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Interactive tools for IGCSE constructions, transformations, and graphs. Practice compass constructions, measure angles, plot functions, and explore coordinate geometry.
Use the Compass tool to draw accurate construction circles — click a centre point, drag to set radius. Use the Angle tool to click three points (A, B vertex, C) and measure the angle at B. All other tools (pencil, line, circle, arc) work as normal.
Looking for basic freehand drawing? Open the Sketch Pad.
Type a function using x as the variable and click Plot. Up to three functions can be plotted simultaneously in different colours. X-intercepts and y-intercepts are automatically detected and labelled.
Examples: x^2 + 2*x - 3 sin(x) 2*x - 1 sqrt(x)
Use x as variable. E.g. x^2 + 2*x - 3, sin(x), 2*x + 1
Plot points on the grid, or use the Distance and Midpoint tools. Click two points and the calculation is shown with the formula. Enable Snap to Grid for integer coordinates.
Click to plot a point on the grid.
Add geometry shapes to the canvas as construction references. Drag them into position. Resize with the + / − buttons. Useful for understanding angle relationships and building compound diagrams.
Drag shapes to reposition. Add multiple shapes to build a construction diagram.
Common exam tips and examiner insights for Paper 3 and 4 geometry questions.
Examiners check your method, not just your answer. If you rub out arcs from a perpendicular bisector, you can lose method marks even if the line is correct.
Set your compass to more than half the line length. Draw arcs from both endpoints — they must cross on both sides. Join the two intersections. A common mistake is drawing arcs of different radius.
Open compass from the vertex. Strike arcs on both arms of the angle. From each intersection, draw equal arcs that cross inside the angle. Join the vertex to that intersection.
Any angle inscribed in a semicircle (with the diameter as the chord) is always 90°. This is the "angle in a semicircle" theorem — a favourite on Paper 2.
When a transversal crosses parallel lines, corresponding angles (F-shape) are equal. Alternate angles (Z-shape) are also equal. Co-interior angles (C-shape) add up to 180°.
The distance formula d = √((x₂−x₁)² + (y₂−y₁)²) is just Pythagoras on a grid. Draw the triangle, find the horizontal and vertical differences, apply Pythagoras.
Apply your construction and graph skills to real IGCSE past paper questions. Our AI tutor gives you step-by-step feedback on every answer.