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WELCOME TO THIS PAGE INTENDED FOR STUDENTS AT THE UNIVERSITY OF THE WESTERN CAPE REGISTERED  FOR THE MODULE:

    QSF  131

                             

    QSF 131 LECTURE WED 10 FEB 2010

                

                                 QSF 131 TUT GROUP 3 : 9 FEBRUARY 2010

TUTORIAL TEST ONE SOLUTIONS

W4 L3                    W6 L3            T2 W2 L2              T2 W6 L1 & 2  

W5 L1                    W7 L1            TUT EQNS           T2 W7 L2

W5 L3                    W7 L2            T2 W4 L3              FRACTIONS : WITH / WITHOUT

W6 L1                    W7 L3            T2 W5 L1              CALCULATOR

                                     THE FARMER PROBLEM

TIME

MONDAY

TUESDAY

WEDNESDAY

THURSDAY

FRIDAY

 

8:30-9:30

Tut 1 G1 (1) (C6)

 

 

 

 

 

 

9:40-10:40

 

Tut G3 (1)

MS 8

Tut G1 (2)

SEM A1

 

Tut G3 (2)

MS 8

 

10:50-11:50

QSF 131…… C9

Tut G4 (1)

MS 2

 

 

Tut G4 (2)

MS 2

 

12:00-13:00

 

 

 

 

QSF 131… GH3

LUNCH

  ------------

  GW TESTS

GW TESTS

      TESTS

-------------

 

14:00-15:00

 

 

QSF 131…GH3

 

 

 

15:10-16:10 

Tut G2 (1)

MS 2

 

 

 

Tut G2 (2)

MS 2

 

 

 

 

 

 

 

 

 

COMPONENT

1

2

3

4

5

6

TUT TESTS

Thurs 11

 Feb

Thurs 25

Feb

Thurs 11 March

Thurs 1

April

Thurs 15

April

Thurs 29

April

CLASS TESTS

Wed 27 Jan

Diagnostic

Thurs 18

Feb

Thurs 4

March

Thurs 8

April

Thurs 22

April

 

TERM TESTS

Fri 26 March

Fri 23 April

 

 

 

 

FINAL EXAM

 

 

 

 

 

 

QSF   :   15 JANUARY 2010

In order to have reasonable prospects of success in your studies, you have to master basic quantitative skills in numbers, fractions, algebra and graphs. (cf p.1, QSF 131 Course Outline 2010)

HOW:                   

·                     PLAN OF ACTION TO TRANSFORM STUDENTS

·                     COURSE: LECTURES/TUTS/TESTS/EXAMS

·                     TAKES PLACE DURING FIRST OR SECOND SEMESTER

SHORT ACTIVITY

OBJECTIVE:         TO GET TO KNOW THE PERSON NEXT TO YOU  BETTER 

                               ‘QUANTITATIVELY’,   speaking.

                              TO GIVE YOU SOME IDEA OF THE QSF COURSE WORK

                              TO GET YOU ‘THINKING’

OUTCOME(S):     THIS IS BEST LEFT UNANSWERED! (IN EFFECT,

                             YOU  CAN WORK IT OUT YOURSELF, if it matters in your opinion!)

Text Box: TWO STUDENTS WHO SIT ADJACENT TO EACH OTHER  CALCULATE: 1.     THE SUM OF THE MATHS SCORES IN THE RECENT 2009 MATRIC EXAMS 2.     THE DIFFERENCE BETWEEN THE SCORES IN THE 2009 MATRIC EXAMS FOR EXAMPLE, if A obtained 77% and B  63%, then the sum is 140 and the difference is 14. Pass these two answers ONLY on to a few students in the same row, who have the task to work out what the matric maths scores or marks  of EACH of the two students are.              

 

 

 

 

 

 

 

 


 

Text Box: HINT SCORE 1 + SCORE 2 = SUM SCORE 1 – SCORE 2 = DIFFERENCE OR :  77 + 63 = 140          77 – 63 = 14             SUM OF (SUM + DIFF) = 154 THEREFORE INDIVIDUAL SCORES ARE: RULE: TAKE SUM and DIVIDE IT by ……..   …………….              SCORES ARE THEREFORE: 77 and 63   WHY? CAN YOU SOLVE THIS ALGEBRAICALLY?  

 

 

 

 

 

 

 

 

 

       ************************

    COURSE READER

 

University of the Western Cape

Faculty of Economic and Management Sciences

B.COM. (GENERAL) Four-year Programme

QUANTITATIVE SKILLS FOUNDATION

QSF 131

                           2010                                       

In her famous diary which describes South African colonial life from 1797 to 1801, Lady Anne Barnard wrote the following on 1 June 1800:

        “ … (The wife of ) Colonel Mercer… is…the longest woman I ever saw in my life

 

   …

        Her Colonel is four inches taller than she ; they measure twelve feet seven inches together”

 

 

QUESTIONS:

 

(a)     How tall, in metres, is the couple altogether? (Use:1 inch = 2.54 cm; Ans : 3.8354 m)

(b)     Express the ratio of the two heights in its simplest form. (Ans :  147 : 155)

(c)     If the couple shared 20 koeksisters in the ratio of their heights, what % did each one have?

(d)     Why it is impossible to have the height of either the man or the woman in feet and inches which are both whole numbers?

(e)     Investigate how you could calculate the respective heights of each of the man and his wife, without using algebraic equations.

 

*Anderson, H.J. South Africa a Century Ago: Letters and Journals (1797-1801) by  Lady Anne Barnard. Cape Town:

        Maskew Miller,  1924.

           

27 JAN 2010 (W1 L2)

 A: LECTURE

 1. CLASS LIST :     QSF MATHS

                                 QLC MATH LIT

 2. COURSE READERS:     NEW FROM PRINTWIZE : FROM MONDAY, 1 FEB

 3. TUTORIALS: NEXT WEEK : COURSE READER : TUT A1-A3 pp. 37, 38,         177 (MAKE COPIES, if you don’t have a Course Reader )

 4. MON:

          PROBLEM 1 : TITLE PAGE of New Course Reader

          PROBLEM 2 : On Website : www.eduhome.co.za

5. INTRODUCTION: COURSE READER, pp.19-21

6. SEXUAL HARASSMENT, CR p.23

7. UNIT 1 : MATHEMATIC THINKING SKILLS

                   GATEWAY TEST 1

1. Example 1.         The WORDS: “Two and Three-quarters” may be represented as follows,  using numbers (mathematically) this can be written (A) as :

                    which means:

          WRITING DOWN SKILLS(A) / CALCULATION SKILLS(B) / THINKING SKILLS (C)

B: Show that this fraction is the same as 275%

C: What is the essential difference between a fraction and a percentage?   

                   CALCULATOR:

                   Get to know your calculator. Explore number/fractions/properties of numbers with it.

2. Example 2: CR, p.25 :    and

          GW question : What is the essential difference(s) between multiplication and addition?

3. Example 3: “Find the cube root of five square plus 4”

B. DIAGNOSTIC TEST

29 JAN 2010

W1 L3

 

A. TUTORIALS  TIME-TABLE

    

    COURSE READER

    DIAGNOSTIC TEST : FIRST TUTORIAL

B. WED LECTURE

  1. QUESTIONS

1.1     Why is ?

      (CALCULATOR SKILLS: USE OF FRACTION KEY)

1.2     What is the essential difference between multiplication and addition

1.3     What is the essential difference between a fraction and a percentage?

1.4     Why does the formula (SUM of  (SUM + DIFF)) divided by 2 work?

1.5     Why is the answer : 6’ and 6’ ”?

B. CR, pp. -----------TERMS, etc.

 MON 1 FEB 2010

W2 L1

            CLASS TEST 1 : THURS 18 FEB

            GATEWAY TEST 1 : START NEXT WEEK : WED/THURS

‘WORD SUMS’

          LANGUAGE: NATURAL LANGUAGE / MATHEMATICAL LANGUAGE

          LOGIC

          TERMS : BUSINESS AND MATHS

  1. VAT, CR. P.32

Example 1: We purchased a washing machine from T. Furnishers on 15 January 2005, with a marked price of R2 295.  The original marked price was R2 795, before discount was given by T. Furnishers because the item was shop soiled. The sales person, upon completing the sales slip filled in the amount before VAT of 14% was added on. When we questioned him on how he arrived at the figure of …………..(fill in yourself), he said that he simply divided R2 295 by 1.14 using his calculator. He told us (proudly) that he completed a Business Course at Technikon (now called University of Technology)!  His thinking, or rather calculations were calculator based: take the amount and divide by 1.14.

 

In mathematical language this means:   R 2 295 χ   1.14.

Putting it down more fully in mathematical language, we have:

                   Selling Price including VAT     =  R2 295

                   Thus,  114% of the Price  (EXCL VAT)          =  R2 295

                   Therefore, 100%,  or the Price (EXCL VAT) =  Χ R 2 295

 

                                                                   = …………..

  1. POPULATION, CR. p. 36

 

1.85 million South Africans (4% of the population) go on holiday at least once a year. (GHS 2004 Tourism Database). 42% of those who went on holiday stayed with family or friends on their last trip. (**GHS 2004 Tourism Database) 11 Jan: A little over one million South African adults (16+) have raveled by air in the past year inside or outside Southern Africa. (*AMPS 2005).

 

Let us suppose that you wish to the determine the following:

  1. What is the total population in South Africa?
  2. What percentage of the total South African population consists of adults (16+)?

In order to solve these questions, you need an understanding of some basic mathematical concepts. Complete the two tables below with two further examples of mathematical concepts relevant to these questions:

 

MATHEMATICAL CONCEPTS

QUESTION 1

NUMBERS

1 AND 2

 

 

 

 

In order to solve the first question, complete the following:

4% of the South African population is:……………………………….persons.

Therefore 1% of the SA population is:……………………………….. (Divide by …….)

There 100%, or the SA population is:………………………………(Multiply by …….)

 

In order to solve the second question, complete the following:

 

The total South African population is:…………………………….(From Question …)

1 million of the SA populations expressed as a fraction is: .

Therefore 1 million of the SA populations as a % is: …………..( Multiply by …….)

 

Clearly, both thinking and basic mathematical skills are involved in the solutions of these simple questions.

 

 

  1. GW 1 : TAX PROBLEM : special exam  CR, P. 272

 

QUESTION 12 (5 marks)

A basic tax of R2000 is charged on an income of R20 000. For amounts more than      R20 000, this tax amount increases by R5.50 for every additional R200 income above (that is, that portion which is more than) R20 000. What does a person pay if he/she earns:

 

12.1       R60 000;

12.2       K rands where K is more than R30 000.                                     (5)

 

 

 

 

W2 TUT 2

 

Course Reader p. 37:

WHAT DOES THE POINT OF INTERSECTION X MEAN?

                           

If the above two lines represent a DEMAND and a SUPPLY (straight line function) respectively, we could say that at the point X:

                   DEMAND =  SUPPLY ………………………(1)

 

Recall that demand is an economic ‘force’ related to the quantity and price of a commodity or product, whereas supply relates to quantity and price as well. This relationship may be represented thus:

                                               

We may rewrite the equation 1 (more clearly and correctly) as follows:

                  

                       The quantity DEMANDed =  The quantity SUPPlied…….(2)

 

And                          The demanded price =  The supplied price

 

         N.B. Please ensure that you can explain the two concepts demand and supply clearly.

W3 L1

CLASS LIST / TUT TEST / GATEWAY TESTS

CALCULATOR SKILLS

                             6.2    

 

 

FORMULAE: FOR NO 12

         

Accumulated Value or Future Value FV after period n, where PV is the present value (Compound Interest)

AF =

Accumulation Factor (AF)

Present Value PV (Compound Interest)

Present Value of an Annuity for a period n:

Future Value of an Annuity for a period n:

WORD SUMS : WHAT A COURSE IN QUANTITATIVE SKILLS DOES NOT/CANNOT TEACH.

A large supermarket displays three types of toilet rolls in the same large basket for R2.49, R3.99 and R4.99 each.

A. Without using your calculator, determine

  1. the cost of 6 toilet rolls at R2.49
  2. the cost of 6 toilet rolls at R3.99
  3. how much more you would pay for 6 of the most expensive rolls than for 6 of the cheapest rolls.
  4. what the chances are of buying each, if the number of toilet rolls  in the basket for each is the same for each type.

B. Discuss the usefulness of a diagram in solving word sums.

C. Discuss the marketing strategy, and what a course in Quantitative Skills does not/cannot teach.

 

 

12.            An insurance agent offers services to clients who are concerned about their personal financial planning for retirement. When explaining the advantages of an early start to investing, she uses the example of 25-year old  Jabu who started to save R2 000 a year for 10 years (and made no further contributions after age 34).  Jabu earned more than Jane who waited 10 years, and then saved R2 000 a year from the age of 35 until her retirement at age 65 (a total of 30 yearly payments!).  Find the net earnings (compound-amount minus contributions) of Jabu and Jane at age 65.  An annual interest rate of 7,5% was applicable and the deposits were made at the beginning of each year.

JABU:       R28 294.17499; R247 714.2342

JANE:      R206 798.805

 

 

  1. WORD SUMS

 

DIAGRAMMATIC REPRESENTATION OF WORD SUMS (STORY SUMS)

REASON:

  1. MOST STUDENTS EXPERIENCE DIFFICULTIES WITH ‘WORD’ SUMS
  2. SERVES AS DIAGNOSTIC TOOL
  3. SERVES  AS MEANS TOWARDS REMEDYING/SOLVING PROBLEMS
  4. EVERYONE CAN DO IT, PROVIDED  they can read

 

 

 

PURPOSE:

  1. To reflect THINKING
  2. To understand mathematical thinking
  3. To categorise thinking
  4. To motivate (I CAN)
  5. To empower (WE CAN)
  6. To aid discussion/investigation/research

 

WHAT IT IS NOT

 

  1. NOT A GUIDE/TOOLBOX TO SOLVE PROBLEMS; DOES NOT GUARANTEE A SOLUTION
  2. NOT AN EXERCISE OF EXCELLENT SKETCHING/DRAWING
  3. NOT ARTISTIC EXPRESSION
  4. NOT TIME CONSUMIGNG

                             

 

PRINCIPLES/ASSUMPTIONS

 

  1. ALL DRAWINGS ARE DIFFERENT, BUT RELATED
  2. EVERYONE CAN MAKE A DRAWING
  3. ENJOYABLE
  4. THINKING OCCURS IN SHAPES AND PATTERNS, NOT LANGUAGE
  5. PROVIDES OUTLINE/FRAMEWORK OR MODLE, NOT SPECIFIC ANSWERS

 

 

Example 12

Only once the CORRECT formula is applied to the individual cases, the FV may be compared:

 

  1. WRITING DOWN ANSWERS

          JABU WILL HAVE AT RETIREMENT =

           JANE WILL HAVE AT RETIREMENT =

           THEREFORE ……………….

 

 

  1. ANXIETY

 

W3 L2

 TUTORIAL TEST 1: BASED ON DIAGNOSTIC TEST (NO CALCULATOR)

DECIMAL NUMBER SYSTEM : 1 ;  CR : p.71

 WHOLE NUMBERS / INTEGERS : 2 – 4,  9 : pp. 81-82

 COMMON FRACTIONS :  5 – 8: pp.49- 54; pp. 93 – 100 ; pp. 149 - 155

DECIMAL FRACTIONS :  10 -12 : pp. 100 - 102

PERCENTAGES : 13, 15 – 16 : pp. 102 – 106 ;  pp. 164 - 166

POWERS : 14 : pp. 131 - 133

ALGEBRA : 17 – 20 : p.83; pp.110 – 133; pp. 155 - 163

Elasticity of Demand = 

KEY BUSINESS CONCEPTS/TERMS:  DEMAND, QUANTITY, PRICE

KEY MATHEMATICAL CONCEPTS/TERMS:  EQUATION/FORMULA, NUMBERS, FRACTIONS, DECIMAL FRACTIONS, PERCENTAGE, VARIABLES (ALGEBRA), GRAPH            

  NUMBERS -----DECIMAL NUMBERS               ALGEBRA  ----   VARIABLES

    

                                                              EXPRESSIONS ----  EQUATIONS                                                                    

                                                                                           FORMULAE         

 

  FRACTIONS ----DECIMAL FRACTIONS         GRAPHS

  PERCENTAGES

FIGURE:  DIAGRAMMATICAL REPRESENTION SHOWING RELATIONSHIPS BETWEEN BASISC MATHEMATICAL CONCEPTS/TERMS RELEVANT TO ABOVE ELASTICITY FORMULA

 

CALCULATOR SKILLS !!!!!!!!!!!! PROBLEM 5.8 and 5.9

 

1.     PROBLEM FORMULATING SKILLS (TASK 1)

 

  IN GENERAL, it is harder to formulate a problem, than to solve it.

 

  N.B. This of course depends on the level of the problem.

Eg.  SOLVE without calculator:

  (a)        19386356 Χ 10983829

or (b)      If three men can dig five graves in 2 days, how long will seven men take to dig 50 graves?

 

5. The word “more” is often confused. What is the difference between the two statements:

     (a) There are b boys and c more girls than boys; and

    (b) There are b boys and c girls, where the girls are more than the boys.

 

6. (a) What is wrong with the following proof of the statement: If n is even, then (-1) =1.

     Proof:   (-1) = 1, and 4 is even, therefore (-1) =1.

7. State whether the following is true or false: 

        (a)         60% of 90 = 90% of 60;

        (b)     of y expressed as a fraction of (a+b) =   of x expressed as a fraction        of (b+a).

8.  Refer Section 2.4.1 on p. 77 dealing with sets.  Draw a large, clear diagram, picture or any representation which represents the problem. (DO NOT SOLVE!!)

2.     NUMBER SYSTEM

©  DESMOND DESAI, DMD EDU-HOME, 2010

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