Monash College Unit Guide

ADDITIONAL MATHEMATICS (MCD1080)

Purpose

The aim of this unit is to provide students with the knowledge and skills to solve problems involving differential and integral calculus, antidifferentiation and binomial and normal distributions.

Prerequisites

MCD1050 Introductory Mathematics for Commerce and IT or equivalent.

Learning outcomes

On completion of this unit, learners should be able to:

1. demonstrate understanding of differential calculus by its application to polynomial, power and rational functions; demonstrate understanding of related concepts and techniques, including finding limits, graphing gradient functions and using the product, quotient and chain rules for finding derivatives.
2. use differential calculus to: find the tangent and the normal at a point on a curve, find linear approximations; sketch graphs of polynomial functions; solve maxima and minima problems; and solve rates of change problems, including straight-line kinematics, and related rates problems.
3. differentiate exponential, natural logarithmic, sine, cosine and tangent functions; solve practical growth, decay and cyclic behaviour problems not requiring a graphics calculator.
4. demonstrate understanding of the antiderivative by its application to polynomial, circular, exponential functions and functions of the forms (ax + b)n, sin(ax + b) and cos(ax + b); use the results of differentiation to find antiderivatives; use integration to find the area under and between curves; use numerical approximations to evaluate integrals (left and right rectangles approximation).
5. demonstrate understanding of binomial probability by its application to problems requiring the calculation of probabilities and numbers of trials; calculate the mean, variance and standard deviation; consider the effect of varying the values of the parameters of the binomial probability distribution on its graph; apply binomial probability to solving practical problems.
6. recognise the standard normal distribution and recognise the family of normal distributions as transformations of the standard normal distribution; recognise the mean, median, mode, variance and standard deviation; consider the effect of varying the values of the parameters of the normal distribution on the graph of the probability density function; calculate probabilities and quantiles for any normal distribution using the standard normal cumulative probability table and symmetry properties; apply normal probability to solving practical problems.

Assessment

Two tests: 40% (each worth 20%)

Examination: 60%

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