11084 MATHEMATICS TERTIARY PREPARATION LEVEL D

Year	No.	Offer	Mode	Description			Cred. Pts
97	11084 	S2  	X 	MATHEMATICS TPP LEVEL D   	1.00

Contents

• Staffing
• Rationale
• Synopsis
• Objectives
• Topics
• Assessment Details
• Other Requirements

STAFFING:

RATIONALE:

Students  intending  to  enrol  in the Bachelor  of  Science  (Applied
Mathematics  major),  Bachelor  of  Information  Technology   (Applied
Computer   Science  or  Industrial  Computing  majors),  Bachelor   of
Engineering  (all majors) and Bachelor of Surveying must be  competent
in  certain  basic  mathematical topics so that  they  are  adequately
prepared  for  units  involving  mathematics  in  their  undergraduate
studies. Furthermore they need to become reflective thinkers  so  that
they  can  monitor, evaluate and control their thinking when  learning
and  applying  mathematics.  This  preparatory  mathematics  unit   is
designed   to   provide   students  with  the  required   mathematical
competencies  and to develop their metacognitive (i.e. thinking  about
their own thinking) skills.

SYNOPSIS:

Using  the  principles of self-paced instruction and mastery learning,
the  unit  guides  students through a carefully  sequenced  series  of
topics  which provide the foundation for understanding the mathematics
they  will  encounter in their tertiary study. A workbook approach  is
used  and students can proceed through the modules of work at  a  pace
suitable  to  their  own needs. Opportunities for  seeking  additional
assistance  are  provided through some of the  assessment  instruments
used  e.g. problem sets and learning diaries. Opportunities  for  self
assessment are provided throughout and at the end of each module.

OBJECTIVES:

OBJECTIVES A
On successful completion of this unit it is expected that a
student will:

1. demonstrate a more positive attitude to mathematics;
   
2. be more able to monitor, evaluate and control their thinking
   when doing mathematics;
   
3. be more confident and correct in predicting their mathematical
   performance;
   
4. know what techniques are best for their learning of
   mathematics.
   

1. calculate and use factorials
   
2. find combinations using a tree diagram
   
3. calculate and use a number of possible combinations
   
4. know and apply the Binomial Theorem
   
5. understand recurrence relations
   
6. find the general term of a sequence or a series
   
7. determine if a series has a finite sum
   
8. recognise arithmetic and geometric series
   
9. find partial sums and sums to infinity of geometric series
   
10. understand the process of mathematical induction
    
11. use mathematical induction to verify mathematical statements
    

1. represent inequalities on the real number line
   
2. express inequalities in interval notation
   
3. perform operations on inequalities
   
4. solve inequalities
   
5. represent linear inequalities graphically
   
6. graphically solve simple linear programming problems
   
7. factorise quadratic expressions
   
8. apply the technique of completing the square
   
9. draw graphs of rational functions
   
10. decompose rational functions into partial fractions
    
11. know the graphs of some common non-linear functions
    
12. solve simultaneous equations algebraically and graphically
    
13. find and sketch inverse algebraic functions
    
14. prove if a function is continuous at a given point
    

1. use matrices to organise data
   
2. identify any element of a matrix
   
3. add and subtract matrices of appropriate dimensions
   
4. multiply a matrix by a scalar
   
5. multiply two matrices of appropriate dimensions
   
6. identify a square matrix, the identity matrix, a zero matrix
   
7. find the transpose of a matrix
   
8. express linear equations in matrix form
   
9. solve a system of linear equations using matrix manipulations
   
10. find the inverse of an appropriate matrix using row reduction
    

1. express any angle in degrees or radians
   
2. convert Cartesian co-ordinates to polar co-ordinates and vice
   versa
   
3. know the common trigonometric identities
   
4. know the common multiple angle relationships
   
5. know the graphs of sin x, cos x and tan x, and their
   reciprocal functions
   
6. draw the inverse trigonometric functions
   
7. find the period of appropriate functions
   
8. identify the amplitude of appropriate functions
   
9. know and use the sine rule and cosine rule
   
10. know the sine and cosine rules for compound angles and double
    angles
    
11. solve graphically equations involving trigonometric functions
    and other types of functions
    
12. use trigonometry to solve problems
    

1. identify if a function is not differentiable at a given point
   
2. perform differentiation from first principles
   
3. know and use the basic rules of differentiation
   
4. know and use the chain, product and quotient rules for
   appropriate combinations of functions
   
5. determine maximum, minimum and points of inflection of a
   function
   
6. use calculus for curve sketching
   
7. solve rates of change problems
   
8. use Newton's method for finding roots of an equation
   

1. understand the relationship between differentiation and
   integration
   
2. perform anti-differentiation using "guess-and-check"
   
3. integrate functions by substitution of algebraic or
   trigonometric functions
   
4. use a Table of Standard Integrals
   
5. perform definite integration using the Fundamental Theorem of
   Calculus
   
6. perform numerical integration using the trapezoidal rule and
   Simpsons Rule
   

TOPICS:

 Description                                                    Weighting(%)

Discrete mathematics                                                  10.00

Algebra, functions and geometry                                       20.00

Matrices                                                              10.00

Trigonometry                                                          15.00

Differentiation                                                       20.00

Integration                                                           20.00

Learning mathematics                                                  5.00

ASSESSMENT DETAILS:

No  *F/S Marks     Due        Description                              Wtg(%)    LBL
1   F              WK 1      REVISION ASSIGNMENT & LEARNING DIARY                Y
2   S              WK 3      ASSIGNMENT 1A & LEARNING DIARY            5.00      Y
3   S              WK 5      ASSIGNMENT 2A & LEARNING DIARY            5.00      Y
4   S              WK 7      ASSIGNMENT 3A & LEARNING DIARY            5.00      Y
5   S              WK 10     ASSIGNMENT 4A & LEARNING DIARY            5.00      Y
6   S              WK 12     ASSIGNMENT 5A & LEARNING DIARY            5.00      Y
7   S              WK 14     ASSIGNMENT 6A & LEARNING DIARY            5.00      Y
8   S              WK 15     LEARNING MATHEMATICS ESSAY                          Y
9   S              END S2    EXAMINATION 3 HOURS                       70.00     N

OTHER REQUIREMENTS:

1    Students  must  perform  satisfactorily in  all  aspects  of  the
     assessment to obtain a pass in the unit.
2    Students  will  be  required  to  submit  extra  work  for   each
     assignment which is deemed unsatisfactory.
3    Grades  for the unit will be awarded using the following  system:
     HD 90% - 100% A 80% - 89% B 70% - 79% C 60% - 69%
4    Students  who do not meet the necessary requirements to obtain  a
     passing  grade  may, under special circumstances,  be  granted  a
     supplementary examination or assignments as appropriate.
5    Supplementary examinations will usually be held in the designated
     university  assessment  period  at  the  end  of  the   following
     semester.
6    Students  who, because of special circumstances have been  unable
     to  complete  the unit, may be eligible for special consideration
     if a request for such consideration is received in writing by the
     examiner before the date of the examination.