Specialist Mathematics flashcards

122 WACE Specialist Mathematics cards across 2 modules (5 definitions, 70 key facts, 6 fill-the-gap, 41 formulas). Each session gives you 20 cards, due cards first. Swipe right for easy, left for hard, down for again. Keyboard: Space to flip, 1 to 4 to rate.

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Definition
Factorising polynomials over the complex numbers (WACE Year 12 Mathematics Specialist Unit 3)
Define Conjugate root theorem
If a polynomial has real coefficients and $z = a + ib$ is a root, then its conjugate $\bar z = a - ib$ is also a root.
Fill the gap
Matrices and linear transformations (WACE Year 12 Mathematics Specialist Unit 4)
Matrix multiplication is associative but ___: in general $AB \neq BA$ .
Matrix multiplication is associative but not commutative: in general $AB \neq BA$ .
Definition
Functions and sketching graphs (WACE Year 12 Mathematics Specialist Unit 3)
Define Domain
State any values excluded by a zero denominator or even root.
Fill the gap
Statistical inference (WACE Year 12 Mathematics Specialist Unit 4)
The quantity $\dfrac{\sigma}{\sqrt{n}}$ is the ___.
The quantity $\dfrac{\sigma}{\sqrt{n}}$ is the standard error.
Definition
Inverse trigonometric (circular) functions (WACE Year 12 Mathematics Specialist Unit 3)
Define Principal domains and ranges
$y = \sin^{-1} x$ has domain $[-1, 1]$ and range $[-\tfrac{\pi}{2}, \tfrac{\pi}{2}]$ . $y = \cos^{-1} x$ has domain $[-1, 1]$ and range $[0, \pi]$ . $y = \tan^{-1} x$ has domain $\mathbb{R}$ and range $(-\tfrac{\pi}{2}, \tfrac{\pi}{2})$ .
Fill the gap
Vector equations of lines and planes (WACE Year 12 Mathematics Specialist Unit 4)
Two lines are ___ if their direction vectors are scalar multiples.
Two lines are parallel if their direction vectors are scalar multiples.
Definition
The complex plane, modulus and argument (WACE Year 12 Mathematics Specialist Unit 3)
Define Modulus
The modulus of $z = x + iy$ is $|z| = \sqrt{x^2 + y^2}$ , the distance from $z$ to the origin.
Key fact
Areas between curves (WACE Year 12 Mathematics Specialist Unit 4)
Tell me about Finding the limits
The limits $a$ and $b$ are usually the $x$ -coordinates of the intersection points, found by solving $f(x) = g(x)$ . Sketch the region to confirm which curve is on top, since that determines the order of subtraction.
Fill the gap
Complex numbers (WACE Year 12 Mathematics Specialist Unit 3)
The ___ $|z| = \sqrt{x^2 + y^2}$ is the distance from the origin.
The modulus $|z| = \sqrt{x^2 + y^2}$ is the distance from the origin.
Key fact
The central limit theorem (WACE Year 12 Mathematics Specialist Unit 4)
Tell me about The mean and standard error of the sample mean
Two exact facts underpin the theorem and hold for any sample size. The mean of the sampling distribution equals the population mean, $\mu_{\bar{X}} = \mu$ , so the sample mean is an unbiased estimator of the population mean.