Specialist Mathematics flashcards

130 VCE Specialist Mathematics cards across 2 modules (18 definitions, 57 key facts, 14 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
Cross product and applications: VCE Specialist Mathematics Unit 3
Define Area
The parallelogram on $\mathbf{a}$ and $\mathbf{b}$ has area $|\mathbf{a} \times \mathbf{b}|$ , and the triangle with those two sides has area $\frac{1}{2}|\mathbf{a} \times \mathbf{b}|$ .
Definition
Hypothesis testing for a mean: VCE Specialist Mathematics Unit 4
Define Type II error
Type II error is failing to reject $H_0$ when it is actually false.
Definition
Proof by mathematical induction: VCE Specialist Mathematics Unit 3
Define Base step
Show $P(n_0)$ is true by direct substitution.
Definition
Mechanics: forces and Newton's laws (former VCE Specialist Mathematics study design)
Define First law
A particle continues at rest or in uniform straight-line motion unless a non-zero resultant force acts. This defines the natural state and identifies acceleration as the signature of a net force.
Definition
Rational functions and graphing: VCE Specialist Mathematics Unit 3
Define Domain and vertical asymptotes
The function is undefined where $Q(x) = 0$ . If $P$ and $Q$ have no common factor there, the line $x = a$ is a vertical asymptote and the graph shoots to $\pm\infty$ on each side. If $P$ and $Q$ share the factor $(x - a)$ , there is instead a hole (point discontinuity) at $x = a$ .
Definition
Mechanics: momentum and connected bodies (former VCE Specialist Mathematics study design)
Define Former study design
Dynamics (Newton's laws, momentum and connected particles) was part of the previous VCE Specialist Mathematics study design and last appeared on the 2022 examinations. The current study design (from 2023) has no dynamics in Units 3 and 4: forces appear only in Units 1 and 2 (vectors applied to statics and motion under a constant force), and the Unit 4 calculus is kinematics (rectilinear motion and vector calculus). Keep this page for Units 1 and 2 vectors, for Physics, or for older resources.
Definition
Reciprocal and modulus transformations: VCE Specialist Mathematics Unit 3
Define Asymptotes become zeros
Where $f(x) \to \pm\infty$ , the reciprocal $\to 0$ , so the new graph approaches the $x$ -axis.
Definition
Related rates of change: VCE Specialist Mathematics Unit 4
Define Identify the variables and rates
Note which rate is given and which is wanted, with units.
Definition
Vector equations of lines and planes: VCE Specialist Mathematics Unit 3
Define Line meets plane
Substitute the parametric coordinates of the line into the plane's Cartesian equation. This gives one equation in $t$ ; solve it, then back-substitute to get the intersection point. If the coefficient of $t$ is zero, the line is parallel to the plane (no intersection, or the line lies in the plane).
Definition
Slope fields and Euler's method: VCE Specialist Mathematics Unit 4
Define Accuracy
Because the method holds the gradient fixed across each step, it drifts away from a curving solution, undershooting or overshooting depending on the concavity. Halving the step size roughly halves the error, so a smaller $h$ gives a better approximation at the cost of more steps.