GCSE Maths: Geometry & Measures — Quick Burst Practice

Inside GCSE Maths: Geometry & Measures — Quick Burst Practice

fire through missing angles, polygon interior and exterior angles, area and perimeter, circle area and circumference, then Pythagoras and basic trig. All auto-marked, no long working. About 10 minutes.

Learning objectives

• angle rules — on a straight line, at a point and in a triangle;
• polygon angles — the (n − 2) × 180° interior sum and the 360° exterior rule;
• area and perimeter of rectangles and triangles;
• circle area (πr²) and circumference (πd), using π = 3.14 and in terms of π;
• Pythagoras’ theorem (a² + b² = c²) and basic right-angled trigonometry.

Activities in this book

1. Round 1 — Angle Rules

   angles on a straight line add to 180°, angles at a point add to 360°, and the angles in a triangle add to 180°. Between parallel lines, co-interior (allied) angles add to 180°.

2. Round 2 — Polygon Angles

   interior angles of an n-sided polygon add to (n − 2) × 180°. Exterior angles always add to 360°, so a regular polygon’s exterior angle is 360° ÷ n and its interior angle is 180° − the exterior angle.

3. Round 3 — Area & Perimeter

   rectangle area = base × height; triangle area = ½ × base × height. Perimeter is the total distance all the way round the edge.

4. Round 4 — Circles

   circle area = πr² and circumference = πd. Each question tells you whether to use π = 3.14 or to leave the answer in terms of π.

5. Round 5 — Pythagoras & Trig

   Pythagoras’ theorem: a² + b² = c², where c is the hypotenuse (the longest side). The triples 6-8-10 and 8-15-17 give exact hypotenuses. For angles use SOHCAHTOA: opposite = hypotenuse × sin(angle).

Suggestions for teaching

• Name the rule first. Ask learners to state the angle or shape rule before typing — recall speed comes from knowing which rule applies.
• Drill the triples. 6-8-10 and 8-15-17 give instant hypotenuses — check them with a² + b² = c².
• Read the π instruction. Point out when to use π = 3.14 and when to leave an answer in terms of π — both appear in GCSE papers.
• Beat the clock. Re-run the drill timed to build fluent, exam-ready recall.