Mathematics Higher Level Robert Joinson

©Sumbooks 2002Higher Level53. Degree of Accuracy1. A length of wood measures 3 metres long by 10cm wide. Smaller pieces of wood are to becut from it, each measuring 10cm by 35mm, the width correct to the nearest millimetre.Calculate the maximum and minimum number of pieces that can be cut from it.2. Mugs are made in the shape of a cylinder, with internal dimensions of 9.3cm tall and 7.5cmdiameter, both measurements correct to the nearest millimetre.a) What is the maximum amount of liquid it will hold?b) What is the minimum amount of liquid it will hold?3. A garden is 15 metres long, correct to the nearest metre. A path is made with cobblesmeasuring 22cm long by 8.5cm wide, both dimensions correct to the nearest millimetre.The cobbles are laid side by side without any space between them, in the way shown in the15 metresdiagram with the long sides touching. How many cobbles must be ordered to ensure thepath is completed?4. Tiles are made to the dimensions shown in the diagram, correct to the nearest millimetre.8.4cm4.1cmx cm gapThey are fitted together in the way shown with two shorter sides against a longer side, andthe top and bottom edges level. Calculate the maximum and minimum values of the gap, x .5. Erasers are made in the shape of a cubiod measuring 1cm by 2cm by 4.5cm. All dimensionscorrect to the nearest millimetre.a) Calculate the maximum volume an eraser can be.b) What is the minimum volume it can be?c) If the manufacturer produces all the erasers to the lower dimensions, what is theirpercentage saving in rubber, over the maximum dimension?6. The plans of a new warehouse show that the floor measures 50 metres by 26 metres, correctto the nearest metre. The concrete floor is to be covered with paint . The paint covers 15m 2per litre.a) What amount of paint needs to be ordered to ensure that the floor is covered?b) What is the maximum amount of paint that will be left over if this is bought?7. Floor tiles measure 20cm square, correct to the nearest millimetre. A rectangular floormeasures 4.21 metres long by 3.84m wide, both measurements correct to the nearestcentimetre.a) What is the maximum number of tiles needed to fit on one row along the length of thefloor?b) What is the maximum number of tiles needed to fit along the width of the room?c) What is the maximum number of tiles needed for the whole of the room?d) Ian buys the maximum number of tiles needed, but finds that they have been made totheir maximum size and the room measured to its minimum size. How many tiles does hehave left over?