IGCSE Mathematics - International (0607) — October–November 2024, Paper 63

A: INVESTIGATION — DIAGONAL SQUARES (30 marks). D(h, w) is the number of diagonal squares in an h by w grid, where h is the number of rows and w is the number of columns. For…

This question is about grids with h = 2. A 2 by 2 grid has 2 rows each with 1 diagonal square and 1 row of 2 diagonal squares, so D(2,2) = 2 × 1 + 1 × 2 = 4. A 2 by 4 grid: D(2,4)…

This question is about grids with h = 3. A 3 by 5 grid has 3 rows each with 4 diagonal squares and 2 rows each with 5 diagonal squares, so D(3,5) = 3 × 4 + 2 × 5 = 22. Work out…

In an h by w grid there are: • h rows with (w − 1) diagonal squares • (h − 1) rows with w diagonal squares. Show that D(h, w) = 2hw − (h + w).

This question is about a square grid with n rows and n columns. This is an n by n grid. D(h, w) = 2hw − (h + w). Show that the number of diagonal squares in an n by n grid, D(n,…

A grid is a rectangle. It has 31 diagonal squares. D(h, w) = 2hw − (h + w) Find the sizes of the possible rectangular grids when h < w.

B: MODELLING — SAFE OVERTAKING (30 marks). This task looks at the distance travelled by a car when overtaking a truck. The table shows the distance of a car from a fixed point on…

A car and a truck travel in the same direction along a road. The sketch graph shows their distances from a fixed point on the road. Write down the number of metres the truck is in…

This question is about what happens when a car overtakes a truck. The diagrams are not to scale. The car has length 7 metres. The truck has length 15 metres. The car moves into…