Mathematics Higher Level Robert Joinson

©Sumbooks 2002Higher Level45. Loci1. A wheel of diameter 3cm rotates aroundthe inside of a rectangle measuring 8cmby 11cm. Draw accurately the locus of thecentre of the wheel.2. A wheel of diameter 3cm rotates aroundthe outside of a rectangle measuring 10cmby 4cm. Draw the locus of the centre of thewheel.3. A rectangular field ABCD is to have a pipeline laid underneath it. The pipe enters the fieldA 170 metres Bthrough the side AD, is parallel to the side AB110metresand 40 metres from it. After some distance itsroute turns at a point X towards corner C.Between X and C it is always equidistant fromDCthe sides BC and CD. It finally leaves the field by the corner C.Copy the plan of the field, using a scale of 1cm to represent 20 metres. On the plan clearlyindicate the path of the pipe line. Measure and record the distance BX.4. The diagram shows the plan of a garden lawn. Draw an10maccurate diagram using the scale of 1cm to represent 1metre. Point X represents an electrical socket on the5mLawnside of the house. An electric lawn mower has a cableattached to it allowing it to travel up to 9 metres fromthe socket. Show clearly on the diagram the area of thelawn which can be mown.5m5mHouse2mX10m5. A ship sails between two rocks X and Y. The ship is atall times equidistant from both rocks. At point P,when it is the same distance from rocks Y and Z, italters course, keeping to a path which is equidistantfrom Y and Z. Draw an accurate diagram to a scale of5cm to represent 1km to show the route of the ship.What is the distance XP?YDirectionof shipNorth1km30°45°XZ1.2km