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SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED UNIT STANDARD: 

Demonstrate understanding of real and complex number systems 
SAQA US ID UNIT STANDARD TITLE
7485  Demonstrate understanding of real and complex 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 4  NQF Level 04 
REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER
Reregistered  2018-07-01  2023-06-30  SAQA 06120/18 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2024-06-30   2027-06-30  

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
  • Use real and non-real numbers and systems to make sense of and solve non-trivial problems. 

  • 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 3. 

    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 including loans, bonds and annuities, using electronic technology
  • Elementary matrices illustrative of a system in which some of the properties of real and complex numbers do not hold.
    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 
  • 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
  • Establish the effect of measurement error on final values calculated. 

  • 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 measurement error and the calculations involved. 

    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 
    Use real and non-real numbers and systems to make sense of and solve non-trivial problems. 
    OUTCOME RANGE 
  • Demonstrate understanding of representations for operations on vectors and matrices and use appropriate technology to solve systems of linear equations
  • Operate on real numbers, vectors and matrices using by-hand operations for simple cases and technology for non-trivial cases. 

  • ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    1. Notation for expressing numbers and symbols is consistent with mathematical conventions. 

    ASSESSMENT CRITERION 2 
    2. Methods of calculation and approximations are appropriate to the problem types. 

    ASSESSMENT CRITERION 3 
    3. Complex numbers are represented in terms of real and imaginary parts. 

    ASSESSMENT CRITERION 4 
    4. Formulae used for calculations are appropriate to the situation. 

    ASSESSMENT CRITERION 5 
    5. Methods used to make sense of and solve problems are efficient and solutions obtained are verified to be correct in terms of the context or problem. 


    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 are 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 complex numbers
  • Financial concepts and instruments
  • Budgets and national and global economic issues
  • Estimation and approximation
  • Compound increase and decrease. 


  • Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
  • Identify and solve problems using critical and creative thinking:
    Solving a variety of numerical and financial problems.
  • 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 financial information to plan and make provision for monitoring budgets and other financial situations. 

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

  • UNIT STANDARD CCFO DEMONSTRATING 
  • See the world as a set of related systems 

  • UNIT STANDARD CCFO CONTRIBUTING 
    Observing and describing the effect of various issues on the economy. 

    REREGISTRATION HISTORY 
    As per the SAQA Board decision/s at that time, this unit standard was Reregistered in 2012; 2015. 

    QUALIFICATIONS UTILISING THIS UNIT STANDARD: 
      ID QUALIFICATION TITLE PRE-2009 NQF LEVEL NQF LEVEL STATUS END DATE PRIMARY OR DELEGATED QA FUNCTIONARY
    Fundamental  14854   National Certificate: Agric Sales and Services  Level 4  NQF Level 04  Reregistered  2023-06-30  AgriSETA 
    Fundamental  22868   National Certificate: Chemical Process Operations  Level 4  NQF Level 04  Passed the End Date -
    Status was "Reregistered" 
    2005-10-09  CHIETA 
    Fundamental  20893   National Certificate: Human Resources Management and Practices Support  Level 4  NQF Level 04  Passed the End Date -
    Status was "Registered" 
    2005-02-13  Was SABPP until Last Date for Achievement 
    Fundamental  21792   National Diploma: Contact Centre Management  Level 5  NQF Level 05  Reregistered  2023-06-30  SERVICES 
    Elective  65110   Further Education and Training Certificate: Management  Level 4  NQF Level 04  Passed the End Date -
    Status was "Reregistered" 
    2009-03-14  As per Learning Programmes recorded against this Qual 


    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. Balemi Consulting Pty Ltd 
    2. Cedara College of Agriculture 
    3. Elsenburg Agricultural Training Institute 
    4. NWK Beperk 
    5. PC Educational Holdings 
    6. RCL Foods-Sugar & Milling 
    7. Sekhukhune FET College - Central Office 
    8. Senwes Beperk 
    9. Suidwes Beleggings Eiendoms Beperk 
    10. VKB LANDBOU (PTY) LTD 



    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.