1. 1
   Two market stalls sell apples ($x$) and oranges ($y$) in matching baskets, with quantities satisfying $x+y=14$ and $x-y=2$. A second pair of baskets satisfies $2x+3y=16$ and $x-y=3$.

   (a)

   Two numbers $x$ and $y$ satisfy $x+y=14$ and $x-y=2$. Find $x$.

   [1 mark]

   • A$6$
   • B$8$
   • C$10$
   • D$12$

   (b)

   Using $x+y=14$ and $x-y=2$, find $y$.

   [1 mark]

   • A$4$
   • B$6$
   • C$8$
   • D$10$

   (c)

   For the second pair of baskets, $2x+3y=16$ and $x-y=3$. What is the value of $x$?

   [1 mark]

   • A$4$
   • B$5$
   • C$6$
   • D$7$

   Total for question 1: 3 marks

2. 2
   A cinema sells adult tickets for $x$ dollars and child tickets for $y$ dollars. Two families' purchases satisfy $2x+3y=37$ and $x+y=15$.

   (a)

   Solve these simultaneous equations to find $x$.

   [2 marks]

   (b)

   Find the value of $y$, the price of a child ticket, and hence state the total cost for 3 adult and 2 child tickets.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A café sells coffee at $c$ dollars and tea at $t$ dollars per cup. Two orders satisfy $3c+2t=13.50$ and $5c+4t=23.50$.

   (a)

   Solve these equations simultaneously to find $c$, showing your elimination method clearly.

   [3 marks]

   (b)

   Using your value of $c$, find $t$, the price of a cup of tea, and check your solution in the second equation.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A drone company models a drone's straight-line flight path as $y=2x-11$ and a circular no-fly zone around an airport as $x^2+y^2=25$, with $x$ and $y$ measured in kilometres from the airport. The company must find where the flight path crosses the boundary of the no-fly zone.

   (a)

   A drone flies along a straight-line path given by $y=2x-11$ and a circular no-fly zone around an airport is modelled by $x^2+y^2=25$, with $x$ and $y$ in kilometres from the airport. Substitute the linear equation into the circle equation and show that this leads to $5x^2-44x+96=0$.

   [4 marks]

   (b)

   Solve $5x^2-44x+96=0$ by factorisation to find the possible values of $x$.

   [4 marks]

   (c)

   Find the corresponding $y$-values for each $x$-value found in part (b), and state both coordinate pairs where the drone's path crosses the no-fly zone boundary.

   [5 marks]

   Total for question 4: 13 marks

End of questions