Singapore A-Level H2 Further Mathematics central themes overview quiz (SEAB 9649) quiz

$4\cos\theta + 4i\sin\theta$

$\cos\theta^4 + i\sin\theta^4$

$\cos 4\theta + i\sin 4\theta$

$\cos\dfrac{\theta}{4} + i\sin\dfrac{\theta}{4}$

$A + \mathbf{v} = \lambda$

$A\mathbf{v} = \lambda\mathbf{v}$

$A\mathbf{v} = \mathbf{0}$ for all $\lambda$

$\mathbf{v}A = \lambda^2$

$y = 2x + c$

$y = A e^{x/2}$

$y = \dfrac{x^2}{2} + c$

$y = A e^{2x}$

$x_{n+1} = x_n + f(x_n)\,f'(x_n)$

$x_{n+1} = x_n - \dfrac{f(x_n)}{f'(x_n)}$

$x_{n+1} = x_n - \dfrac{f'(x_n)}{f''(x_n)} + f(x_n)$

$x_{n+1} = x_n - f(x_n)$

Determinant $-3$, trace $2$

Determinant $2$, trace $-3$

Determinant $3$, trace $-1$

Determinant $-4$, trace $3$

Only a particular integral, since any single solution of the full equation already fixes the answer

Only the complementary function, which solves the homogeneous equation with its arbitrary constants

The complementary function plus a particular integral, $y = y_c + y_p$

The product of the complementary function and a particular integral, written as $y = y_c \, y_p$

When the sample is very large and clearly normal, since large samples always rule out a parametric test

Whenever a graphing calculator is available, because the calculator can only run non-parametric procedures

Only when the population variance is already known exactly, which is the precondition for any rank-based test

When the population cannot be assumed normal, for example small skewed samples or ordinal data

Because eigenvalues and eigenvectors decouple the system and give its solution structure

Because matrices cannot be used in calculus at all, so the two strands are kept entirely separate

Because differential equations can never be written in any matrix form, even when the system is linear

Because diagonalisation removes all of the derivatives from the system, leaving purely algebraic equations

A single point sitting on the positive real axis at a distance one from the origin

$n$ points all spaced equally along the imaginary axis, above and below the origin

$n$ equally spaced points on the unit circle

A straight line of $n$ points passing through the origin at forty-five degrees

To avoid ever using calculus at all, replacing every integral and derivative with a purely arithmetic shortcut

To guarantee exact closed-form answers for every root, integral and differential equation that is met

To replace rigorous proof with informal guessing, since approximate methods need no mathematical basis

To approximate solutions, with an understanding of the error involved, when exact methods are unavailable

By evaluating a limit of a definite integral as the bound tends to infinity

By simply ignoring the infinite limit and treating the integral as an ordinary definite integral

By assuming that any integral with an infinite limit always diverges and so has no finite value

By differentiating the integrand instead of integrating it, then substituting the infinite bound

Because it simply repeats the whole of H2 Mathematics with no genuinely new content of its own at all

Because it assumes H2 Mathematics as a foundation and extends it with greater depth and new strands

Because it shares no overlap whatsoever with H2 Mathematics and is studied as a fully independent subject

Because taking it removes the need for a graphing calculator in both papers across the two subjects