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### Number and algebra

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# Cushion Ball

If you draw copies of the table reflected in the cushions then the reflection of the path of the ball after hitting a cushion appears as a straight line in the image of the table.

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If you draw copies of the table reflected in the cushions then the reflection of the path of the ball after hitting a cushion appears as a straight line in the image of the table.

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.