Section 1
Graphs
Find the gradient, $m$, and $y$-intercept, $c$, of the following graphs, and sketch them:a $y=x+1$b $y=x-1$c $y=3 x+5$d $y=\frac{1}{2} x-7$e $y-\pi=0$f $y+\pi-x=0$
Sketch the following graphs:a $y=3$b $x=3$c $2 x+2 y=6$d $x+2 y=-3$e $x-y-3=0$f $2 x+7 y-5=0$
Q? [mechanics] Hooke's law states that the force $F$ (N) exerted on a spring for an extension $x(\mathrm{~m})$ is given by$$F=k x$$where $k$ is the spring stiffness (constant) $(\mathrm{N} / \mathrm{m})$. Plot the graphs of $F$ against $x$ for
[fluid mechanics] The streamlines of a fluid flow are given by$$y=3 x+c$$where $c$ is a constant. On the same axes, sketch the graphs for $c=-10,-5,-1,0,1,5$ and 10
across a capacitor is given by$$V= \begin{cases}2 t & 0 \leq t<1 \\ 4-2 t & t \geq 1\end{cases}$$Sketch the graph of $V$ against $t$ for $0 \leq t \leq 2$[Hint: The graph of $V$ is given in two parts. You sketch $V=2 t$ for $0 \leq t<1$ and then sketch $V=4-2 t$ for $t \geq 1 .]$