AS Core Maths constructions
Setting students problems that require them to construct objects in Geogebra can test their understanding of ideas and reinforce generalisation.
AS Core Maths constructions contains examples from AS Core Mathematics.
- Create a two points A and B on the x axis. Construct a quadratic graph that passes through A and B.
Example 0 - Create two points A and B. Construct a third point C which lies on the line perpendicular to AB passing through A and is twice as far away from A as B is.
Example 1 - Create points A, B and C fixed to the x-axis and D fixed to the y-axis. Construct a cubic that
passes through A, B, C and D.
Example 2 - Create a triangle with one point on the origin and one point on the x-axis. Construct circles
centred on each vertex such that all three circles touch each other.
Example 3 - Create a graph of a quadratic equation that can be moved by dragging the vertex.
a. Construct the tangent to the curve with gradient 2 (that works for the vertex in any position).
b. Construct the tangent to the curve with gradient b (that works for the vertex in any position).
Example 4b
Example 4b - Draw the graph of a straight line through the origin. NB this must be defined as a function, e.g. f(x)= x or f(x)=2x. Add a point A on the positive x-axis.
a. Construct a point B such that the integral of f(x) between A and B is 8.
b. Construct a point B such that the integral of f(x) between A and B is d.
c. Construct a point B such that the integral of f(x)=mx between A and B is d for any value of m or d.
Example 5a
Example 5b
Example 5c - Construct a triangle with sides a and b and angle A that demonstrates the ambiguous case of the
Sine rule.
Example 6 - Draw the graph of y=ax and add the point A on the curve. Construct a point B based on A that you can use with the Trace function to obtain the shape of
y = logax.
Example 7 - Create two points A and B. Construct a cubic that has stationary points at A an B. (Hint – the
midpoint of A and B may help).
Example 8
