Mathematics AI: GRAPHS Topical Past Paper Questions

[Maximum mark:26] This question considers whether it is reasonable to go on all the rides in a theme park and get back to the entrance in two and a half hours. Martin is visiting a theme park. He will enter the park at 09:00 and must leave the park by 11:30. He uses information a…

[Maximum mark: 9] Consider the function $f(x)=x\sqrt{3-x^{2}}$, $-\sqrt{3}\leq x\leq\sqrt{3}$. (a) Sketch the graph of $y = f(x)$ on the following pair of axes. [2] The area between the graph of $y = f(x)$ and the x-axis is rotated through $360^{\circ}$ about the x-axis. (b) (i)…

[Maximum mark: 5] Gloria wants to model the curved edge of a butterfly wing. She inserts a photo of the wing into her graphing software and finds the coordinates of four points on the edge of the wing. Gloria thinks a cubic curve will be a good model for the butterfly wing. (a) F…