SPM 2024 Add Maths Paper 1, Question 9Differentiation

Diagram 6 shows the rectangle ABCD where AB = (5x − 1) cm and BC = 2x cm. At an instant, the value of x changes from 3 cm to (3 + p) cm, such that p is a small value. Using differentiation, express in terms of p, the small change in the area of ABCD, in cm², at that instant.

Diagram 7 shows two lots of land, P and Q. Both lots will be planted completely with the same type of grass. Lot P is a rectangle with dimensions x m by (x − 1) m, and the perimeter of lot P is 54 m. Lot Q is a trapezium with parallel sides 3y m (top) and 5y m (bottom), and perpendicular height (38 − 8y) m; the area of lot Q is A m². (i) Using differentiation, find the value of y such that A is a maximum.

Lot Q is a trapezium with parallel sides 3y m (top) and 5y m (bottom), and perpendicular height (38 − 8y) m. (ii) Hence, determine the lot that will be planted with the most grass. Justify your answer.