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Tennis
A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area?
How Big?
If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?
Triangular Tantaliser
Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
Age 11 to 14 Challenge Level:
Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
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Pythagoras' theorem. Enlargements and scale factors. 2D shapes and their properties. Circle properties and circle theorems. Creating and manipulating expressions and formulae. Mathematical reasoning & proof. Visualising. Regular polygons and circles. Similarity and congruence. Area - circles, sectors and segments.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.