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Parabola in a Parallelogram

A parabola is given with the x-coordinate of the minimum point, and two points on the parallelogram shown. The points are joined and then a parallel line is drawn that is a...

How Close

The coordinates of two points on a line are given. The task is to find the shortest distance from the line of a third given point. The task involves finding the equation of...

Find f(2)

The maximum value of a quadratic function is given, together with the value of f(3) and the information that this is equal to f(-1). The challenge is to determine the coefficients of the quadratic. This involves the use of symmetry and solution of a simultaneous equation.

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Quadratic Segments

The investigation begins by looking at the area of three segments related to a quadratic. The first segment is the area between the curve and the x-axis. Each of the other...

Sine Rule Discovery

The investigation begins by looking at the area of three segments related to a quadratic. The investigation begins with a practical investigation using measurement of lengths and angles. The...

Parallelogram in a Quadrilateral (grid version)

There are a series of quadrilaterals presented on a grid. The initial task is to form the shape derived by joining the midpoints of each side. The resulting quadrilateral is in each case a...

Parallelogram in a Quadrilateral (Construction)

There are a series of quadrilaterals on is presented on plain paper. The initial task is to form the shape derived by joining the midpoints of each side. The resulting quadrilateral is in each...

Trapezium and Diagonals

The opposite corners of a trapezium are joined, creating four triangles within the trapezium. The areas of the triangles formed using the parallel sides as is given. The task is to calculate the...

Four Crescents

A diagram is shown with a circle, centred on a rectangle with given dimensions.  Semi-circular arcs are drawn with the sides of the rectangle as diameters. The areas between the semi-circles and the circles form crescents. The task is to calculate the area of the crescents.

When working on the numerical...

Triangle xy Area

A circle is drawn that is tangent to the three sides of the triangle. The two constituent lengths of the hypotenuse are given and the challenge is to calculate the area of the triangle. When...

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