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SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED UNIT STANDARD THAT HAS PASSED THE END DATE: 

Demonstrate understanding of real and imaginary numbers and real number systems 
SAQA US ID UNIT STANDARD TITLE
14106  Demonstrate understanding of real and imaginary numbers and real number systems 
ORIGINATOR
SGB Math Literacy, Math, Math Sciences L 2 -4 
PRIMARY OR DELEGATED QUALITY ASSURANCE FUNCTIONARY
-  
FIELD SUBFIELD
Field 10 - Physical, Mathematical, Computer and Life Sciences Mathematical Sciences 
ABET BAND UNIT STANDARD TYPE PRE-2009 NQF LEVEL NQF LEVEL CREDITS
Undefined  Regular-Fundamental  Level 3  NQF Level 03  2 
REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER
Passed the End Date -
Status was "Reregistered" 		 2003-12-03  2006-12-03  SAQA 1351/03 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2007-12-03   2010-12-03  

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 
This unit standard will be useful to people who aim to achieve recognition at some level in Further Education and Training or to meet the Fundamental requirement of a wide range of qualifications registered on the National Qualifications Framework.
People credited with this unit standard are able to:
  • Use and analyse computational tools and strategies, and make estimates and approximations
  • Demonstrate understanding of numbers and relationships among numbers and number systems, and represent numbers in different ways. 
    		•

    LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING 
    The credit value is based on the assumption that people starting to learn towards this unit standard are competent in Mathematics and Communications at NQF level 2. 

    UNIT STANDARD RANGE 
    This unit standard covers:
  • Approximation in relation to the use of computing technologies, the distinction between exact and approximate answers in a variety of problem settings and measurement error and its effect on subsequent calculations,
  • The mathematical treatment of exponential increase and decrease in relation to financial issues using electronic technology
    Operations on complex numbers are excluded from this unit standard
    More detailed range statements are provided for specific outcomes and assessment criteria as needed. 
    		•

    Specific Outcomes and Assessment Criteria: 

    SPECIFIC OUTCOME 1 
    Use and analyse computational tools and strategies, and make estimates and approximations. 
    OUTCOME RANGE 
    This outcome includes the need to:
  • Use technology such as calculators
  • Demonstrate understanding of mathematical relationships and principles involved in computations
  • Use numerical methods to find approximate solutions to suitable equations
  • Rationalise denominators. 
    		•

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    1. Computational tools are used efficiently and correctly and solutions obtained are verified in terms of the context or problem. 

    ASSESSMENT CRITERION 2 
    2. Algorithms are executed appropriately in calculations. 

    ASSESSMENT CRITERION 3 
    3. Solutions involving irrational numbers are reported or recorded to degrees of accuracy appropriate to the problem. 

    ASSESSMENT CRITERION 4 
    4. Measurements are reported or recorded in accordance with the degree of accuracy of the instrument used. The effect of measurement error on the final values calculated is reflected through the use of simple methods. 

    ASSESSMENT CRITERION 5 
    5. Estimates and approximations are used appropriately in terms of the situation and distinctions are made between the appropriate uses of estimates versus approximations. 
    ASSESSMENT CRITERION RANGE 
    Technological and non-technological settings.
     

    ASSESSMENT CRITERION 6 
    6. Approximate solutions to equations are justified in terms of the use of the approximation and the context where applicable. 

    ASSESSMENT CRITERION 7 
    7. The roles and limitations of particular algorithms are identified in terms of efficiency and the complexity of the algebraic formulation. 

    ASSESSMENT CRITERION 8 
    8. The viability of selected algorithms is verified and justified in terms of appropriateness to context and efficiency. 

    SPECIFIC OUTCOME 2 
    Demonstrate understanding of numbers and relationships among numbers and number systems. 
    OUTCOME NOTES 
    Demonstrate understanding of numbers and relationships among numbers and number systems, and represent numbers in different ways 
    OUTCOME RANGE 
  • Real and imaginary numbers
  • Do calculations involving surds
  • Indicate imaginary solutions to equations
  • Interpret and use absolute value notation with real numbers. 
    		•

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    1. Notation for expressing numbers is consistent with mathematical conventions. 
    ASSESSMENT CRITERION RANGE 
    Real and imaginary numbers and absolute value notation.
     

    ASSESSMENT CRITERION 2 
    2. Methods of calculation and approximation are appropriate to the problem type. 

    ASSESSMENT CRITERION 3 
    3. Imaginary numbers are represented as the square root of negative numbers as appropriate to the context. 

    ASSESSMENT CRITERION 4 
    4. Calculations involving surds are correct and reported or recorded in simplified surd form. 


    UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS 
    Providers of learning towards this unit standard will need to meet the accreditation requirements of the GENFETQA.

    Moderation Option:
    The moderation requirements of the GENFETQA must be met in order to award credit to learners for this unit standard. 

    UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE 
    The following essential embedded knowledge will be assessed through assessment of the specific outcomes in terms of the stipulated assessment criteria. Candidates re unlikely to achieve all the specific outcomes, to the standards described in the assessment criteria, without knowledge of the listed embedded knowledge. This means that the possession or lack of the knowledge can be inferred directly from the quality of the candidate`s performance against the standards.
  • Number systems and real and imaginary numbers
  • Estimation and approximation. 
    		•


    Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
  • Use mathematics:
    Use mathematics to analyse, describe and represent realistic and abstract situations and to solve problems. 
    		•

    UNIT STANDARD CCFO COLLECTING 
    Collect, analyse, organise and critically evaluate information:
    Gather, organise, evaluate and interpret numerical information. 

    UNIT STANDARD CCFO COMMUNICATING 
    Communicate effectively:
    Use everyday language and mathematical language to describe relationships, processes and problem solving methods 

    QUALIFICATIONS UTILISING THIS UNIT STANDARD: 
      ID QUALIFICATION TITLE PRE-2009 NQF LEVEL NQF LEVEL STATUS END DATE PRIMARY OR DELEGATED QA FUNCTIONARY
    Fundamental  57879   National Certificate: Manufacturing of Surface Coatings  Level 3  NQF Level 03  Passed the End Date -
    Status was "Reregistered"     		 2023-06-30  CHIETA 
    Elective  48963   National Certificate: Air-Conditioning, Refrigeration and Ventilation  Level 3  NQF Level 03  Passed the End Date -
    Status was "Reregistered"     		 2009-03-12  Was MERSETA until Last Date for Achievement 


    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.
     
    1. Colors Packhouse (Pty) Ltd 
    2. Hi-Veld Fruit Packers (Pty) Ltd 
    3. In House Media Instruction 
    4. Kromco (Pty) Limited 
    5. LUCKY STAR 
    6. Mobile Agri Skills Development and Training NPC 


    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.