Mathematics Applications flashcards

79 TCE Mathematics Applications cards across 2 modules (18 definitions, 38 key facts, 5 fill-the-gap, 18 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
Arithmetic and Geometric Sequences - TCE Mathematics Applications (Tasmania)
Define Arithmetic versus geometric
Arithmetic sequence: each term is the previous term plus a fixed common difference $d$ . Geometric sequence: each term is the previous term times a fixed common ratio $r$ .
Definition
Annuities and Perpetuities - TCE Mathematics Applications (Tasmania)
Define Annuity and perpetuity
An annuity is an investment that pays a fixed regular amount over time, funded by an initial lump sum that earns interest as it is drawn down. A perpetuity is an annuity that pays out indefinitely because each payment takes only the interest earned, never the principal.
Definition
Eulerian and Hamiltonian Paths - TCE Mathematics Applications (Tasmania)
Define Walk, trail, and path
A walk is any sequence of connected edges. A trail is a walk that repeats no edge.
Definition
Annuity Investments and Superannuation - TCE Mathematics Applications (Tasmania)
Define Annuity investment
A fund that earns compound interest each period and also receives a fixed regular contribution. The balance grows from both the interest on what is already there and the new money added.
Definition
Financial Mathematics - TCE Mathematics Applications (Tasmania)
Define Compounding period
The interval at which interest is calculated and added to the balance. Common periods are annually, semi-annually (twice a year), quarterly (4), monthly (12), and weekly (52).
Definition
Assignment and Matching - TCE Mathematics Applications (Tasmania)
Define Assignment problem
A problem of pairing $n$ workers with $n$ tasks so that each worker does exactly one task and each task is done by exactly one worker, with the goal of minimising the total of the chosen costs from a square cost matrix.
Definition
First-Order Linear Recurrence Relations - TCE Mathematics Applications (Tasmania)
Define First-order linear recurrence
A rule of the form $V_{n+1} = R\,V_n + d$ , with a given starting value $V_0$ .
Definition
Bivariate Data and Regression - TCE Mathematics Applications (Tasmania)
Define Explanatory and response variables
The explanatory (independent) variable is the one used to predict; it goes on the horizontal axis. The response (dependent) variable is the one being predicted; it goes on the vertical axis.
Definition
Linear Programming - TCE Mathematics Applications (Tasmania)
Define The three ingredients
Decision variables: the unknown quantities you choose, often $x$ and $y$ . Objective function: a linear expression such as $P = 8x + 5y$ to be maximised or minimised.
Definition
Critical Path Analysis - TCE Mathematics Applications (Tasmania)
Define Activity network and precedence
An activity network is a directed graph where each activity has a duration and arrows show which activities must finish before others can start (precedence). An activity cannot begin until all its immediate predecessors are complete.