← Additional Mathematics syllabus

SingaporeAdditional Mathematics

Coordinate Geometry and Circles

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How can we find the area of a polygon directly from the coordinates of its vertices?

Find the area of a triangle or polygon from the coordinates of its vertices using the shoelace determinant method
A focused answer to the O-Level A-Maths outcome on areas from coordinates. The shoelace method for the area of a triangle or polygon, vertex ordering, and using a zero area as a collinearity test.
8 min answer →

How do gradients, distances and midpoints let us describe and relate straight lines in the plane?

Find the gradient, length and midpoint of a line segment, write the equation of a line, and use the conditions for parallel and perpendicular lines
A focused answer to the O-Level A-Maths outcome on straight lines. The gradient, distance and midpoint formulae, forms of the equation of a line, and the parallel and perpendicular conditions.
9 min answer →

How do we write the equation of a circle and recover its centre and radius from either standard or general form?

Write the equation of a circle in standard and general form and find the centre and radius by completing the square
A focused answer to the O-Level A-Maths outcome on the circle. The standard and general equations of a circle, finding the centre and radius by completing the square, and building the equation from given data.
9 min answer →

How do we find where a line meets a circle and the equation of a tangent to a circle?

Find the intersection of a line and a circle, determine tangency using the discriminant or perpendicular radius, and find tangent equations
A focused answer to the O-Level A-Maths outcome on lines meeting circles. Finding intersection points, deciding tangency via the discriminant or perpendicular radius, and writing the equation of a tangent.
9 min answer →