Edexcel A-Level Further Mathematics Core Pure overview quiz quiz

$x - iy$

$x + iy$

$-x + iy$

$y + ix$

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

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

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

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

The matrix has a well-defined inverse that can be found in the usual way

The matrix must be the identity matrix that leaves every vector unchanged

The matrix is singular and has no inverse

The transformation it represents doubles the area of every shape it acts on

$0$

$2$

It diverges

$1$

$\pi\int_a^b y^2\,dx$

$\pi\int_a^b y\,dx$, using the curve height rather than its square

$2\pi\int_a^b y\,dx$, the formula for the curved surface area instead

$\int_a^b y^2\,dx$, leaving out the factor of $\pi$ for the disc

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

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

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

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

$e^{x}$

$3x$

$e^{3x}$

$e^{x^2}$

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

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

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

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

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

That the statement is true for the very first case $n = 1$, the base case of the proof

That the statement turns out to be false for at least one particular value of $n$

That the statement holds true for every real number, not just the positive integers

$-2 + 5i$

$2 - 5i$

$5 + 2i$

$-2 - 5i$

$\int_{\alpha}^{\beta} r\,d\theta$, using the radius rather than its square

$\int_{\alpha}^{\beta} r^2\,d\theta$, leaving out the factor of one half

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

$\frac{1}{2}\int_{\alpha}^{\beta} r\,d\theta$, using the radius not its square

The scalar product of their two direction vectors, which gives a single number

The sum of the position vectors of a point on each of the two skew lines

The modulus of one of the direction vectors taken on its own

The vector product $\mathbf{d}_1 \times \mathbf{d}_2$ of their directions