General Mathematics flashcards

186 VCE General Mathematics cards across 2 modules (41 definitions, 66 key facts, 33 fill-the-gap, 46 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
Annuities and regular withdrawals: VCE General Mathematics Unit 3 Recursion and financial modelling
Define Interest
Interest is always calculated on the previous balance: $400\,000 \times 0.004 = 1600$ , then $398\,600 \times 0.004 = 1594.40$ .
Definition
Critical path analysis, dummy activities and crashing: VCE General Mathematics Unit 4 Networks and decision mathematics
Define Every critical path must be reduced
With two or more critical paths, look for an activity common to all of them, and compare its cost with shortening each path separately.
Definition
Boxplots and the five-number summary: VCE General Mathematics Unit 3 Data analysis
Define The five-number summary
The five-number summary is the minimum, $Q_1$ , the median $M$ , $Q_3$ and the maximum. The range is maximum $-$ minimum and the interquartile range is $\text{IQR} = Q_3 - Q_1$ , the spread of the middle $50\%$ of the data.
Definition
Leslie matrices and population models: VCE General Mathematics Unit 4 Matrices
Define Leslie matrix
Leslie matrix is a square matrix whose first row contains the birth rates of each age group and whose subdiagonal contains the survival rates from each age group to the next, with all other elements zero. It is used in the recurrence relation $S_{n+1} = LS_n$ , where $S_n$ is the column matrix of the number of females in each age group after $n$ time periods.
Definition
Correlation and causation, observation and experimentation for VCE General Mathematics Unit 3 Data analysis
Define A confounding (lurking) variable, or common response
A third variable, not included in the analysis, affects both variables. Ice cream sales and sunburn cases rise together because both respond to hot sunny weather. Children's shoe size and reading age rise together because both increase with age.
Definition
Matrix arithmetic, determinants and inverses: VCE General Mathematics Unit 4 Matrices
Define Quantity times price
If $Q$ holds quantities and $P$ holds prices, and the labels line up (the columns of the left matrix name the same things as the rows of the right matrix), the product holds money. A $1 \times 3$ price row times a $3 \times 3$ quantity matrix (items by days) gives a $1 \times 3$ matrix of revenue per day.
Definition
Correlation and least-squares regression: VCE General Mathematics Unit 3 Data analysis
Define Rounding
Answers are often required to a number of significant figures. Leading zeros do not count: 0.002 857 14 to four significant figures is 0.002 857, and 1 050 360.6 is 1 050 000. If the calculator shows 1.05036E6, that means $1.05036 \times 10^6 = 1\,050\,360$ .
Definition
Matrix types, order, the transpose and constructing matrices for VCE General Mathematics Unit 4 Matrices
Define Identity
$\subset$ diagonal $\subset$ symmetric, and diagonal matrices are also both upper and lower triangular.
Definition
Data transformation to linearise: VCE General Mathematics Unit 3 Data analysis
Define Solving backwards
Solving backwards (response given, explanatory unknown): rearrange for the transformed $x$ , then undo it last. For height $= -3.8 + 12.6 \log_{10}(\text{age})$ and height 8.52 m, $\log_{10}(\text{age}) = 0.9778$ and age $= 10^{0.9778} = 9.5$ years.
Definition
Trees, minimum spanning trees and Prim's algorithm: VCE General Mathematics Unit 4 Networks and decision mathematics
Define An edge must be included
An edge must be included (an existing road, a fixed link): put it in first, then carry on choosing the cheapest edges that avoid cycles. The total can only stay the same or rise.