66 3 H C1 C1 for good clear diagram showing perpendiculars to Y Drop perpendiculars down to Y and X and and Z complete the trapezium, with the top triangle being ABT, as shown. Length TB will be the same as YZ. Use theorem on triangle ABT. Pythagoras’ TB2 = 92 32 – = 81 9 – = 72 C1 C1 for clear diagram of ABT TB = = 8.485 281 4 C1 C1 for clear explanation of how the triangle ABT has been formed M1 M1 for use of theorem Pythagoras’ A1 A1 for correct statement 8.49 cm A1 A1 for correct answer to 2 or 3 sf 6 67 Circle Theorem 1 states The angle at the P2 3 P1 for stating Theorem 1 H centre of a circle is twice the angle at the P1 for extending this to this proof circumference when they are both C1 C1 for clear overall explanation and clarity subtended by the same arc.Theorem 1 tells you that any angle subtended from arc AB at a point C on the circumference is always half the angle subtended from arc AB at the centre. C1 C1 for use of diagram and mathematical language. Therefore, every possible angle subtended from arc AB at the circumference will correspond to the same angle at the centre. Hence angles subtended at the circumference are equal. 4
66 Drop perpendiculars down to Y and X and complete the trapezium, with the top triangle being ABT, as shown. Length TB will be the same as YZ. Use Pythagoras’ theorem on triangle ABT. TB2 = 92 – 32 = 81 – 9 = 72 TB = = 8.485 281 4 8.49 cm C1 C1 C1 M1 A1 A1 3 C1 for good clear diagram showing perpendiculars to Y and Z C1 for clear diagram of ABT C1 for clear explanation of how the triangle ABT has been formed M1 for use of Pythagoras’ theorem A1 for correct statement A1 for correct answer to 2 or 3 sf H 6 67 Circle Theorem 1 states The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc.Theorem 1 tells you that any angle subtended from arc AB at a point C on the circumference is always half the angle subtended from arc AB at the centre. Therefore, every possible angle subtended from arc AB at the circumference will correspond to the same angle at the centre. Hence angles subtended at the circumference are equal. P2 C1 C1 3 P1 for stating Theorem 1 P1 for extending this to this proof C1 for clear overall explanation and clarity C1 for use of diagram and mathematical language. H 4
Higher_Skills_Geometry_MarkScheme_Edexcel.docx