1. 1
   A book club charges a joining fee plus a per-book fee, modelled using linear equations in $x$, the price per book in dirhams.

   (a)

   Given the equation $3x + 4 = 10$, where $x$ is the price per book in dirhams, solve for $x$.

   [1 mark]

   • A$x = 2$
   • B$x = 3$
   • C$x = 4$
   • D$x = 4.67$

   (b)

   A rival book club's pricing satisfies $5 - 2x = 3(x + 7)$. Solve for $x$.

   [1 mark]

   • A$x = -1.6$
   • B$x = 3.2$
   • C$x = -3.2$
   • D$x = 2.6$

   (c)

   A third club's offer satisfies $2(x + 3) = 5x - 6$. Solve for $x$.

   [1 mark]

   • A$x = 3$
   • B$x = 4$
   • C$x = 2$
   • D$x = 6$

   Total for question 1: 3 marks

2. 2
   A greenhouse must keep its temperature within a safe range for growing plants.

   (a)

   A greenhouse must keep its temperature, $T$ degrees Celsius, strictly above 15 and no higher than 28. Write this condition as a single inequality in $T$.

   [2 marks]

   (b)

   Describe how the inequality $15 < T \leq 28$ would be represented on a number line, referring to the type of circle used at each end.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A theme park sets height and speed restrictions for a new ride using linear inequalities.

   (a)

   A theme park ride requires a rider's height, $h$ cm, to satisfy $3h < 2h + 400$. Solve this inequality for $h$, and interpret your answer in context.

   [3 marks]

   (b)

   The ride's speed, $v$ km/h, must satisfy $-3 \leq 3v - 2 < 7$. Solve this compound inequality for $v$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A furniture manufacturer plans weekly production of chairs and tables subject to labour and material constraints.

   (a)

   A furniture manufacturer produces $x$ chairs and $y$ tables per week. Production requires $2x + 3y \leq 60$ (labour hours) and both $x \geq 0$, $y \geq 0$. Explain, without drawing a graph, what each inequality means in the context of the factory, and state whether the boundary lines should be regarded as solid or broken.

   [4 marks]

   (b)

   The manufacturer also has a material constraint: making $x$ chairs and $y$ tables uses wood such that $x + 2y < 30$. The company wants to check if producing $x = 10$ chairs and $y = 8$ tables satisfies all three constraints ($2x+3y \leq 60$, $x+2y<30$, $x,y \geq 0$). Determine, with full working, whether this production plan is feasible.

   [4 marks]

   (c)

   The manufacturer wants to list the full set of inequalities that define the feasible region for weekly production, given the labour constraint $2x+3y \leq 60$, the material constraint $x+2y<30$, a minimum order requirement of at least 5 tables ($y \geq 5$), and non-negative production. Write out the complete list of inequalities that define this region, and explain in words what point would represent producing no chairs at all but the maximum tables allowed by the labour constraint.

   [5 marks]

   Total for question 4: 13 marks

End of questions