1. 1
   A taxi firm charges a fixed call-out fee of $a$ dirhams plus $b$ dirhams for every kilometre travelled, so a journey of $k$ kilometres costs $C = a + bk$ dirhams.

   (a)

   If $a = 5$, $b = 2$ and $k = 12$, what is $C$?

   [1 mark]

   • A$C = 17$
   • B$C = 24$
   • C$C = 29$
   • D$C = 34$

   (b)

   Two taxi firms are compared for a journey. Firm X's total cost in dirhams is $3a + 2b$ and Firm Y's total cost is $a + 5b$. What is the simplified expression for the combined cost of using both firms?

   [1 mark]

   • A$4a + 7b$
   • B$3a + 7b$
   • C$4a + 10b$
   • D$2a + 3b$

   (c)

   The taxi firm doubles its call-out fee and a customer travels 3 km further than $k$ kilometres. Which expression correctly represents the new cost?

   [1 mark]

   • A$a + 2b(k+3)$
   • B$2a + b(k+3)$
   • C$2a + bk + 3$
   • D$2(a + bk) + 3$

   Total for question 1: 3 marks

2. 2
   A school tuck shop sells apples for $x$ pence each and cereal bars for $y$ pence each. A student buys 3 apples and 2 cereal bars.

   (a)

   Write an expression for the total cost in pence, then evaluate it when $x = 25$ and $y = 40$.

   [2 marks]

   (b)

   Another student's total spend across two visits to the tuck shop is $4x + 5y - x + 3y$ pence. Simplify this expression fully by collecting like terms.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A warehouse packs crates that each weigh $w$ kg empty. Each crate is loaded with $n$ identical boxes weighing $p$ kg each.

   (a)

   Construct an expression for the total weight of one loaded crate, then find the total weight when $w = 4$, $n = 6$ and $p = 3$.

   [3 marks]

   (b)

   On a delivery day, the warehouse records the combined weight of several crates as $5w + 3np - 2w + np$ kg. Simplify this expression fully, explaining each step.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A mobile phone contract charges a fixed monthly fee of $f$ dirhams which includes $m$ minutes of calls. Extra minutes beyond $m$ cost $c$ dirhams each.

   (a)

   Construct an expression for the monthly bill of a customer who uses $t$ minutes, where $t > m$, and evaluate it when $f = 80$, $m = 200$, $c = 0.5$ and $t = 250$.

   [4 marks]

   (b)

   A customer compares two months' bills using the expressions $3f + 2c(t-m) - f + c(t-m)$ dirhams. Simplify this expression fully by collecting like terms.

   [4 marks]

   (c)

   The phone company introduces a loyalty scheme: after 12 months, the fixed fee $f$ is reduced by $d$ dirhams, and included minutes rise to $m + 50$. Construct an expression for the total bill over the 13th month for a customer using $t$ minutes where $t > m+50$, in terms of $f$, $d$, $c$, $t$ and $m$. Then evaluate it when $f = 80$, $d = 10$, $c = 0.5$, $t = 300$ and $m = 200$.

   [5 marks]

   Total for question 4: 13 marks

End of questions