Coordinate Geometry · Paper 1 — Free Maths AI HL Practice Questions

The cost, $C$ dollars, of renting a bicycle is modelled by $C = mt + c$, where $t$ is the rental time in hours, $m$ is the hourly rate in dollars per hour, and $c$ is a fixed booking fee in dollars. For a 3-hour rental the cost is 22 USD. For a 7-hour rental the cost is 42 USD.

A small business sells handmade candles. The weekly profit, $P$ dollars, is modelled as a linear function of the number of candles sold, $x$. When $20$ candles are sold, the profit is $\text{USD }50$. When $50$ candles are sold, the profit is $\text{USD }230$.

A small aircraft is flying at constant altitude on a straight path. At 14:00 its position is $A(10, 8, 2)$, where coordinates are in kilometres relative to a control tower at origin $O$, with $x$ East, $y$ North, and $z$ vertical. At 14:06 it passes point $B(28, 14, 2)$.