5c Award mark for a correct answer using their value of from part b. p Pearson Progression Step Q Scheme Marks AOs and Progress descriptor States the recurrence relation. Choice of variable is not 6a M1 3.1a 5th important. or Work with sequences defined Defines the first value. Accept either use of or . or M1 3.1a by simple recurrence relations. (2) Makes an attempt to find the height, for example is seen. 3.1a 5th 6b M1 Work with the nth States that the maximum height would be 13.445… cm. Accept A1 1.1b term formula for awrt 13.4 geometric sequences. (2) Attempts to make use of the sum to infinity. For example, or is 6c M1 3.1a 6th seen. Use geometric sequences and Understands that the ball travels upwards and then downwards, M1 3.1a series in context. so multiplies by 2. or is seen. Recognises that when the ball is dropped, it initially only travels M1 3.1a downwards. Either or is seen or implied. States a fully correct answer of cm. Accept awrt 453.3 cm. 1.1b A1 (4) is very unlikely that the ball will not bounce vertically’ or 3.5 6th 6d B1 ‘It assumes the ball will continue to bounce forever’. ‘This Understand convergent geometric series and the sum to infinity. (1)
5c Award mark for a correct answer using their value of p from part b. Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 6a States the recurrence relation. Choice of variable is not important. or M1 3.1a 5th Work with sequences defined by simple recurrence relations. Defines the first value. Accept either use of or . or M1 3.1a (2) 6b Makes an attempt to find the height, for example is seen. M1 3.1a 5th Work with the nth term formula for geometric sequences. States that the maximum height would be 13.445… cm. Accept awrt 13.4 A1 1.1b (2) 6c Attempts to make use of the sum to infinity. For example, or is seen. M1 3.1a 6th Use geometric sequences and series in context. Understands that the ball travels upwards and then downwards, so multiplies by 2. or is seen. M1 3.1a Recognises that when the ball is dropped, it initially only travels downwards. Either or is seen or implied. M1 3.1a States a fully correct answer of cm. Accept awrt 453.3 cm. A1 1.1b (4) 6d ‘It is very unlikely that the ball will not bounce vertically’ or ‘This assumes the ball will continue to bounce forever’. B1 3.5 6th Understand convergent geometric series and the sum to infinity. (1)