1. 1
   Amir and his sister's ages are linked by algebraic expressions.

   (a)

   Amir's age is $n$ years. His sister is 2 years older than him. Which expression represents his sister's age?

   [1 mark]

   • A$n + 2$
   • B$n - 2$
   • C$2n$
   • D$\frac{n}{2}$

   (b)

   Their father's age is three times Amir's age, minus 5 years. If Amir is $n$ years old, which expression represents his father's age?

   [1 mark]

   • A$5 - 3n$
   • B$3(n-5)$
   • C$3n + 5$
   • D$3n - 5$

   (c)

   The sum of Amir's age, his sister's age ($n+2$), and his father's age ($3n-5$) is 62 years. Solve for $n$.

   [1 mark]

   • A$n = 15$
   • B$n = 11$
   • C$n = 13$
   • D$n = 9$

   Total for question 1: 3 marks

2. 2
   A rectangular field's dimensions are linked by its perimeter, given algebraically.

   (a)

   A rectangular field has length $(x+7)$ m and width $x$ m. Its perimeter is 74 m. Form an equation in $x$ using the perimeter formula.

   [2 marks]

   (b)

   Solve the equation formed in part (a) to find the width, $x$, and hence the length of the field.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A triangular sail's dimensions are linked by its area, given algebraically.

   (a)

   A triangular sail has a base of $(x+3)$ m and a height of $x$ m. Its area is 20 m². Form a quadratic equation in $x$ using the area formula for a triangle.

   [3 marks]

   (b)

   Solve the equation $x^2 + 3x - 40 = 0$ formed in part (a) to find the height, $x$, of the sail, rejecting any solution that is not physically sensible.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A café orders coffee beans and tea leaves at unknown prices per kilogram, forming simultaneous equations.

   (a)

   A café orders coffee beans and tea leaves. Buying 4 kg of coffee beans and 3 kg of tea leaves costs 176 dirhams. Buying 2 kg of coffee beans and 5 kg of tea leaves costs 144 dirhams. Letting $c$ be the cost per kg of coffee beans and $t$ the cost per kg of tea leaves, form a pair of simultaneous equations for this information.

   [4 marks]

   (b)

   Solve the simultaneous equations $4c + 3t = 176$ and $2c + 5t = 144$ to find the cost per kg of coffee beans, $c$, and tea leaves, $t$.

   [4 marks]

   (c)

   The café's supplier then offers a bulk deal: 3 kg of coffee beans and 2 kg of tea leaves for 25 dirhams less than the individual rates found in part (b) would suggest. Using $c=32$ and $t=16$, form and solve an equation to find the discount, $d$, in dirhams.

   [5 marks]

   Total for question 4: 13 marks

End of questions