This mini-lesson covers the Geometry & measures strand of AQA GCSE Maths (8300): angles, polygons, Pythagoras, trigonometry (SOHCAHTOA), area & volume, circle theorems, transformations, vectors, and bearings.
These games test recall of facts, formulae and methods — not full multi-step working. Answer the questions as you go and collect ⭐ stars. Press Start when you're ready.
Learn the key angle sums — they're the building blocks of every angle problem:
A triangle has angles 90° and 35°. Find the third.
Angles in a triangle sum to 180°.
180 − 90 − 35 = 55°
Parallel lines: co-interior (allied) angles add to 180°; alternate ("Z") and corresponding ("F") angles are equal.
For a polygon with n sides:
Sum of interior angles of a hexagon (n = 6).
(6 − 2) × 180 = 4 × 180 = 720°
Regular polygons: each exterior angle = 360 ÷ n. For a regular hexagon that's 60°, so each interior angle is 180 − 60 = 120°.
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides:
Finding a shorter side? Rearrange: a² = c² − b². Subtract, don't add, when the hypotenuse is already known.
In a right-angled triangle, the sides are named relative to an angle: opposite, adjacent and hypotenuse.
Find the opposite side when the angle is 30° and the hypotenuse is 10 cm.
sin 30° = O ÷ 10, and sin 30° = 0.5
O = 10 × 0.5 = 5 cm
Exact values to know: sin 30° = ½, cos 60° = ½, tan 45° = 1, sin 90° = 1.
Learn the standard formulae. For a circle of radius r:
Area of a circle with radius 5 cm (use π ≈ 3.14).
area = π × 5² = π × 25
≈ 3.14 × 25 = 78.5 cm²
Don't mix them up: circumference uses the diameter (πd) or 2πr; area uses r squared (πr²).
The key circle theorems each give an angle relationship:
The angle at the circumference is 40°. Find the angle at the centre on the same arc.
Centre angle = 2 × circumference angle = 2 × 40 = 80°
Tangent facts: a tangent meets a radius at 90°, and two tangents from a point are equal in length.
A bearing is an angle measured clockwise from North, always written with three figures.
The bearing of B from A is 070°. Find the bearing of A from B (the back-bearing).
Add 180°: 70 + 180 = 250°
Three figures always: a bearing of 40° must be written 040°. Back-bearing: add 180° if under 180, subtract 180° if over.
Tap a quantity on the left, then its correct formula on the right.
A congruent transformation keeps the shape the same size (translation, rotation, reflection). A similar transformation (enlargement, scale factor ≠ 1) changes the size but keeps the shape. Tap a transformation, then the box it belongs in.
Angles: line = 180°, point = 360°, triangle = 180°; parallel-line rules.
Polygons: interior sum = (n − 2)×180°; exterior sum = 360°.
Pythagoras: a² + b² = c² for right-angled triangles.
Trig: SOHCAHTOA — sin = O/H, cos = A/H, tan = O/A.
Area & volume: circle area = πr², triangle = ½bh, cuboid = lwh.
Circle theorems: centre = 2× circumference; semicircle = 90°.
Bearings: clockwise from North, 3 figures; back-bearing ± 180°.
Transformations & vectors: translations, rotations, reflections keep size; enlargements change it.
You've covered every Geometry & Measures sub-topic in AQA 8300. Press Finish to see your score.
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