1. 1
   A physics class studies motion formulae. The first is $v=u+at$, where $v$ is final velocity, $u$ is initial velocity, $a$ is acceleration and $t$ is time. The second is $s=\frac{1}{2}(u+v)t$. The third involves a pendulum's period, $T=2\pi\sqrt{\frac{l}{g}}$.

   (a)

   Make $t$ the subject of $v=u+at$.

   [1 mark]

   • A$t=\frac{a}{v-u}$
   • B$t=\frac{v+u}{a}$
   • C$t=v-u-a$
   • D$t=\frac{v-u}{a}$

   (b)

   Make $u$ the subject of $s=\frac{1}{2}(u+v)t$.

   [1 mark]

   • A$u=\frac{2s}{t}+v$
   • B$u=\frac{2s}{t}-v$
   • C$u=2s-vt$
   • D$u=\frac{s}{t}-v$

   (c)

   Make $l$ the subject of $T=2\pi\sqrt{\frac{l}{g}}$.

   [1 mark]

   • A$l=\frac{T^2}{4\pi^2g}$
   • B$l=\frac{4\pi^2g}{T^2}$
   • C$l=\frac{gT^2}{4\pi^2}$
   • D$l=g\left(\frac{T}{2\pi}\right)$

   Total for question 1: 3 marks

2. 2
   A carpenter uses the perimeter formula $P=2l+2w$ for a rectangular frame, and later needs to convert temperatures using $F=\frac{9C}{5}+32$.

   (a)

   The perimeter of a rectangle is given by $P=2l+2w$, where $l$ is length and $w$ is width. Make $w$ the subject of the formula.

   [2 marks]

   (b)

   The formula $F=\frac{9C}{5}+32$ converts a temperature $C$ in Celsius to $F$ in Fahrenheit. Make $C$ the subject of this formula.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A quarry stores gravel in conical piles with volume $V=\frac{1}{3}\pi r^2h$. The quarry also uses a formula for average speed over a journey, $S=\frac{D}{T}$, and needs it rearranged in terms of the travel time, $T$, where the total distance is split into two legs.

   (a)

   The volume of a cone is given by $V=\frac{1}{3}\pi r^2h$, where $r$ is the base radius and $h$ is the height. Make $h$ the subject of this formula, showing your working.

   [3 marks]

   (b)

   A delivery van's average speed is given by $S=\frac{D_1+D_2}{T_1+T_2}$, where $D_1,D_2$ are two distances and $T_1,T_2$ are two times. Make $T_2$ the subject of this formula.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   An engineer uses the kinetic energy formula $E=\frac{1}{2}mv^2$, where $m$ is mass in kilograms and $v$ is speed in metres per second. The same engineer also studies the formula for the surface area of a sphere, $A=4\pi r^2$, and a formula relating the period of oscillation of a spring, $T=2\pi\sqrt{\frac{m}{k}}$, where the subject $m$ needs to be made the subject after appearing under a square root.

   (a)

   An engineer uses the formula $E=\frac{1}{2}mv^2$ for kinetic energy, where $m$ is mass and $v$ is speed. Make $v$ the subject of the formula, showing every step and stating any restriction on the sign of your answer.

   [4 marks]

   (b)

   Make $r$ the subject of the surface area formula $A=4\pi r^2$, stating any restriction on the sign of your answer.

   [4 marks]

   (c)

   For a spring's oscillation period, $T=2\pi\sqrt{\frac{m}{k}}$, make $m$ the subject of the formula, showing every algebraic step clearly.

   [5 marks]

   Total for question 4: 13 marks

End of questions