Mathematics AI: DIFFERENTIATION Topical Past Paper Questions

[Maximum mark: 16] Jenny designs a flexible suspension bridge, spanning 10 metres over the Swinburne Creek. Jenny believes that when no people are on the bridge, the height, y, of the walkway on the bridge above the creek can be modelled by $$ y=ax^{2}+bx+c\text{for}0\leq x\leq10…

[Maximum mark:21] Andrew designs a fibreglass water slide for a water park. Let x be the horizontal distance, in metres, from the start of the water slide. Let h be the height, in metres, of the water slide above the horizontal ground. The following diagram shows a cross section…

## [Maximum mark: 19] Howell Industries is an international company that sells travel coffee mugs. Their market research predicts that the average number of mugs they will sell each month is modelled by the equation $$ n = 20\,000 - 1000x $$ where $x$ represents the selling price…