NZ NCEA Level 3 Mathematics and Statistics

Flashcards for NZ NCEA Level 3 Mathematics and Statistics, covering the six externally examined achievement standards: complex numbers, differentiation and integration (91577 to 91579, Level 3 Calculus) and statistically based reports, probability concepts and probability distributions (91584 to 91586, Level 3 Statistics). Split by standard and then by topic.

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Some of its cards

• What is the imaginary unit $i$ defined by?

  $i^2 = -1$
• $(r\operatorname{cis}\theta)^n = r^n\operatorname{cis}(n\theta)$, for any integer $n$

  De Moivre's theorem
• What is implicit differentiation used for?

  Finding $\dfrac{dy}{dx}$ when $y$ is not given explicitly as a function of $x$, such as in $x^2 + y^2 = 25$
• What is a random variable?

  A variable whose value is a numerical outcome of a random process
• What is conditional probability?

  The probability of an event happening, given that another event is known to have happened
• Add $(3 + 4i) + (1 - 2i)$.

  $4 + 2i$
• $^nP_r = \dfrac{n!}{(n-r)!}$

  Permutation formula, $^nP_r$
• What four conditions make a binomial model appropriate?

  A fixed number of trials, each with two possible outcomes, the same probability of success on every trial, and the trials are independent
• What is the probability density function of a continuous uniform distribution on $[a, b]$?

  $f(x) = \dfrac{1}{b - a}$ for $a \leq x \leq b$, and $0$ elsewhere
• What does $\displaystyle\lim_{x \to a} f(x)$ mean?

  The value $f(x)$ approaches as $x$ gets closer and closer to $a$

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