1. 1
   A plumber charges a call-out fee of 30 dollars plus 25 dollars per hour worked, $h$. His formula is $C=25h+30$, where $C$ is total cost in dollars. A rival plumber's formula for area covered by pipework is $A=\pi r^2$, where $r$ is a radius in metres.

   (a)

   Which formula gives the total cost, $C$, in dollars?

   [1 mark]

   • A$C=30h+25$
   • B$C=30+25+h$
   • C$C=55h$
   • D$C=25h+30$

   (b)

   The rival plumber uses the formula $A=\pi r^2$ to find the area of a circular pipe cross-section. Which equation correctly makes $r$ the subject?

   [1 mark]

   • A$r=\sqrt{\frac{A}{\pi}}$
   • B$r=\frac{A}{\pi}$
   • C$r=\sqrt{A\pi}$
   • D$r=\frac{\sqrt{A}}{\pi}$

   (c)

   Using $C=25h+30$, if a customer is charged 155 dollars, how many hours, $h$, did the plumber work?

   [1 mark]

   • A$4$
   • B$5$
   • C$6$
   • D$7$

   Total for question 1: 3 marks

2. 2
   A cinema calculates total ticket revenue in dollars using $T=8a+5c$, where $a$ is the number of adult tickets and $c$ is the number of child tickets sold. On Saturday, 40 child tickets were sold with total revenue of 520 dollars.

   (a)

   Form and solve an equation to find $a$, the number of adult tickets sold.

   [2 marks]

   (b)

   Rearrange the formula $T=8a+5c$ to make $a$ the subject.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A cyclist's distance travelled is described as speed multiplied by time, minus 2 km lost to a detour, giving $D=st-2$. Later the cyclist wants to make $t$ the subject of this formula.

   (a)

   A cyclist's speed is described in words: 'the distance travelled in kilometres is found by multiplying the average speed by the time taken in hours, then subtracting 2 kilometres lost to a detour.' Write this as a formula for distance $D$ in terms of speed $s$ and time $t$, then find $D$ when $s=18$ and $t=2.5$.

   [3 marks]

   (b)

   Make $t$ the subject of the formula $D=st-2$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A water company builds a spherical tank of radius $r$ metres with volume $V=\frac{4}{3}\pi r^3$. The company also plans a rectangular tank whose length is 4 metres more than its width $w$, and whose area must equal 96 square metres. A third scenario models the number of tanks $n$ built per year using $n^2-3n=40$.

   (a)

   A spherical water tank has volume given by $V=\frac{4}{3}\pi r^3$, where $r$ is the radius in metres. Make $r$ the subject of this formula, showing every step clearly.

   [4 marks]

   (b)

   A rectangular tank has width $w$ metres and length $(w+4)$ metres, with area 96 square metres. Form a quadratic equation in $w$ from this information and show that it can be written as $w^2+4w-96=0$.

   [4 marks]

   (c)

   Solve $w^2+4w-96=0$ by factorisation to find the width of the rectangular tank, $w$, stating why only one solution is valid in context.

   [5 marks]

   Total for question 4: 13 marks

End of questions