SAQA All qualifications and part qualifications registered on the National Qualifications Framework are public property. Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.
SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED UNIT STANDARD THAT HAS PASSED THE END DATE: 

Understand and apply mathematical systems for commercial applications 
SAQA US ID UNIT STANDARD TITLE
115453  Understand and apply mathematical systems for commercial applications 
ORIGINATOR
SGB Building Construction 
PRIMARY OR DELEGATED QUALITY ASSURANCE FUNCTIONARY
-  
FIELD SUBFIELD
Field 12 - Physical Planning and Construction Physical Planning, Design and Management 
ABET BAND UNIT STANDARD TYPE PRE-2009 NQF LEVEL NQF LEVEL CREDITS
Undefined  Regular  Level 6  Level TBA: Pre-2009 was L6  18 
REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER
Passed the End Date -
Status was "Registered" 		 2004-08-11  2007-08-11  SAQA 1055/04 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2008-08-11   2011-08-11  

In all of the tables in this document, both the pre-2009 NQF Level and the NQF Level is shown. In the text (purpose statements, qualification rules, etc), any references to NQF Levels are to the pre-2009 levels unless specifically stated otherwise.  

This unit standard does not replace any other unit standard and is not replaced by any other unit standard. 

PURPOSE OF THE UNIT STANDARD 
A person credited with this unit standard will be able to understand and apply mathematical systems such as linear algebra, linear programming, differential calculus and integral calculus. The learner will also be able to perform financial calculations.These learning outcomes form part of the Fundamental learning of the Bachelors Degree in Construction Management.
This unit standard will contribute to the full development of a professional community of Construction Managers.
The skills, knowledge and understanding demonstrated within this unit standard are essential for social and economic transformation and upliftment within the construction environment. 

LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING 
The following knowledge, skills attitude and / or equivalent:
  • FETC Mathematical Science 
    		•

    UNIT STANDARD RANGE 
    The typical scope of this unit standard:
    Linear Algebra includes:
  • Linear equations and matrices
  • Matrix operations
  • Inverse matrices
    Linear programming includes:
  • Linear programming and the geometry of linear programming
  • Matrices and linear programming
  • The Simplex method
    Mathematics of Finance includes:
  • Simple interest
  • Discount
  • Compound interest, annuities, sinking funds and amortization
    Differential Calculus includes:
  • Variables, functions and rate of change
  • Limits and continuity
  • The derivative and differentiation of functions
  • Maxima, minima, optimization and curve sketching
    Integral Calculus includes:
  • Integration
  • Integration of functions
  • Plane areas and volumes of revolution 
    		•

    Specific Outcomes and Assessment Criteria: 

    SPECIFIC OUTCOME 1 
    Understand and apply linear algebra. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Systems of linear equations are applied and solved 

    ASSESSMENT CRITERION 2 
    Matrix algebra is understood and matrices are solved 

    ASSESSMENT CRITERION 3 
    Matrix operations including Gaussian reduction are undertaken 

    ASSESSMENT CRITERION 4 
    Inverse matrices are calculated 

    SPECIFIC OUTCOME 2 
    Understand and apply linear programming. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    The geometry of linear programming is understood 

    ASSESSMENT CRITERION 2 
    Applications of linear programming are undertaken 

    ASSESSMENT CRITERION 3 
    Matrices are utilised to solve linear programming problems 

    ASSESSMENT CRITERION 4 
    The "simplex method" is utilised to solve linear programming problems 

    SPECIFIC OUTCOME 3 
    Understand and perform financial calculations. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Simple interest is understood and calculated 

    ASSESSMENT CRITERION 2 
    Discount is calculated 

    ASSESSMENT CRITERION 3 
    Compound interest is understood and calculated 

    ASSESSMENT CRITERION 4 
    Annuities and sinking funds are understood and calculated 

    ASSESSMENT CRITERION 5 
    Amortization is understood and calculated 

    SPECIFIC OUTCOME 4 
    Understand and apply differential calculus. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Variables and functions are understood 

    ASSESSMENT CRITERION 2 
    Rate of change is understood 

    ASSESSMENT CRITERION 3 
    The limits and continuity of functions are calculated 

    ASSESSMENT CRITERION 4 
    The derivative is calculated 

    ASSESSMENT CRITERION 5 
    Differentiation of algebraic functions is performed 

    ASSESSMENT CRITERION 6 
    Maximum and minimum values are calculated and curve sketching is undertaken 

    ASSESSMENT CRITERION 7 
    Applied problems in maxima and minima are undertaken (optimisation) 

    ASSESSMENT CRITERION 8 
    Differentiation of trigonometric, inverse trigonometric, exponential and logarithmic functions are undertaken 

    ASSESSMENT CRITERION 9 
    Differential calculus is applied to commercial problems 

    SPECIFIC OUTCOME 5 
    Understand and apply integral calculus. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Fundamental integration formulas are understood 

    ASSESSMENT CRITERION 2 
    Integration by parts and integration by substitution is undertaken 

    ASSESSMENT CRITERION 3 
    Trigonometric integrals and substitutions are undertaken 

    ASSESSMENT CRITERION 4 
    Integration by partial fractions is undertaken 

    ASSESSMENT CRITERION 5 
    Plane areas by integration are undertaken 

    ASSESSMENT CRITERION 6 
    Volumes of solids of revolution are calculated 


    UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS 
  • Anyone assessing a learner or moderating the assessment of a learner against this unit standard must be registered as an assessor with the relevant ETQA for The Bachelors Degree in Construction Management, NQF Level 6
  • Any institution offering learning that will enable the achievement of this unit standard must be accredited as a provider with the relevant ETQA
  • The relevant ETQA or other ETQA's, who have a Memorandum of Understanding in place with relevant ETQA, would be responsible for moderation of learner achievements of learners who meet the requirements of this qualification. 
    		•

    UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE 
  • Matrices and systems of linear equations
  • The geometry of linear programming, as well as the applications of linear programming
  • The following financial mathematics concepts: Simple interest; discount; compound interest; annuities, sinking funds and amortization
  • Variables and functions
  • Rate of change
  • Application of differential calculus
  • Fundamental integration formulas and application of integral calculus 
    		•

    UNIT STANDARD DEVELOPMENTAL OUTCOME 
    N/A 

    UNIT STANDARD LINKAGES 
    N/A 


    Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
    Identify and solve problems

    Specific outcome:
  • Understand and apply linear algebra
  • Understand and apply linear programming
  • Understand and perform financial calculations
  • Understand and apply differential calculus
  • Understand and apply integral calculus

    Assessment criteria:
  • Matrix algebra is understood and matrices are solved
  • Systems of linear equations are applied and solved
  • The "simplex method" is utilised to solve linear programming problems
  • Differential calculus is applied to commercial problems
  • Applied problems in maxima and minima are undertaken (optimisation) 
    		•

    UNIT STANDARD CCFO WORKING 
    Work effectively with others

    Specific outcome:
    Understand and perform financial calculations

    Assessment criteria:
  • Applications of linear programming are undertaken
  • Annuities and sinking funds are understood and calculated
  • Differential calculus is applied to commercial problems
  • The geometry of linear programming is understood 
    		•

    UNIT STANDARD CCFO ORGANISING 
    Employ self management

    Specific outcome:
  • Understand and apply linear algebra
  • Understand and apply linear programming
  • Understand and apply differential calculus
  • Understand and apply integral calculus

    Assessment criteria:
  • Fundamental integration formulas are understood
  • Trigonometric integrals and substitutions are undertaken 
    		•

    UNIT STANDARD CCFO COLLECTING 
    Manage information

    Specific outcome:
  • Understand and apply linear algebra
  • Understand and apply linear programming
  • Understand and perform financial calculations
  • Understand and apply differential calculus
  • Understand and apply integral calculus

    Assessment criteria:
  • Matrices are utilised to solve linear programming problems
  • Maximum and minimum values are calculated and curve sketching is undertaken 
    		•

    UNIT STANDARD CCFO COMMUNICATING 
    Communicate effectively

    Specific outcome:
    ·Understand and apply linear algebra

    Assessment criteria:
  • Rate of change is understood
  • Maximum and minimum values are calculated 
    		•

    UNIT STANDARD CCFO SCIENCE 
    Demonstrate scientific and technological competence

    Specific outcome:
  • Understand and apply linear algebra
  • Understand and apply linear programming
  • Understand and perform financial calculations
  • Understand and apply differential calculus
  • Understand and apply integral calculus

    Assessment criteria:
  • Differentiation of trigonometric, inverse trigonometric, exponential and logarithmic functions are undertaken
  • The geometry of linear programming is understood 
    		•

    UNIT STANDARD CCFO DEMONSTRATING 
    Understand Contextual world-systems

    Specific outcome:
  • Understand and apply linear algebra
  • Understand and apply linear programming
  • Understand and perform financial calculations
  • Understand and apply differential calculus
  • Understand and apply integral calculus

    Assessment criteria:
  • Matrices are utilised to solve linear programming problems
  • Annuities and sinking funds are understood and calculated 
    		•

    UNIT STANDARD ASSESSOR CRITERIA 
    N/A 

    UNIT STANDARD NOTES 
    N/A 

    QUALIFICATIONS UTILISING THIS UNIT STANDARD: 
      ID QUALIFICATION TITLE PRE-2009 NQF LEVEL NQF LEVEL STATUS END DATE PRIMARY OR DELEGATED QA FUNCTIONARY
    Core  63689   Bachelor of Arts: Geographical Information Science  Level 6  Level TBA: Pre-2009 was L6  Passed the End Date -
    Status was "Reregistered"     		 2018-06-30   
    Fundamental  48700   Bachelor of Construction Management: Built Environment  Level 6  Level TBA: Pre-2009 was L6  Passed the End Date -
    Status was "Reregistered"     		 2012-06-30  CHE 


    PROVIDERS CURRENTLY ACCREDITED TO OFFER THIS UNIT STANDARD: 
    This information shows the current accreditations (i.e. those not past their accreditation end dates), and is the most complete record available to SAQA as of today. Some Primary or Delegated Quality Assurance Functionaries have a lag in their recording systems for provider accreditation, in turn leading to a lag in notifying SAQA of all the providers that they have accredited to offer qualifications and unit standards, as well as any extensions to accreditation end dates. The relevant Primary or Delegated Quality Assurance Functionary should be notified if a record appears to be missing from here.
     
    NONE 


    All qualifications and part qualifications registered on the National Qualifications Framework are public property. Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.