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SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED UNIT STANDARD: 

Utilise algebraic processes 
SAQA US ID UNIT STANDARD TITLE
243829  Utilise algebraic processes 
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 provides learners with the opportunity to develop a more comprehensive understanding of algebra and to provide rigorous proof of algebraic propositions.

A person credited with this unit standard is able to:
  • Work with the exponential and logarithmic functions and the laws relating to these functions.
  • Make graphical representations of exponential and logarithmic functions.
  • Prove a mathematical proposition by Induction.

    In order to see this unit standard with its exact formulae, please use the link at the end of the Searchable Database home page. SAQA is in the process of adapting the National Learners' Records Database to accommodate such formulae. 

  • LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING 
  • Mathematics at NQF Level 3 or equivalent. 

  • UNIT STANDARD RANGE 
    Utilisation includes the use of investigation of logarithmic and exponential functions; and their graphs; and the graphs of rational functions; and mathematical induction. 

    Specific Outcomes and Assessment Criteria: 

    SPECIFIC OUTCOME 1 
    Work with the exponential and logarithmic functions and the laws relating to these functions. 
    OUTCOME RANGE 
    Includes base e. 

    ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    The laws of exponents and logarithms are used in the simplification and manipulation of given functions. 

    ASSESSMENT CRITERION 2 
    An understanding of the number e is demonstrated in problems involving exponents and logarithms. 

    ASSESSMENT CRITERION 3 
    Simple exponential equations are solved using the laws of exponents and algebraic manipulation. 

    ASSESSMENT CRITERION 4 
    Simple logarithmic equations are solved using the laws of logarithms and algebraic manipulation. 

    SPECIFIC OUTCOME 2 
    Make graphical representations of exponential and logarithmic functions. 

    ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    Exponential graphs, including (see the formula shown in the MS document), are drawn using a given exponential function. 

    ASSESSMENT CRITERION 2 
    Logarithmic graphs, including y = ln x, are drawn using a given logarithmic function. 

    ASSESSMENT CRITERION 3 
    Equations for the reflections of the exponential or logarithmic functions are determined using the properties of reflections in the x and y axes. 

    ASSESSMENT CRITERION 4 
    Exponential and logarithm functions are found by determining the inverse of a function. 

    SPECIFIC OUTCOME 3 
    Prove a mathematical proposition by Induction. 

    ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    The process is explained to reflect the logic and order of proof by mathematical induction. 

    ASSESSMENT CRITERION 2 
    Statements of summation of series are proved using mathematical induction. 

    ASSESSMENT CRITERION 3 
    Statements related to factoring with Natural numbers are proved using mathematical induction on the given statement. 


    UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS 
  • The assessment will be governed by the policies and guidelines of the relevant Education and Training Quality Assuror (ETQA) that has jurisdiction over this field of learning.
  • The assessor will be accredited, have the competence of this unit standard and be a subject matter expert in this learning area. 

  • UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE 
  • Define the exponential and logarithmic functions (including natural logarithms).
  • Apply the basic laws to these functions.
  • Graph exponential and logarithmic functions.
  • Investigate proof by Induction.
  • Draw exponential graphs, including (see the formula shown in the MS document).
  • Draw logarithmic graphs, including y = ln x.
  • Find the equation for the reflections of the exponential or logarithmic functions using the properties of reflections in the x and y axes.
  • Find the equation of the exponential and logarithm functions by determining the inverse of a function.
  • Proof of statements of summation of series using mathematical induction.
  • Proof of factoring with Natural numbers using mathematical induction(?). 

  • UNIT STANDARD DEVELOPMENTAL OUTCOME 
    N/A 

    UNIT STANDARD LINKAGES 
    N/A 


    Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
    Identifying and solving problems in which responses display that responsible decisions using critical and creative thinking have been made when:
  • Using critical and creative thinking where mathematical models can be useful tools in the solution of real problems. 

  • UNIT STANDARD CCFO WORKING 
    Working effectively with others as a member of a team, group, organisation, and community during:
  • Class investigation, projects and groupwork. 

  • UNIT STANDARD CCFO ORGANISING 
    Organising and managing oneself and one's activities responsibly and effectively when:
  • Doing investigations and projects. 

  • UNIT STANDARD CCFO COLLECTING 
    Collecting, analysing, organising and critically evaluating information to better understand and explain:
  • Collect, analyse and critically evaluate information to apply exponential models and make judgment regarding the exponential models. 

  • UNIT STANDARD CCFO COMMUNICATING 
    Communicating effectively using visual, mathematical and/or language skills in the modes of oral and/or written persuasion when:
  • Communicate effectively using mathematical notation and symbolism, and visual representations in both oral and written presentation. 

  • UNIT STANDARD CCFO SCIENCE 
    Using science and technology effectively and critically, showing responsibility towards the environment and health of others when:
  • Calculating areas of segments and arc lengths of circles using trigonometric functions.
  • Connecting differentiation to rate of change. 

  • UNIT STANDARD CCFO DEMONSTRATING 
    Demonstrating an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation when:
  • Recognising that mathematical argument, proof and problem-solving do not exist in isolation of the broader mathematical community and the applications of mathematical in a social world. 

  • UNIT STANDARD ASSESSOR CRITERIA 
    N/A 

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

    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
    Fundamental  59057   Further Education and Training Certificate: Telecommunication Network Operations  Level 4  NQF Level 04  Reregistered  2023-06-30  MICTS 


    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. TELKOM SA SOC LTD 
    2. Tira Telecoms 
    3. Triple Play Fibre Optic Solutions 



    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.