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A Fractional Sequence

The initial investigation uses an inductive formula and two initial values to derive a sequence that results in a series of fractions before returning to the initial two values of the sequence. A spreadsheet is provided that performs the calculations given in the inductive formula. This is helpful for both checking...

Area Between Parabolas

Two parabolas are shown, one with a positive quadratic coefficient, the other with a negative quadratic coefficient. Each has the same linear coefficient and between the...

Skew Lines

This problem involves using vectors to model 3D space. Two skew lines are presented and the challenge is to find the shortest distance between the lines. In addition, the...

Survey Plot

There are a series of 8 sided polygons for which the areas are to be calculated. The area of each one turns out to be the same. This provides a lead in to asking how the...

Volume of a Tetrahedron

The coordinates of the vertices of a tetrahedron is given. The challenge is to work out the volume of the tetrahedron. This involves calculating the area of the base,...

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...

Galapagos Conservation (Ages 16-19) *suitable for home teaching*

From ARKive, these resources help students to learn about the Galapagos Islands, their biodiversity and conservation. Through a series of activities, students look at: * the scientific history and importance of the Galapagos Islands * the species that inhabit the islands including the concept of endemic species *...

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