Singapore A-Level H2 Mathematics central themes overview quiz (SEAB 9758) quiz

$2x \ln x$

$x(2\ln x + 1)$

$2x + \dfrac{1}{x}$

$x^2 \cdot \dfrac{1}{x}$

$8 + \ln 2$

$7$

$7 + \ln 2$

$9 + \ln 2$

$15$

$\infty$ (it diverges)

$8$

$16$

$\sqrt{2}\left(\cos\dfrac{\pi}{4} + i\sin\dfrac{\pi}{4}\right)$

$2\left(\cos\dfrac{\pi}{4} + i\sin\dfrac{\pi}{4}\right)$

$\sqrt{2}\left(\cos\dfrac{\pi}{2} + i\sin\dfrac{\pi}{2}\right)$

$1\left(\cos\dfrac{\pi}{4} + i\sin\dfrac{\pi}{4}\right)$

$5$; the vectors would be parallel

$2$; the vectors would be perpendicular

$5$; the vectors would be perpendicular

$6$; the vectors would be equal

$X \sim B\left(5, \dfrac{1}{6}\right)$, $P(X=2) = \binom{5}{2}\left(\dfrac{1}{6}\right)^2\left(\dfrac{5}{6}\right)^3$

$X \sim B\left(5, \dfrac{1}{2}\right)$, $P(X=2) = \binom{5}{2}\left(\dfrac{1}{2}\right)^5$

$X \sim \text{Po}(5)$, $P(X=2) = \dfrac{5^2 e^{-5}}{2!}$

$X \sim B\left(6, \dfrac{1}{5}\right)$, $P(X=2) = \binom{6}{2}\left(\dfrac{1}{5}\right)^2\left(\dfrac{4}{5}\right)^4$

The sample mean is always exactly normally distributed for any sample size, however small the sample is

The sample mean has exactly the same variance as the population, no matter how many values are sampled

The sample mean equals the population mean exactly in every single sample that is ever drawn at random

For a large sample, the sample mean is approximately normal regardless of the population distribution

It is only ever needed for the statistics paper and plays no real role at all anywhere in the pure mathematics

Understanding a curve's shape, asymptotes and turning points makes calculus and equation-solving tractable

It entirely replaces the need for differentiation, since a careful sketch gives every gradient exactly

It is required only for the complex numbers topic and is not used in functions, calculus or conics

The method of differences

The scalar product

The Maclaurin series

Mathematical induction

Writing only the final p-value with no hypotheses, test statistic or conclusion to support it

Reporting the sample size on its own, without stating any hypotheses or interpreting the outcome

Drawing only the normal curve and shading the tail, without stating or interpreting the test

Stating the hypotheses precisely and interpreting the result in the context of the problem

Both are algebraic objects that carry geometric meaning

Both are used only in the statistics strand and never appear anywhere in the pure mathematics paper

Both are simply scalars with a size but no direction, exactly like an ordinary real number on a line

Both can only ever be added or subtracted, and neither vectors nor complex numbers can be multiplied

Permutations and combinations, where arrangements of objects are counted using factorial formulae

Continuous random variables and the area under a probability density function

Listing the outcomes of a discrete sample space and adding up their separate individual probabilities

Counting the number of possible arrangements of items using the binomial coefficient from the pure half