1. 1
   A courier company uses several formulas to calculate delivery costs and times.

   (a)

   A courier company uses the formula $C = 5n + 8$ to calculate the delivery cost $C$ in dirhams for $n$ parcels. Which formula correctly makes $n$ the subject?

   [1 mark]

   • A$n = \frac{C-8}{5}$
   • B$n = \frac{C+8}{5}$
   • C$n = \frac{C}{5} - 8$
   • D$n = 5(C-8)$

   (b)

   The company also uses $T = \frac{d}{s}$ to find delivery time $T$ from distance $d$ and speed $s$. Which formula correctly makes $s$ the subject?

   [1 mark]

   • A$s = \frac{T}{d}$
   • B$s = \frac{d}{T}$
   • C$s = dT$
   • D$s = d - T$

   (c)

   A third formula, $P = 2(l+w)$, gives the perimeter of a rectangular parcel label. Which formula correctly makes $l$ the subject?

   [1 mark]

   • A$l = \frac{P}{2} + w$
   • B$l = \frac{P-w}{2}$
   • C$l = \frac{P}{2} - w$
   • D$l = 2P - w$

   Total for question 1: 3 marks

2. 2
   A landscaper designs circular and conical garden features using standard area and volume formulas.

   (a)

   A circular garden pond has area $A = \pi r^2$, where $r$ is the radius. Make $r$ the subject of the formula.

   [2 marks]

   (b)

   A conical fountain has volume $V = \frac{1}{3}\pi r^2 h$. Make $h$ the subject of the formula.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A physics student rearranges formulas describing the motion of a falling object, where the subject sometimes appears more than once.

   (a)

   A physics student uses the formula $v^2 = u^2 + 2as$ for motion, where $a$ appears once but $v$ and $u$ appear squared. Make $a$ the subject.

   [3 marks]

   (b)

   The student also uses $s = ut + \frac{1}{2}at^2$, where the subject $t$ appears both linearly and squared, but for a specific problem $u=0$. Simplify this formula when $u=0$, then make $t$ the subject.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   An engineer rearranges complex formulas used in force and energy calculations where the subject appears twice or under a root.

   (a)

   An engineer uses the formula $F = \frac{k(x - a)}{x + a}$ to model a force $F$, where the subject $x$ appears twice. Make $x$ the subject of the formula, showing every step.

   [4 marks]

   (b)

   The engineer also uses $E = \sqrt{\frac{2m}{v} - c}$ to model energy, where $m$ is under both a root and a fraction. Make $m$ the subject of the formula.

   [4 marks]

   (c)

   Finally, the engineer must rearrange $T = 2\pi\sqrt{\frac{l}{g}} + k(l - r)$, where $l$ appears both under a root and linearly, to make $l$ the subject as far as possible in terms of a quadratic-type equation in $\sqrt{l}$. Show all steps and explain any substitution used to simplify the process.

   [5 marks]

   Total for question 4: 13 marks

End of questions