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
W4 L3 W6 L3 T2 W2 L2 T2 W6 L1 & 2
W5 L3 W7 L2 T2 W4 L3 FRACTIONS : WITH / WITHOUT
W6 L1 W7 L3 T2 W5 L1 CALCULATOR
TIME 
MONDAY 
TUESDAY 
WEDNESDAY 
THURSDAY 
FRIDAY 
8:309:30 
Tut 1 G1 (1) (C6) 




9:4010:40 

Tut G3 (1) MS 8 
Tut G1 (2) SEM A1 

Tut G3 (2) MS 8 
10:5011:50 
QSF 131 C9 
Tut G4 (1) MS 2 


Tut G4 (2) MS 2 
12:0013:00 




QSF 131 GH3 
LUNCH 
 
GW TESTS 
GW TESTS 
TESTS 
 
14:0015:00 


QSF 131 GH3 


15:1016:10 
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!)
************************
COURSE READER
B.COM. (GENERAL) Fouryear Programme
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 (17971801) 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 A1A3 pp. 37, 38, 177 (MAKE COPIES, if you dont 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.1921
6. SEXUAL HARASSMENT, CR p.23
7. UNIT 1 : MATHEMATIC THINKING SKILLS
GATEWAY TEST 1
1. Example 1. The WORDS: Two and Threequarters 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 TIMETABLE
DIAGNOSTIC TEST : FIRST TUTORIAL
B. WED LECTURE
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
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
= ..
1.85 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:
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.
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
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 25year 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 (compoundamount 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
DIAGRAMMATIC REPRESENTATION OF WORD SUMS (STORY SUMS)
REASON:
PURPOSE:
WHAT IT IS NOT
PRINCIPLES/ASSUMPTIONS
Example 12
Only once the CORRECT formula is applied to the individual cases, the FV may be compared:
JABU WILL HAVE AT RETIREMENT =
JANE WILL HAVE AT RETIREMENT =
THEREFORE .
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. 8182
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 EDUHOME, 2010
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