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# Mathematics B

Course Carole Godfrey
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Introduction to functions, rates of change, periodic applications, exponential and logarithmic functions, derivatives, integration, and statistical analysis.

Mathematics B:

• Is a pre-requisite for tertiary studies in many fields such as engineering, science and technology, finance;
• helps to make informed decisions in areas such as buying and selling a house, superannuation, interpreting media presentations;
• is important as concepts and application of functions, rates of change, overall change and optimisation are used in the professional setting;
• develops analytical and problem-solving skills useful in everyday life;
• provides the capacity to justify and communicate in a variety of forms; and
• has provided a basis for the development of technology it has substantially influenced the evolution of technology.

Here is the course outline:

## 1. Revision of Algebraic concepts

1 - expansion and factorization of polynomials. 2 - basic algebraic manipulation. 3 - identities.

## 2. Trigonometry and Applications

1 - Sine, cosine and tangent ratios. 2 - Sine and Cosine Rules. 3 - Radian measure. 4 - Definition of sine, cosine and tangent of any. angle in degrees and radians.

## 3. Introduction to Functions

1 - Graphs, functions, relations. 2 - Quadratic equations, functions and graphs.

## 4. Periodic Functions

1 - Trig functions of sine, cosine and tangent. 2 - Graphics calculator. 3 - Practical applications of periodic functions

## 5. Applied Statistical Analysis

1 - discrete and continuous variables. 2 - interpretation of graphical displays of discrete and continuous data - bar charts, stem-and leaf plots, histograms. 3 - Summation notation. 4 - Interpretation of graphical displays. 5 - mean, median, mode. 6 - measures of spread - range, interquartile. range, standard deviation, variance. 7 - box-and-whisker plots; five-number summaries. 8 - sample statistics as estimation of population parameters.

## 6. Rates of Change

1 - concept of rate of change. 2 - average rates of change. 3 - average rate of change as gradient of secant.

## 7. Derivatives

1 - limits. 2 - definition of derivative of a function. 3 - differentiation from definition i.e. from 1st principles. 4 - rules for differentiation. 5 - evaluation of derivative at a point. 6 - use of derivative - instantaneous rate of change, gradient of function, practical applications.

## 8. Indices and Logarithms

1 - definitions of. 2 - index laws and definitions. 3 - log laws and definitions

## 9. Introduction to Integration – Reversing Differentiation

1 - fundamental theorem of calculus (definition of definite integral), area under curve. 2 - value of limit of sum as a definite integral. 3 - indefinite integral. 4 - rules for integration. 5 - practical applications of integral.

## 10. Applied statistical analysis-Probability

1 - measure of chance; relative frequency. 2 - Discrete variables and probability distributions; binomial distribution; tables of binomial probabilities. 3 - uniform (rectangular distribution). 4 - mean and standard deviation of binomial distribution.

## 11. Applications of Integration

1 - areas under curves. 2 - areas between curves. 3 - trapezoidal rule.

## 12. Calculus of trig. functions

1 - derivatives of sin x and cos x. 2 - applications of these derivatives in life-related situations. 3 - applications of periodic functions. 4 - Indefinite integrals of:sin (ax + b) and cos (ax + b). 5 - use of integration to find area. 6 - practical applications of integral.

## 13. Exponential and Logarithmic functions

1 - definition of the exponential function. 2 - graphs of exponential and log functions. 4 - solution of index equations. 5 - derivatives of exponential and log functions for base “e”. 6 - indefinite integrals for simple exponentials. 7 - practical applications of integral. 8 - practical application of exponential and log functions. 9. and the derivative of exp. Functions.

## 14. Financial Maths

1 - simple interest. 2 - compound interest. 3 - effective and nominal rates of interest. 4 - past, present and future values. 5 - annuities-future value, present value and amortising a loan as applications of GP.

## 15. Normal Distribution

1 - random samples and bias. 2 - discrete variable, binomial probability. 3 - expected value. 4 - mean and standard deviation of binomial. 5 - continuous variables, standard normal distribution, normal distribution tables and their use.

## 16. Optimisation - using derivatives (maxima and minima)

1 - sign of derivative. 2 - stationary points. 3 - local max and min. 4 - relationship between function and its derivative. 5 - nature of stationary points. 6 - least and greatest values of a function. 7 - construction of function to be optimized. 8 - interpretation of mathematical solution.

Weeks 1 - 5

## 19. Mathematics B Subject Handouts 2019

Class Handouts to be used for further study.

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