with arrows.
  • Alternate angles Equal angles on opposite sides of a transversal between two parallel lines, forming a Z shape.
Three diagrams of parallel lines cut by a transversal, showing alternate angles, corresponding angles and co-interior angles.

Area, Perimeter and Circles

Areas of standard shapes and compound shapes, and the circumference and area of circles, semicircles and sectors.

  • Perimeter The total distance around the outside of a shape.
  • Area The amount of surface inside a shape, measured in square units.
  • Compound shape A shape made up of simpler shapes joined together.
Four labelled shapes, a rectangle, triangle, parallelogram and trapezium, each with its area formula.

Volume and Surface Area

Volumes and surface areas of cuboids, prisms, cylinders, cones and spheres.

  • Volume The amount of space inside a 3D shape, measured in cubic units.
  • Surface area The total area of all the faces of a 3D shape.
  • Cuboid A 3D shape with six rectangular faces.
A triangular prism with its cross-section shaded and the rule that volume equals the area of the cross-section multiplied by the length.

Pythagoras' Theorem

Using Pythagoras' theorem to find sides, test for right angles and solve problems.

  • Right-angled triangle A triangle with one angle of 90 degrees.
  • Hypotenuse The longest side of a right-angled triangle, opposite the right angle.
  • Pythagoras' theorem In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
A 3, 4, 5 right-angled triangle with a square drawn on each side, showing that the two smaller squares have areas 9 and 16 that add up to the largest square of area 25.

Trigonometry in Right-Angled Triangles

Using sine, cosine and tangent, and the exact trigonometric values, to find sides and angles.

  • Trigonometry The study of the links between the sides and angles of triangles.
  • Sine The ratio of the opposite side to the hypotenuse in a right-angled triangle.
  • Cosine The ratio of the adjacent side to the hypotenuse in a right-angled triangle.
A right-angled triangle with the angle theta marked and the sides labelled hypotenuse, opposite and adjacent.