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ACMEM174

use technology and a recurrence relation to model a reducing balance loan

ACMGM057

model a linear relationship by fitting a least-squares line to the data

ACMGM058

use a residual plot to assess the appropriateness of fitting a linear model to the data

ACMMM143

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

ACMSM063

prove irrationality by contradiction for numbers such as \(\sqrt[{}]2\) and \(\log_25\)

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.

ACMMM011

recognise features of the graph of the general quadratic \(y=ax^2+bx+c\)

ACMSM067

define the imaginary number i as a root of the equation \(x^2=-1\)

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

ACMMM007

recognise features of the graphs of \(y=x^2\), \(y=a{(x-b)}^2+c\), and \(y=a\left(x-b\right)\left(x-c\right)\) including their parabolic nature, turning points, axes of symmetry and intercepts

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

ACMGM082

apply Euler’s formula, \(v+f-e=2\), to solve problems relating to planar graphs.

ACMMM021

recognise features of the graph of \(y^2=x\) including its parabolic shape and its axis of symmetry.

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