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ACMMM143

use a Bernoulli random variable as a model for two-outcome situations

ACMGM042

interpret, in context, the slope and intercept of a straight-line graph used to model and analyse a practical situation

ACMGM092

fit a least-squares line to model long-term trends in time series data.

ACMMM138

recognise uniform discrete random variables and use them to model random phenomena with equally likely outcomes

ACMMM146

use Bernoulli random variables and associated probabilities to model data and solve practical problems.

ACMEM002

apply arithmetic operations according to their correct order

ACMGM068

display the terms of an arithmetic sequence in both tabular and graphical form and demonstrate that arithmetic sequences can be used to model linear growth and decay in discrete situations

ACMGM072

display the terms of a geometric sequence in both tabular and graphical form and demonstrate that geometric sequences can be used to model exponential growth and decay in discrete situations

ACMGM097

use a recurrence relation to model a reducing balance loan and investigate (numerically or graphically) the effect of the interest rate and repayment amount on the time taken to repay the loan

ACMGM099

use a recurrence relation to model an annuity, and investigate (numerically or graphically) the effect of the amount invested, the interest rate, and the payment amount on the duration of the annuity

ACMSM131

examine slope (direction or gradient) fields of a first order differential equation

ACMGM043

construct and analyse a straight-line graph to model a given linear relationship; for example, modelling the cost of filling a fuel tank of a car against the number of litres of petrol required.

use a recurrence relation to model a compound interest loan or investment, and investigate (numerically or graphically) the effect of the interest rate and the number of compounding periods on the future value of the loan or investment

ACMGM016

use matrices, including matrix products and powers of matrices, to model and solve problems; for example, costing or pricing problems, squaring a matrix to determine the number of ways pairs of people in a communication network can communicate with each …

ACMGM047

interpret piece-wise linear and step graphs used to model practical situations; for example, the tax paid as income increases, the change in the level of water in a tank over time when water is drawn off at different intervals and for different periods …

ACMSM127

use numerical integration using technology \(f\left(t\right)=\lambda e^{-\lambda t}\) for \(t\geq0\) of the exponential random variable with parameter \(\lambda>0,\), and use the exponential random variables and associated probabilities and quantiles …

ACMGM075

use a general first-order linear recurrence relation to generate the terms of a sequence and to display it in both tabular and graphical form

ACMGM076

recognise that a sequence generated by a first-order linear recurrence relation can have a long term increasing, decreasing or steady-state solution

ACMGM070

use arithmetic sequences to model and analyse practical situations involving linear growth or decay; for example, analysing a simple interest loan or investment, calculating a taxi fare based on the flag fall and the charge per kilometre, or calculating …

ACMGM074

use geometric sequences to model and analyse (numerically, or graphically only) practical problems involving geometric growth and decay; for example, analysing a compound interest loan or investment, the growth of a bacterial population that doubles in …

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