64100 FOUNDATION MATHEMATICS

Year	No.	Offer	Mode	Description			Cred. Pts
98	64100 	S1  	X 	FOUNDATION MATHEMATICS    	1.00

Contents


STAFFING:

Examiner: D. MANDER
Moderator: H. BUTLER

RATIONALE:

This unit covers the basic mathematics required for a scientific or engineering course at the tertiary level.


SYNOPSIS:

This unit covers: basic algebra, logarithms and exponential functions; elementary matrix algebra including addition, subtraction and multiplication of matrices, inverse and transpose of matrices, application to solution of equations; basic geometry including graphing basic functions; trigonometry; introductory calculus including differentiation of basic and compound functions, related rate problems, Newton's method, integration by standard methods and simple numerical integration.


OBJECTIVES:

On completion of this unit students will be able to:

  1. simplify expressions involving algebraic symbols and decimal
    numbers;
  2. use scientific notation and correct units of the metric
    system;
  3. expand and factorize algebraic expressions;
  4. combine algebraic fractions;
  5. manipulate equations;
  6. find the solutions (if any) of a quadratic equation;
  7. solve systems of simultaneous equations in two or three
    variables;
  8. determine the order, and find any nominated element of a
    matrix;
  9. understand and use matrix algebra;
  10. use the method of row reduction to solve sets of simultaneous
    equations in two or three variables;
  11. find the inverses (if they exist) of matrices of order 2 or 3
    and use these to solve sets of simultaneous equations;
  12. recognize the general equations and shapes of the graphs for
    straight lines, parabolas, hyperbolas, circles, and the
    trigonometric ratios, and be able to sketch them;
  13. find the equation of a straight line given either two points
    on the line or its slope and one point on the line;
  14. find the equation of a circle given its centre and radius and
    vice versa;
  15. find the distance between two points in two or three
    dimensions;
  16. draw graphs to find approximate solutions to equations; x x
  17. use a calculator to evaluate log x, ln x, 10 and e for any
    acceptable value of x;
  18. apply the logarithmic laws to simplify algebraic equations;
  19. evaluate trigonometric ratios for any angle;
  20. evaluate inverse trigonometric functions;
  21. solve problems using the relationships between the
    trigonometric ratios and compound angle formulae;
  22. apply the sine and cosine rule;
  23. find the area of a triangle;
  24. understand and use radian measure;
  25. find the length of an arc and the area of a sector of a
    circle;
  26. find the derivatives and integrals of basic functions;
  27. use the chain rule, product rule and quotient rule to
    differentiate combinations of basic functions;
  28. solve problems involving rate of change;
  29. find the local maximum and minimum values (if any) of a
    function;
  30. find the solution of an equation to a given accuracy using
    Newton's Method;
  31. use the method of substitution to determine integrals of
    functions;
  32. evaluate definite integrals;
  33. find the area beneath a curve using definite integrals;
  34. use the Trapezoidal Rule and Simpson's Rule to approximate the
    area beneath a curve.

TOPICS:

 Description                                                    Weighting(%)
  1. Algebra 16.00 - indices; scientific notation; metric system; factorization and expansion of algebraic terms; transposition of equations; solution of quadratic equations; algebraic solution of simultaneous equations.

  2. Matrices 19.00 - definition of matrices; addition and subtraction; trans- posing; matrix multiplication; inverse; matrix solution of simultaneous equations.

  3. Geometry 16.00 - introduction to analytic geometry; equations for lines, parabolas, circles and hyperbolas, slope and distance formulae; logarithmic and exponential functions; graphical presentation of these functions; graphical solution of equation.

  4. Trigonometry 16.00 - trigonometric ratios and identities; double angle formulae; sine and cosine rules; area of triangle; radian measure; graphs of trigonometric functions; inverse trigonometric functions.

  5. Differentiation 20.00 - differentiation of basic functions; chain, product and quotient rule; rates of change; maxima and minima; Newton's method.

  6. Integration 13.00 - integration of basic functions; integration by sub- stitution; definite integrals; Trapezoidal and Simpson's rules.


RECOMMENDED REFERENCE MATERIALS:

Coady, C. & Gosling, J. 1996, Introductory Mathematics, Pascal
Press.

Dobson, A.J. & Stokoe, J. 1990, Self Paced Introductory Mathematics,
ANU Press.


STUDENT WORKLOAD REQUIREMENTS:

	ACTIVITY				HOURS
Private Study                                 	148
Examinations                                  	3
Assessments                                   	15

ASSESSMENT DETAILS:

No  *F/S Marks     Due        Description                              Wtg(%)    LBL WWW
1   S              20/02/98  PRELIMINARY TEST                                    Y
2   S                        CML TEST S1                               2.50      Y
3   S                        CML TEST S2                               2.50      Y
4   S                        CML TEST S3                               2.50      Y
5   S                        CML TEST S4                               2.50      Y
6   S              END S1    3 HOUR RESTRICTED EXAMINATION             90.00     N
7   F                        CML TEST F1A                                        Y
8   F                        CML TEST F1B                                        Y
9   F                        CML TEST F2A                                        Y
10  F                        CML TEST F2B                                        Y
11  F                        CML TEST F3A                                        Y
12  F                        CML TEST F3B                                        Y
13  F                        CML TEST F4A                                        Y
14  F                        CML TEST F4B                                        Y
15  S              END SEM   3 HOUR RESTRICTED EXAMINATION             90.00     N
16  F                        QUIZ 1A                                             Y
17  F                        QUIZ 1B                                             Y
18  F                        QUIZ 2A                                             Y
19  F                        QUIZ 2B                                             Y
20  F                        QUIZ 3A                                             Y
21  F                        QUIZ 3B                                             Y
22  F                        QUIZ 4A                                             Y
23  F                        QUIZ 4B                                             Y
24  F                        QUIZ 5A                                             Y
25  F                        QUIZ 5B                                             Y
26  F                        QUIZ 6A                                             Y
27  F                        QUIZ 6B                                             Y
28  F                        QUIZ 7A                                             Y
29  F                        QUIZ 7B                                             Y

*F=Formative, S=Summative

OTHER REQUIREMENTS:

(i)  Students   must  complete  the  preliminary  test  before   being
     permitted to begin CML tests S1 to S4.
(ii) On  the  basis  of  preliminary test  results,  students  may  be
 directed to complete prescribed preparatory modules before commencing
     the CML tests.
(iii)There are no individual due dates for submission of CML tests but
     all  summative CML tests must be completed by the end of semester
     2 teaching period.
(iv) Students  who  do  not preform satisfactorily in  assignments  in
     semester  1 may not be permitted to complete the unit in semester
     2  and  will  be  given an immediate F grade.  (see  Introductory
     Booklet for guidelines on satisfactory performance).
(v) Students must perform satisfactorily in the CML tests and the exam
     to pass the unit.
(vi) Students  may  nominate  to  sit for an  examination  during  the
     examination  period at the end of semester 2.  (See  Introductory
     Booklet for further details).
(vii) Students  need  only sit for one of the two 3 hour  examinations.
     (See Introductory Booklet for further details).
Restricted  Examination: a restricted examination  is  an  examination
where  only  those  materials specified in the examination  paper  are
permitted during the examination.

This information is accurate as at 04/11/98