11083 MATHEMATICS TERTIARY PREPARATION LEVEL C

Year	No.	Offer	Mode	Description			Cred. Pts
01	11083 	S1  	X 	MATHEMATICS TPP LEVEL C   	1.00

Contents

STAFFING:

Examiner: L. GALLIGAN
Moderator: J. TAYLOR
Instructional design: M. DORMAN

RATIONALE:


Students  who  intend  to  enrol in Science (other  than  Psychology),
Bachelor   of   Technology  and  Associate  Degrees  of   Engineering,
Surveying,  Mathematics and Computing, will be  required  to  complete
this  unit. This preparatory mathematics course is designed to provide
students  with the basic mathematical competencies for these  tertiary
studies.

SYNOPSIS:


Using the concepts of self-paced instruction and mastery learning, the
course  guides students through a carefully sequenced series of topics
which  will  provide the foundation for understanding the  mathematics
that will be encountered in their tertiary study.

The self-paced structure of the course allows students to work through
the  material  at a pace suitable to their needs, permitting  them  to
work  quickly  through  familiar material, as  well  as  allowing  the
opportunity to seek additional assistance in areas of uncertainty. The
mastery  approach  will  ensure  that they  successfully  achieve  the
objectives  of each topic before progressing to the next topic,  which
will build further on the earlier material.

OBJECTIVES:

On successful completion of this unit a student should be able
to: MODULE 1 Managing Mathematics Level C

  1. reflect on your attitude to mathematics;
  2. study mathematics more effectively;
  3. develop an action plan around the structure of the materials;
  4. formulate a study schedule; MODULE 2 Do You Understand This?
  5. revise the required prerequisite content for this unit and
    understand the importance of the following:
  6. Index laws;
  7. Algebraic expressions;
  8. Solving linear, quadratic, exponential & logarithic equations;
  9. Graphing straight lines, parabolas, exponentials and
    logarithms
  10. Trigonometrical ratios and functions;
  11. Matrices.
  12. Practice using the graphing package; MODULE 3 Relations and
    Functions
  13. demonstrate an understanding of the concept of a function;
  14. demonstrate an understanding of the concept of continuity;
  15. use functional notation;
  16. recognise, sketch and use polynomial, exponential, and
    logarithmic functions;
  17. demonstrate an understanding of the inverse of
    polynomial,exponential, and logarithmic function;
  18. recognize relations that are not functions;
  19. investigate functions over the integer domain - Sequences and
    series;
  20. understand the concept of limit;
  21. recognize convergent and divergent sequences and functions;
  22. find the sums of series; MODULE 4 Trigonometrical Functions
  23. demonstrate an understanding of the concept of radian
    measurement;
  24. convert from degrees to radians and vise versa;
  25. use radian measure in various applications;
  26. define and calculate trigonometric ratios for any angle;
  27. describe and sketch trigonometric functions of sine, cosine
    and tangent;
  28. calculate the amplitude, vertical shift, period and phase of a
    function from its equation and graph;
  29. understand the nature of inverse trigonometric functions and
    solve trigonometric equations using trigonometric identities;
    MODULE 5 Analytical Geometry - Representing Points and Curves
  30. identify points using rectangular coordinates, polar
    coordinates, and vectors;
  31. change from polar to rectangular coordinates and vise versa;
  32. demonstrate an understanding of a vector;
  33. express vectors in terms of column matrix and i and j;
  34. identify characteristics of straight line segments including
    equation, distance and mid-point;
  35. identify characteristics of standard curves (polynomial,
    exponential, logarithmic, circular, and hyperbolas);
  36. examine transformations of linear, parabolic, exponential,
    logarithmic, circular curves and rectangular hyperbolas; and
    examine other curves and investigate the importance of
    parameters in their equations. MODULE 6 Describing Change - An
    Introduction to Differential Calculus
  37. use graphs and algebra to describe the rate of change of a
    function;
  38. determine the instantaneous rate of change of a function;
  39. apply the power, sum and difference rules to find the
    derivative of certain polynomial functions;
  40. apply calculus to velocity and acceleration and other real
    life problems;
  41. use gradient functions to determine the derivatives of
    trigonometric, exponential and logarithmic functions;
  42. locate local stationary points of a function; and
  43. solve optimization problems. MODULE 7: Total Change - An
    Introduction to Integral Calculus
  44. find areas using various geometric methods;
  45. find areas under curves using definite integrals;
  46. demonstrate an understanding of the relationship between
    differentiation and integration;
  47. find indefinite integrals;
  48. apply calculus to various practical situations.

TOPICS:

 Description                                                    Weighting(%)
    

  1. Managing Mathematics

    

  2. Revision topics- Do you understand this?

    

  3. Relations and Functions                                               15.00

    

  4. Trigonometric Functions                                               20.00

    

  5. Analytical geometry - representing points and curves                  20.00

    

  6. Describing change - An introduction to differential calculus          25.00

    

  7. Total change - An introduction to integral calculus                   20.00

TEXT and MATERIALS required to be PURCHASED or accessed:

Scientific calculator. Students need access to a computer.

ASSESSMENT DETAILS:

No  *F/S Marks     Due        Description                              Wtg(%)    LBL WWW
1   F              WK 1      ASSIGNMENT 1                                        Y   N
2   S              WK 3      ASSIGNMENT 2                              5.00      Y   N
3   S              WK 6      ASSIGNMENT 3                              7.00      Y   N
4   S              WK 10     ASSIGNMENT 4                              7.00      Y   N
5   S              WK 12     ASSIGNMENT 5                              9.00      Y   N
6   S              WK 14     ASSIGNMENT 6                              7.00      Y   N
7   S              END S1    END OF SEMESTER EXAM - 3 HOURS            65.00     N   N

*F=Formative, S=Summative

OTHER REQUIREMENTS:

1    Normally,  to  gain  a passing grade, students  must  submit  ALL
     assignments  before  the exam period and  obtain  a  satisfactory
     result  in each assessment item. Students who are unable to  meet
     these   requirements   and  who  wish  to   apply   for   special
     consideration are required to apply in writing to the  Unit  Team
     Leader  prior to the examination. In these cases students may  be
     granted   a   supplementary   examination   or   assignments   as
     appropriate.
2    Students may be required to submit extra work for each assignment
     which is deemed unsatisfactory.
3    The time it will take to complete this mathematics unit will vary
     and  will  depend  on the student's background  and  experiences;
     times indicated above are a guideline only.
This information is accurate as at 15/01/02