1. 1
   A gym charges membership using the formula $C = 15m + 25$, where $C$ is the total cost in pounds and $m$ is the number of months of membership.

   (a)

   Work out the value of $C$ when $m = 6$.

   [1 mark]

   • A£115
   • B£120
   • C£130
   • D£140

   (b)

   A member paid a total of £160. Which equation could be used to find $m$?

   [1 mark]

   • A$25m + 15 = 160$
   • B$15m - 25 = 160$
   • C$15(m+25) = 160$
   • D$15m + 25 = 160$

   (c)

   The gym removes the one-off joining fee from the formula. Which formula should now be used to calculate the cost?

   [1 mark]

   • A$C = 15(m+25)$
   • B$C = 15m + 25$
   • C$C = 15m$
   • D$C = 25m$

   Total for question 1: 3 marks

2. 2
   A mobile phone company models the cost of a call lasting $t$ minutes using the function $f(t) = 0.05t + 10$, where $f(t)$ is the cost in pence and $10$ pence is a fixed connection charge.

   (a)

   A customer makes a call lasting 200 minutes. Work out the cost of the call, in pence, using $f(t)$.

   [2 marks]

   (b)

   The company defines a new function $g(t) = f(t) - 10$. Show that $g(t) = 0.05t$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The formula $F = \frac{9}{5}C + 32$ converts a temperature of $C$ degrees Celsius into $F$ degrees Fahrenheit. A greenhouse thermostat opens the roof vents automatically once the Celsius temperature rises above $30°C$.

   (a)

   Rearrange the formula $F = \frac{9}{5}C + 32$ to make $C$ the subject.

   [3 marks]

   (b)

   The thermostat sensor reads $F = 95$. Using the rearranged formula, work out the Celsius temperature and state whether the roof vents will open.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A courier company defines two functions for a parcel of mass $x$ kg: $f(x) = 2x + 3$ gives the base delivery cost in pounds, and $g(x) = x - 1$ gives a loyalty-adjusted weight used before the cost is calculated. The composite function $h(x) = fg(x)$ gives the final delivery charge, in pounds, for a loyalty customer.

   (a)

   Find $fg(x)$ and show that $h(x) = fg(x) = 2x + 1$.

   [4 marks]

   (b)

   Find the inverse function $h^{-1}(x)$ and use it to work out the maximum mass, in kg, of a parcel a customer can send for a budget of £11.

   [4 marks]

   (c)

   Prove that $h(x)$ is always an odd number for every integer value of $x$.

   [5 marks]

   Total for question 4: 13 marks

End of questions