1. 1
   At a market stall, mango and papaya prices satisfy a pair of simultaneous equations.

   (a)

   At a market stall, 2 mangoes and 3 papayas cost 26 dirhams, so $2m + 3p = 26$, and 1 mango and 1 papaya cost 10 dirhams, so $m + p = 10$. What is the value of $p$?

   [1 mark]

   • A$p = 6$
   • B$p = 4$
   • C$p = 8$
   • D$p = 2$

   (b)

   Using the same equations, $2m + 3p = 26$ and $m + p = 10$, what is the value of $m$?

   [1 mark]

   • A$m = 8$
   • B$m = 6$
   • C$m = 3$
   • D$m = 4$

   (c)

   A customer buys 3 mangoes and 2 papayas. Using $m=4$ and $p=6$, how much does this cost in dirhams?

   [1 mark]

   • A20
   • B24
   • C26
   • D30

   Total for question 1: 3 marks

2. 2
   A cinema sells adult and child tickets, and two families' purchases give simultaneous equations for the prices.

   (a)

   A cinema sells adult tickets for $a$ dirhams and child tickets for $c$ dirhams. One family buys 2 adult and 3 child tickets for 76 dirhams, and another buys 3 adult and 1 child ticket for 72 dirhams. Construct a pair of simultaneous equations to represent this information.

   [2 marks]

   (b)

   Solve the simultaneous equations $2a + 3c = 76$ and $3a + c = 72$ to find the price of an adult ticket, $a$, and a child ticket, $c$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A café tracks combined orders of coffee and pastries using simultaneous equations.

   (a)

   A café sells coffees for $x$ dirhams and pastries for $y$ dirhams. The equations $5x + 2y = 31$ and $3x + 4y = 27$ describe two orders. Solve these simultaneous equations using the elimination method, showing full working.

   [3 marks]

   (b)

   Using your solution to part (a), calculate the total cost of 2 coffees and 3 pastries.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A rectangular garden's perimeter and area lead to a pair of simultaneous equations, one linear and one non-linear.

   (a)

   A rectangular garden has a perimeter of 34 m, so $2(x+y) = 34$ where $x$ and $y$ are the side lengths. The garden's area is $60$ m², so $xy = 60$. Form the pair of simultaneous equations (one linear, one non-linear) that represent this situation.

   [4 marks]

   (b)

   Solve the simultaneous equations $x + y = 17$ and $xy = 60$ to find both possible pairs of values for $x$ and $y$.

   [4 marks]

   (c)

   A different rectangular garden measures 9 m by 5 m. A path of constant width $w$ is built around the inside edge, reducing the remaining planting area to 21 m². Form and solve an equation for $w$, showing full working, and state which solution is valid in context.

   [5 marks]

   Total for question 4: 13 marks

End of questions