Specialist Mathematics flashcards

69 SACE Specialist Mathematics cards across 6 modules (7 definitions, 30 key facts, 10 fill-the-gap, 22 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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What this deck covers

Topic 1: Mathematical Induction (4 cards, 1 dot point)
- Proof by mathematical induction (SACE Stage 2 Specialist Mathematics) (4)
Topic 2: Complex Numbers (16 cards, 3 dot points)
Topic 3: Functions and Sketching Graphs (13 cards, 3 dot points)
Topic 4: Vectors in Three Dimensions (17 cards, 3 dot points)
Topic 5: Integration Techniques (12 cards, 3 dot points)
Topic 6: Rates of Change and Differential Equations (7 cards, 2 dot points)
- Modelling with differential equations (SACE Stage 2 Specialist Mathematics) (3)
- Separable differential equations (SACE Stage 2 Specialist Mathematics) (4)

Sample cards from this deck

Definition
Proof by mathematical induction (SACE Stage 2 Specialist Mathematics)
Define Mathematical induction
Mathematical induction is the standard tool for proving such statements rigorously.
Definition
Complex arithmetic and the Argand plane (SACE Stage 2 Specialist Mathematics)
Define Complex conjugate
The conjugate of $z=a+bi$ is $\bar z=a-bi$ . Conjugating reflects the point across the real axis.
Definition
Composite and inverse functions (SACE Stage 2 Specialist Mathematics)
Define One-to-one and the horizontal line test
A function is one-to-one (injective) if different inputs always give different outputs. Graphically, it passes the horizontal line test: no horizontal line meets the graph more than once.
Definition
The cross product (SACE Stage 2 Specialist Mathematics)
Define Anticommutative
$\mathbf{b} \times \mathbf{a} = -(\mathbf{a} \times \mathbf{b})$ . Order changes the direction.
Fill the gap
Integration by parts (SACE Stage 2 Specialist Mathematics)
To choose $u$ , prefer whichever type comes first in ___: Logarithmic, Inverse trig, Algebraic (powers of $x$ ), Trigonometric, Exponential.
To choose $u$ , prefer whichever type comes first in LIATE: Logarithmic, Inverse trig, Algebraic (powers of $x$ ), Trigonometric, Exponential.
Key fact
Modelling with differential equations (SACE Stage 2 Specialist Mathematics)
Tell me about Exponential growth and decay
The simplest model, $\dfrac{dy}{dt} = ky$ , solves to $y = A e^{kt}$ (see the separable-equations method). Use two pieces of data: one to find $A$ , another to find $k$ .
Definition
Polar form and De Moivre's theorem (SACE Stage 2 Specialist Mathematics)
Define Polar form
Polar form describes the same number by how far it is from the origin and in what direction.
Definition
Modulus functions (SACE Stage 2 Specialist Mathematics)
Define The modulus function
Useful facts: $|x|^2 = x^2$ , $|ab| = |a||b|$ , and $|x| = c$ (for $c > 0$ ) means $x = c$ or $x = -c$ .
Fill the gap
Vector and cartesian equations of lines and planes (SACE Stage 2 Specialist Mathematics)
Writing components gives the ___ $x = a_1 + t d_1$ , $y = a_2 + t d_2$ , $z = a_3 + t d_3$ .
Writing components gives the parametric equations $x = a_1 + t d_1$ , $y = a_2 + t d_2$ , $z = a_3 + t d_3$ .
Fill the gap
Partial fractions (SACE Stage 2 Specialist Mathematics)
Partial fractions apply to a ___ rational function (numerator degree less than denominator degree).
Partial fractions apply to a proper rational function (numerator degree less than denominator degree).