Mathematics AI: INTEGRATION Topical Past Paper Questions

[Maximum mark: 29] In this question researchers are trying to find the most accurate model to use when modelling a population of wolves. Historically, a population of wolves in an area had a stable size of 200. After some years of disruption, the population was reduced to 40 wolv…

The following diagram shows a model of the side view of a water slide. All lengths are measured in metres. The curved edge of the slide is modelled by $$ f(x)=-\frac{1}{4}x^{2}+2x\text{for}0\leq x\leq4. $$ The remainder of the slide is modelled by $$ g(x)=\left\{\begin{aligned}4,…

## [Maximum mark: 12] Gabriel is investigating the shape of model airplane wings. A cross-section of one of the wings is shown, graphed on the coordinate axes. The shaded part of the cross-section is the area between the x-axis and the curve with equation $$ y=2\sqrt{x}-\frac{x}{…