Simultaneous equations Past Paper Questions — 4037 Paper 2

Q62025 Oct/Nov·P239MMediumSimultaneous equations

The line $y = 3x + 4$ meets the curve $y = 2x^2 + 8x + 1$ at two points $A$ and $B$ .

Find the equation of the perpendicular bisector of $AB$ , giving your answer in the form $ax + by + c = 0$ , where $a$ , $b$ and $c$ are integers.

Q12024 Oct/Nov·P223MMedium-EasySimultaneous equations

Solve the following simultaneous equations.

\frac{y}{x} = \frac{3}{2}

\frac{y^4}{x^5} = \frac{27}{16}

Q22023 Oct/Nov·P225MMediumQuadratic functions

Find the non-zero value of $k$ for which the line $y = -2x - 6k - 1$ is a tangent to the curve $y = x(x + 2k)$ .

Q12022 Oct/Nov·P225MMedium-EasySimultaneous equations

Solve the following simultaneous equations.

\begin{aligned} x + 5y &= -4 \\ 3y - xy &= 6 \end{aligned}

Q52021 May/Jun·P218MMediumSimultaneous equations

The curves $y = x^2$ and $y^2 = 27x$ intersect at $O(0, 0)$ and at the point $A$ . Find the equation of the perpendicular bisector of the line $OA$ .

Q92021 May/Jun·P226MMediumSimultaneous equations

Solve the following simultaneous equations.

\begin{aligned} 4x^2 + 3xy + y^2 &= 8 \\ xy + 4 &= 0 \end{aligned}

Q52021 May/Jun·P244MMedium-EasySimultaneous equations

Solve the simultaneous equations

3y = x - 20 \quad \text{and} \quad x^2 + y^2 - 2x + 6y = 0

Q22021 Oct/Nov·P235MMedium-EasySimultaneous equations

Solve the following simultaneous equations. Give your answers in the form $a + b\sqrt{3}$ , where $a$ and $b$ are rational.

\begin{aligned} x + y &= 3 \\ 2x - \sqrt{3}y &= 5 \end{aligned}

Q62020 May/Jun·P216MMediumQuadratic functions

Find the values of $k$ for which the line $y = kx - 7$ and the curve $y = 3x^2 + 8x + 5$ do not intersect.

Q32020 May/Jun·P226MMediumQuadratic functions

Find the values of $k$ for which the line $y = x - 3$ intersects the curve $y = k^2 x^2 + 5kx + 1$ at two distinct points.