Simultaneous equationsEdexcel A-Level Maths: Subtopic test

1. 1
   The line $y=x+1$ meets the curve $y=x^2-3x-4$ at two points.

   (a)

   Eliminating $y$ gives which equation?

   [1 mark]

   • A$x^2-2x-5=0$
   • B$x^2-4x-3=0$
   • C$x^2-4x-5=0$
   • D$x^2-4x+5=0$

   (b)

   What are the $y$-coordinates of the two points of intersection?

   [1 mark]

   • A$0$ and $6$
   • B$-1$ and $5$
   • C$0$ and $5$
   • D$1$ and $6$

   (c)

   The line $y=x+c$ is a tangent to the curve $y=x^2-3x-4$. Find the value of $c$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A rectangle has perimeter 34 cm and its diagonal has length 13 cm. Its sides have lengths $x$ cm and $y$ cm.

   (a)

   Eliminating $y$ gives which quadratic equation in $x$?

   [1 mark]

   • A$x^2-17x+120=0$
   • B$x^2-17x+60=0$
   • C$x^2+17x+60=0$
   • D$x^2-17x+229=0$

   (b)

   What are the dimensions of the rectangle?

   [1 mark]

   • A8 cm by 9 cm
   • B6 cm by 11 cm
   • C4 cm by 13 cm
   • D5 cm by 12 cm

   (c)

   Without solving a quadratic equation, find the area of the rectangle.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Real numbers $x$ and $y$ satisfy $2^{x}\times4^{y}=32$ and $\frac{8^{x}}{2^{y}}=2$.

   (a)

   Show that $x+2y=5$ and $3x-y=1$.

   [3 marks]

   (b)

   Hence solve the equations for $x$ and $y$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A linear equation and a quadratic equation in two unknowns can be solved by substitution. No calculator may be used.

   (a)

   Solve the simultaneous equations $2x-3y=6$ and $x^2-y^2+3x=50$.

   [6 marks]

   (b)

   The line $y=2x+k$ meets the curve $y=x^2-4x+8$. (i) Show that the $x$-coordinates of the points of intersection satisfy $x^2-6x+8-k=0$. (ii) Given that the line is a tangent to the curve, find the value of $k$ and the coordinates of the point of contact.

   [6 marks]

   Total for question 4: 12 marks

End of questions