AQA A-Level Further Mathematics Core pure overview quiz quiz

$x - yi$

$x + yi$

$-x + yi$

$y + xi$

$\cos\theta + i\sin n\theta$

$\cos n\theta + i\sin n\theta$

$n\cos\theta + ni\sin\theta$

$\cos n\theta - i\sin n\theta$

The matrix has a unique inverse and is non-singular

The matrix must be the two by two identity matrix

The matrix has no inverse (it is singular)

The transformation it represents doubles every area

$0$

$2$

It diverges

$1$

$\int_a^b \sqrt{1 + \left(\frac{dy}{dx}\right)^2}\,dx$

$\int_a^b \sqrt{1 + \frac{dy}{dx}}\,dx$

$\int_a^b \sqrt{1 - \left(\frac{dy}{dx}\right)^2}\,dx$

$\int_a^b \sqrt{1 + 2\pi\left(\frac{dy}{dx}\right)}\,dx$

$\cosh^2 x + \sinh^2 x = 1$

$\cosh^2 x - \sinh^2 x = 1$

$\sinh^2 x - \cosh^2 x = 1$

$\cosh^2 x - \sinh^2 x = 0$

$e^{x}$

$3x$

$e^{3x}$

$e^{x^2}$

$y = Ae^{2x} + Be^{3x}$

$y = (A + Bx)e^{2x}$

$y = e^{3x}(A\cos 2x + B\sin 2x)$

$y = e^{2x}(A\cos 3x + B\sin 3x)$

That if the statement is true for $n = k$ then it is true for $n = k + 1$

That the statement is true for the base case where $n = 1$ to begin with

That the statement is false for at least one particular value of $n$ chosen

That the statement is true for every real number and not just integers

$-2 + 5i$

$2 - 5i$

$5 + 2i$

$-2 - 5i$

$2\pi\int_{\alpha}^{\beta} r\,d\theta$

$\frac{1}{2}\int_{\alpha}^{\beta} r^2\sin\theta\,d\theta$

$\frac{1}{2}\int_{\alpha}^{\beta} r^2\,d\theta$

$\frac{1}{4}\int_{\alpha}^{\beta} r^2\,d\theta$

The scalar product of their directions

The sum of their position vectors

The modulus of one direction

The vector product of their directions