8 (a) (i) Write down the order of rotational symmetry of the diagram. ................................................. [1] (ii) On the diagram, draw all the lines of symmetry. [2] (b) The grid shows the first three diagrams in a sequence. Each diagram is made using small grey and small white squares to make grey and white columns. Diagram 1 Diagram 2 Diagram 3 Diagram 4 (i) On the grid, draw Diagram 4. [1] (ii) (a) Complete this statement. Diagram n has ............................. grey columns. [1] (b) Find an expression, in terms of n, for the total number of columns in Diagram n. ................................................. [2] (c) Find an expression, in terms of n, for the fraction of columns that are grey in Diagram n. ................................................. [1] © UCLES 2023 0580/32/F/M/23 15 (iii) Diagram number 1 2 3 4 5 Number of grey squares 6 8 10 Number of white squares 3 8 15 Total number of squares 9 16 25 (a) Complete the table. [3] (b) Write an expression, in terms of n, for the number of grey squares in Diagram n. ................................................. [2] (c) The number of white squares in Diagram n is n(n+2). Work out the number of white squares in Diagram 30. ................................................. [2] (d) Diagram k has a total of 1296 squares. Work out the value of k. k = ................................................ [2] Question 9 is printed on the next page. © UCLES 2023 0580/32/F/M/23 [Turn over 16