IGCSE Mathematics - International (0607) — May–June 2024, Paper 63

A: INVESTIGATION — CHANGING THE ORDER OF OPERATIONS (30 marks). This investigation is about the results of two calculations when you change the order of operations. Each…

Show that when x = 3, y = 4 and z = 9 the two calculations give the same result.

y = 5 and z = 6. Find the value of x when the two calculations give the same result.

Complete the table. x y z Result of calculation 1 Result of calculation 2 --- --- --- --- --- 6 11 12 138 138 7 13 14 189 8 15 16 248 9 17 18

In this question x, y and z are consecutive, for example 15, 16 and 17. Write y and z in terms of x.

When the result of calculation 1 is the same as the result of calculation 2, x(y + z) = x + yz. x(x − 1) = (y − x)(z − x) Expand the brackets and rearrange to show that this…

B: MODELLING — FARMERS' FIELDS (30 marks). This task looks at the area of a field inside a fence. A farmer uses 600 metres of fencing to make a rectangular field. The length of…

The farmer uses a wall as one side of the field. The farmer uses 500 metres of fencing for this field. The length of the field (the side parallel to the wall) is x metres. Find a…

The farmer uses the model A = x(300 − x). These are the costs for making the field: grass seed $0.27 per square metre; fertiliser $0.08 per square metre; a total of $7000 for…

The farmer makes a rectangular field. The length of the diagonal is 200 metres. The angle between the diagonal and one side is w. Show that a model for the area, A m², of this new…