Key Concepts: Angles in polygons, circle theorems, area and perimeter calculations. Sum of interior angles in an n-sided polygon = (n-2) × 180°. Circle area = πr², circumference = 2πr.
Section A: Angles and Polygons
1. Calculate the sum of interior angles in: [3]
(a) A pentagon
(b) An octagon
(c) A decagon
2. A regular hexagon has interior angles. [2]
(a) Calculate each interior angle
(b) Calculate each exterior angle
Section B: Circle Properties
3. A circle has radius 7 cm. [3]
(a) Calculate the circumference (use π = 22/7)
(b) Calculate the area
4. A circular garden has diameter 14 m. [2]
(a) Calculate the area of the garden
(b) If fencing costs £12 per meter, calculate the cost to fence the perimeter
Section C: Composite Shapes
5. A shape consists of a rectangle 8 cm by 5 cm with a semicircle on one 5 cm side. [3]
(a) Calculate the total area
(b) Calculate the total perimeter
Total marks: 20
Mark Scheme
1. (a) (5-2) × 180° = 540° [1]
(b) (8-2) × 180° = 1080° [1]
(c) (10-2) × 180° = 1440° [1]
2. (a) Sum = (6-2) × 180° = 720°; Each angle = 720°/6 = 120° [2]
(b) Exterior angle = 180° - 120° = 60° (or 360°/6) [1]
3. (a) C = 2πr = 2 × (22/7) × 7 = 44 cm [2]
(b) A = πr² = (22/7) × 49 = 154 cm² [1]
4. (a) r = 7 m; A = π × 49 = 154 m² [1]
(b) C = 44 m; Cost = 44 × 12 = £528 [1]
5. (a) Rectangle area = 40 cm²; Semicircle area = π(2.5)²/2 = 9.82 cm²; Total ≈ 49.82 cm² [2]
(b) Perimeter = 8 + 5 + 8 + semicircle arc = 21 + π(2.5) ≈ 28.85 cm [1]