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ACMMM128

recognise and use the additivity and linearity of definite integrals.

ACMMM129

understand the concept of the signed area function \(F\left(x\right)=\int_a^xf\left(t\right)dt\)

ACMMM130

understand and use the theorem \(F'\left(x\right)=\frac d{dx}\left(\int_a^xf\left(t\right)dt\right)=f\left(x\right)\), and illustrate its proof geometrically

ACMMM131

understand the formula \(\int_a^b{f\left(x\right)dx=F\left(b\right)-F(a)}\) and use it to calculate definite integrals.

ACMMM132

calculate the area under a curve

ACMMM133

calculate total change by integrating instantaneous or marginal rate of change

ACMMM134

calculate the area between curves in simple cases

ACMMM135

determine positions given acceleration and initial values of position and velocity

ACMMM136

understand the concepts of a discrete random variable and its associated probability function, and their use in modelling data

ACMMM137

use relative frequencies obtained from data to obtain point estimates of probabilities associated with a discrete random variable

ACMMM138

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

ACMMM139

examine simple examples of non-uniform discrete random variables

ACMMM140

recognise the mean or expected value of a discrete random variable as a measurement of centre, and evaluate it in simple cases

ACMMM141

recognise the variance and standard deviation of a discrete random variable as a measures of spread, and evaluate them in simple cases

ACMMM142

use discrete random variables and associated probabilities to solve practical problems.

ACMMM143

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

ACMMM144

identify contexts suitable for modelling by Bernoulli random variables

ACMMM145

recognise the mean \(p\) and variance \(p(1-p)\) of the Bernoulli distribution with parameter \(p\)

ACMMM146

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

understand the concepts of Bernoulli trials and the concept of a binomial random variable as the number of ‘successes’ in \(n\) independent Bernoulli trials, with the same probability of success \(p\) in each trial

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