11084 MATHEMATICS TERTIARY PREPARATION LEVEL D

Year	No.	Offer	Mode	Description			Cred. Pts
01	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. Metacognitive development
is  encouraged  through the use of specific surveys and  the  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:
Module 1

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
    Module 2
    
12. represent inequalities on the real number line
    
13. express inequalities in interval notation
    
14. perform operations on inequalities
    
15. solve inequalities
    
16. represent linear inequalities graphically
    
17. graphically solve simple linear programming problems
    
18. factorise quadratic expressions
    
19. apply the technique of completing the square
    
20. draw graphs of rational functions
    
21. decompose rational functions into partial fractions
    
22. know the graphs of some common non-linear functions
    
23. solve simultaneous equations algebraically and graphically
    
24. find and sketch inverse algebraic functions
    
25. prove if a function is continuous at a given point
    Module 3
    
26. use matrices to organise data
    
27. identify any element of a matrix
    
28. add and subtract matrices of appropriate dimensions
    
29. multiply a matrix by a scalar
    
30. multiply two matrices of appropriate dimensions
    
31. identify a square matrix, the identity matrix, a zero matrix
    
32. find the transpose of a matrix
    
33. express linear equations in matrix form
    
34. solve a system of linear equations using matrix manipulations
    
35. find the inverse of an appropriate matrix using row reduction
    Module 4
    
36. express any angle in degrees or radians
    
37. convert Cartesian co-ordinates to polar co-ordinates and vice
    versa
    
38. know the common trigonometric identities
    
39. know the common multiple angle relationships
    
40. know the graphs of sin x, cos x and tan x, and their
    reciprocal functions
    
41. draw the inverse trigonometric functions
    
42. find the period of appropriate functions
    
43. identify the amplitude of appropriate functions
    
44. know and use the sine rule and cosine rule
    
45. know the sine and cosine rules for compound angles and double
    angles
    
46. solve graphically equations involving trigonometric functions
    and other types of functions
    
47. use trigonometry to solve problems
    Module 5
    
48. identify if a function is not differentiable at a given point
    
49. perform differentiation from first principles
    
50. know and use the basic rules of differentiation
    
51. know and use the chain, product and quotient rules for
    appropriate combinations of functions
    
52. determine maximum, minimum and points of inflection of a
    function
    
53. use calculus for curve sketching
    
54. solve rates of change problems
    
55. use Newton's method for finding roots of an equation
    Module 6
    
56. understand the relationship between differentiation and
    integration
    
57. perform anti-differentiation using "guess-and-check"
    
58. integrate functions by substitution of algebraic or
    trigonometric functions
    
59. use a Table of Standard Integrals
    
60. perform definite integration using the Fundamental Theorem of
    Calculus
    
61. 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                                                          20.00

Differentiation                                                       20.00

Integration                                                           20.00

ASSESSMENT DETAILS:

No  *F/S Marks     Due        Description                              Wtg(%)    LBL WWW
1   F              WK 1      REVISION ASSIGNMENT & LEARNING DIARY                Y   N
2   S              WK 3      ASSIGNMENT 1A & LEARNING DIARY            6.00      Y   N
3   S              WK 5      ASSIGNMENT 2A & LEARNING DIARY            6.00      Y   N
4   S              WK 7      ASSIGNMENT 3A & LEARNING DIARY            6.00      Y   N
5   S              WK 10     ASSIGNMENT 4A & LEARNING DIARY            6.00      Y   N
6   S              WK 12     ASSIGNMENT 5A & LEARNING DIARY            6.00      Y   N
7   S              WK 14     ASSIGNMENT 6A & LEARNING DIARY            6.00      Y   N
8   S              END S2    EXAMINATION 3 HOURS                       64.00     N   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    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.
4    Supplementary examinations will usually be held in the designated
     university  assessment  period  at  the  end  of  the   following
     semester.
5    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.