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Math Applications HL Paper 1 (May 2025, TZ2)

  1. [Maximum mark: 7]

A climate scientist is modelling an ice sheet as a rectangle.

She believes that the width (x km) is increasing at a constant rate of 10 km per year and the length (y km) is decreasing at a constant rate of 5 km per year.

The time, t, is measured in years, and the area, A, is measured in km².

When t = 0 then x = 75 and y = 40.

(a) Find dA/dt when t = 0. [3]

(b) State, with justification, whether the area of the ice sheet is increasing or decreasing when t = 0. [1]

(c) Find the change in the area of the ice sheet between t = 0 and t = 1. [3]