67 a Yes B1 2 B1 for yes M B1 B1 for clear diagram or explanation Yes Yes b B1 B1 for yes Yes B1 B1 for clear diagram or explanation c B1 B1 for yes B1 B1 for clear diagram or explanation B1 B1 for yes B1 B1 for clear diagram or explanation 8 68 If cuboid has dimensions and False B1 2 B1 for false H x, y t The surface area = 2(xy + + M1 M1 for surface area with either specific lengths or a xt yt) generalisation Volume = xyt Double the lengths gives dimensions as 2x, M1 M1 for volume with either specific lengths or a generalisation 2y and 2t So surface area = 2( 2x × 2y + 2x × 2t + 2y M1 M1 for showing correct follow through of double the lengths × 2t) = 2(4xy + 4xt + 4yt) = 8(xy + + B1 M1 for a correct statement of surface area with their xt yt) data Which is 4 times the first area B1 B1 for 4 times area And = 2x × 2y × 2t V B1 B1 for a correct statement of volume with their data = 8xyt B1 B1 for 8 times volume which is 8 times the first volume. 8
67 a b c Yes Yes Yes Yes B1 B1 B1 B1 B1 B1 B1 B1 2 B1 for yes B1 for clear diagram or explanation B1 for yes B1 for clear diagram or explanation B1 for yes B1 for clear diagram or explanation B1 for yes B1 for clear diagram or explanation M 8 68 If cuboid has dimensions x, y and t The surface area = 2(xy + xt + yt) Volume = xyt Double the lengths gives dimensions as 2x, 2y and 2t So surface area = 2( 2x × 2y + 2x × 2t + 2y × 2t) = 2(4xy + 4xt + 4yt) = 8(xy + xt + yt) Which is 4 times the first area And V = 2x × 2y × 2t = 8xyt which is 8 times the first volume. False B1 M1 M1 M1 B1 B1 B1 B1 2 B1 for false M1 for surface area with either specific lengths or a generalisation M1 for volume with either specific lengths or a generalisation M1 for showing correct follow through of double the lengths M1 for a correct statement of surface area with their data B1 for 4 times area B1 for a correct statement of volume with their data B1 for 8 times volume H 8