Simultaneous equationsEdexcel International A Level Maths: Subtopic test

1. 1
   Consider the simultaneous equations $y=x+1$ and $x^2+y^2=25$.

   (a)

   Substituting $y=x+1$ into $x^2+y^2=25$ and simplifying gives which equation?

   [1 mark]

   • A$x^2-12=0$
   • B$2x^2+2x+26=0$
   • C$x^2+x-12=0$
   • D$x^2+x+12=0$

   (b)

   Which of these is a solution of the simultaneous equations?

   [1 mark]

   • A$x=3,\ y=4$
   • B$x=4,\ y=3$
   • C$x=-3,\ y=-2$
   • D$x=-4,\ y=3$

   (c)

   Find the other solution of the simultaneous equations.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Pens cost £$p$ each and notebooks cost £$n$ each. Four pens and three notebooks cost £11.60. Two pens and five notebooks cost £13.50.

   (a)

   What is the cost of one notebook?

   [1 mark]

   • A£0.95
   • B£1.18
   • C£1.25
   • D£2.20

   (b)

   What is the cost of one pen?

   [1 mark]

   • A£2.20
   • B£1.25
   • C£2.50
   • D£2.90

   (c)

   Find the cost of three pens and two notebooks.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The line $L$ has equation $y=2x-5$ and the curve $C$ has equation $y=x^2-3x+1$.

   (a)

   Find the $x$-coordinates of the points where $L$ meets $C$.

   [3 marks]

   (b)

   The line $y=x+2$ also meets $C$ at two points. Find the exact coordinates of these points.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A rectangle has perimeter $34$ cm and diagonal $13$ cm. Its length is $x$ cm and its width is $y$ cm, where $x>y$.

   (a)

   Find the length and the width of the rectangle.

   [6 marks]

   (b)

   A second rectangle has the same perimeter but a diagonal of $12$ cm. Show that no such rectangle exists.

   [6 marks]

   Total for question 4: 12 marks

End of questions