Exercise 1 — Cambridge IGCSE 0580 Mar 2023 Paper 12 Q13
Show mark scheme
Cambridge IGCSE·Mathematics 0580·Extended
Regions On The Plane
Key knowledge — Co Ordinate Geometry
Formulas & equations
Distance between two points: d = √((x₂−x₁)² + (y₂−y₁)²)Midpoint: M = ((x₁+x₂)/2 , (y₁+y₂)/2)Equation of a line through (x₁,y₁) with gradient m: y−y₁ = m(x−x₁)Gradient: m = (y₂−y₁) ÷ (x₂−x₁)
Key facts & rules
- Parallel lines: same gradient.
- Perpendicular lines: gradients multiply to −1.
- The equation of a circle with centre (a,b) and radius r: (x−a)² + (y−b)² = r².
- A tangent to a circle is perpendicular to the radius at the point of contact.
IGCSE Co-ordinate geometry — Regions on the plane Practice Extended
7 Cambridge IGCSE 0580 questions on regions on the plane at the Extended tier — each with its full mark scheme. For the Core tier on the same skill, click here.
How to approach regions on the plane — open the study guide
Regions on the plane on IGCSE 0580
Draw boundary lines for each inequality. Use a dashed line for strict inequalities (< or >) and a solid line for ≤ or ≥. Shade the required region or label it R. Test a point to confirm which side to shade.
Practice exercises
Exercise 2 — Cambridge IGCSE 0580 Mar 2023 Paper 22 Q3
Show mark scheme
Exercise 3 — Cambridge IGCSE 0580 Jun 2023 Paper 22 Q20
Show mark scheme
Exercise 4 — Cambridge IGCSE 0580 Jun 2023 Paper 23 Q11
Show mark scheme
Exercise 5 — Cambridge IGCSE 0580 Jun 2023 Paper 41 Q8
Show mark scheme
Exercise 6 — Cambridge IGCSE 0580 Jun 2024 Paper 12 Q13
Show mark scheme
Exercise 7 — Cambridge IGCSE 0580 Jun 2024 Paper 21 Q11
Show mark scheme
