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: 

Work with a wide range of patterns and inverses of functions and solve related problems 
SAQA US ID UNIT STANDARD TITLE
7470  Work with a wide range of patterns and inverses of functions and solve related problems 
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:
  • Express and justify mathematical generalisations of situations
  • Express mathematical functions and relationships between variables in terms of numerical, graphical, verbal and symbolic approaches
  • Analyse and represent mathematical situations and structures using symbolic forms
  • Use mathematical models to represent and deal with problems that arise in real and abstract contexts. 

  • 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 includes the requirement to:
  • Use algebraic notions to express generality
  • Make conjectures and prove their validity by logical deduction
  • Recognise equivalence among expressions and situations in which we need to manipulate and rearrange for a specific purpose
  • For trigonometric functions, work with compound angle and double angle identities
  • Work with inverses of functions.
  • Work with the laws governing the log function
  • Work with the inverse trigonometric functions in solving trigonometric equations
  • Represent, interpret and solve problems mathematically using the above functions
    More detailed range statements are provided for specific outcomes and assessment criteria as needed. 

  • Specific Outcomes and Assessment Criteria: 

    SPECIFIC OUTCOME 1 
    Express and justify mathematical generalisations of situations. 
    OUTCOME RANGE 
    This outcome includes the requirement to:
  • deal with situations involving the functions listed in the main range statement
  • distinguish between patterns, which apply to limited sets of data, and generalisations, which can apply to, extended sets of data
  • develop generalisations from sets of data which relate to a wide range of contexts, both concrete, such as performing experiments, and abstract, such as investigating open ended mathematical situations. 

  • ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    1. Generalisations are based on systematic investigations and adequate evidence. 
    ASSESSMENT CRITERION NOTES 
    4.1 Contextual problems are represented correctly and comprehensively.

    4.2 Representations are analysed and manipulated efficiently in arriving at results.

    4.3 Solutions are obtained through careful analysis and interpretation of the mathematical representation and solutions are reinterpreted correctly in terms of the problem context. 
    ASSESSMENT CRITERION RANGE 
    This outcome includes the requirement to:

    Represent the problem mathematically using functions, systems of equations and/or inequalities. This could include using the constant speed equation to solve distance, time and speed problems.
     

    ASSESSMENT CRITERION 2 
    2. Generalisations are expressed in symbolic form using functions appropriate to the situation. 

    ASSESSMENT CRITERION 3 
    3. Conjectures are supported by acceptable arguments and claims. 

    ASSESSMENT CRITERION 4 
    4. Generalisations that are not possible are supported by coherent reasoning. 

    SPECIFIC OUTCOME 2 
    Express mathematical functions and relationships. 
    OUTCOME NOTES 
    Express mathematical functions and relationships between variables in terms of numerical, graphical, verbal and symbolic approaches. 
    OUTCOME RANGE 
    This outcome includes the requirement to:
  • Translate from one representation to another
  • Identify, contrast and compare the features of the functions listed in the main range statement. 

  • ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    1. The interchange of functions from one representation to another is fluent. 

    ASSESSMENT CRITERION 2 
    2. Symbolic computations in dealing with functions are accurate. 

    ASSESSMENT CRITERION 3 
    3. The key features of the graphs of functions and the effects of transformations on them are described and interpreted correctly. 

    ASSESSMENT CRITERION 4 
    4. Representations are expressed in an appropriate and integrated way and assist in the formulation and explanation of relationships as functions and relations embedded in contexts. 

    SPECIFIC OUTCOME 3 
    Analyse and represent mathematical situations and structures using symbolic forms. 
    OUTCOME RANGE 
    This outcome includes the requirement to:
  • Use expressions, functions, equations, inequalities and systems of equations to represent situations that involve variable quantities
  • Use the properties of exponential functions and logarithmic functions
  • Demonstrate the interrelationships between exponential and logarithmic functions
  • Operate on polynomials, vectors and simple matrices using manual or mental means.
  • Develop strategies for deciding whether symbolic representations are reasonable and interpret such representations
  • Represent and solve systems of linear equations using matrices and determinants. 

  • ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    1. Situations are represented correctly and comprehensively. 

    ASSESSMENT CRITERION 2 
    2. Representations are analysed and manipulated efficiently in arriving at results. 

    ASSESSMENT CRITERION 3 
    3. Results are interpreted correctly in terms of the situation. 

    SPECIFIC OUTCOME 4 
    Use mathematical models to represent and deal with problems that arise in real and abstract contexts 
    OUTCOME RANGE 
    This outcome includes the requirement to:
  • Represent the problem mathematically using functions, systems of equations and/or inequalities.
    This includes more general rates of change than in the study of motion such as in chemical reactions
  • Work with contexts that involve log functions
  • Use exponents to model phenomena such as bouncing balls, illumination, irradiation, and bacteria count and photo reduction and enlargement. 

  • ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    1. Contextual problems are represented correctly and comprehensively. 

    ASSESSMENT CRITERION 2 
    2. Representations are analysed and manipulated efficiently in arriving at results. 

    ASSESSMENT CRITERION 3 
    3. Solutions are obtained through careful analysis and interpretation of the mathematical representation and solutions are reinterpreted correctly in terms of the problem context. 

    ASSESSMENT CRITERION 4 
    4. A variety of different situations that can be modelled by a particular type of function are identified. 


    UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS 
    Accreditation Option: 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.
  • Mathematical relations and functions
  • Representations of functions and relations. 


  • Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
  • Identify and solve problems using critical and creative thinking:
    Solving a variety of problems based on patterns and functions
  • 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 information to compare and represent relationships and functions. 

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

  • 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  48978   Further Education and Training Certificate: Electrical Network Control  Level 4  NQF Level 04  Reregistered  2023-06-30  EWSETA 
    Fundamental  66370   Further Education and Training Certificate: Roof Truss Technology  Level 4  NQF Level 04  Passed the End Date -
    Status was "Reregistered" 
    2015-06-30  FPMSETA 
    Fundamental  48399   Further Education and Training Certificate: Sugar Processing  Level 4  NQF Level 04  Reregistered  2023-06-30  AgriSETA 
    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  21871   National Certificate: Clothing Manufacturing Technology  Level 4  Level TBA: Pre-2009 was L4  Passed the End Date -
    Status was "Reregistered" 
    2015-06-30  FPMSETA 
    Fundamental  22211   National Certificate: Footwear Technology  Level 4  Level TBA: Pre-2009 was L4  Passed the End Date -
    Status was "Reregistered" 
    2015-06-30  FPMSETA 
    Fundamental  23678   National Certificate: Fossil Power Plant Operation  Level 4  Level TBA: Pre-2009 was L4  Reregistered  2023-06-30  EWSETA 
    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  23733   National Certificate: Nuclear Power Plant Operation  Level 4  Level TBA: Pre-2009 was L4  Reregistered  2023-06-30  EWSETA 
    Fundamental  23675   National Certificate: Management of Building Construction Processes  Level 5  Level TBA: Pre-2009 was L5  Reregistered  2023-06-30  CETA 
    Fundamental  49011   National Diploma: Animal Production  Level 5  NQF Level 05  Reregistered  2023-06-30  AgriSETA 
    Fundamental  21872   National Diploma: Clothing Manufacturing Technology  Level 5  NQF Level 05  Passed the End Date -
    Status was "Reregistered" 
    2015-06-30  FPMSETA 
    Fundamental  21792   National Diploma: Contact Centre Management  Level 5  NQF Level 05  Reregistered  2023-06-30  SERVICES 
    Fundamental  22212   National Diploma: Footwear Technology  Level 5  NQF Level 05  Passed the End Date -
    Status was "Reregistered" 
    2015-06-30  FPMSETA 
    Fundamental  23683   National Diploma: Management of Civil Engineering Construction Processes  Level 5  NQF Level 05  Reregistered  2023-06-30  CETA 
    Fundamental  49010   National Diploma: Plant Production  Level 5  NQF Level 05  Reregistered  2023-06-30  AgriSETA 


    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. Construction Resource Development Centre 
    4. Elsenburg Agricultural Training Institute 
    5. ESKOM DUVHA POWER STATION - OPERATIONS 
    6. ESKOM GROOTVLEI POWER STATION OPERATIONS 
    7. ESKOM KOEBERG - RADIATION PROTECTION 
    8. ESKOM MEDUPI POWER STATION OPERATIONS TRAINING 
    9. Mitek Industries SA ( Pty) Ltd 
    10. MPACT 
    11. Mthashana FET College - Vryheid Campus 
    12. NWK Beperk 
    13. PC Educational Holdings 
    14. RCL Foods-Sugar & Milling 
    15. Sekhukhune FET College - Central Office 
    16. Senwes Beperk 
    17. South African Value Education (Pty) Ltd 
    18. STUDIO 05 HOUSE OF FASHION 
    19. Suidwes Beleggings Eiendoms Beperk 
    20. 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.