Conjecturing and generalising

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Favourite

Vector Journeys

Age

14 to 18

Challenge level

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
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Favourite

Which Spinners?

Age

14 to 18

Challenge level

Can you work out which spinners were used to generate the frequency charts?
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Favourite

Summing Geometric Progressions

Age

14 to 18

Challenge level

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
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Favourite

Negative Powers

Age

14 to 18

Challenge level

What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?
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All Tangled Up

Age

14 to 18

Challenge level

Can you tangle yourself up and reach any fraction?
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Difference of Odd Squares

Age

14 to 18

Challenge level

$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?
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Degree Ceremony

Age

16 to 18

Challenge level

Can you find the sum of the squared sine values?
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Chord

Age

16 to 18

Challenge level

Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.
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Least of All

Age

16 to 18

Challenge level

A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.
problem
Favourite

Tangled Trig Graphs

Age

16 to 18

Challenge level

Can you work out the equations of the trig graphs I used to make my pattern?