[Registered Qual & Unit Std Home page] [Search Qualifications] [Search Unit Standards]
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 basic functions and solve related problems 
SAQA US ID UNIT STANDARD TITLE
14086  Work with a wide range of patterns and basic 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 3  NQF Level 03  3 
REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER
Passed the End Date -
Status was "Registered" 		 2001-10-10  2004-10-10  SAQA 0838/01 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2005-10-10   2008-10-10  

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 generalizations 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 1. 

    UNIT STANDARD RANGE 
    This unit standard includes the requirement to:
  • Use algebraic notions to express generality
  • Make conjectures, demonstrate and explain their validity
  • Recognise equivalence among expressions and situations in which we need to manipulate and rearrange for a specific purpose.
  • Work with the following basic functions in terms of their shape and symmetry:

    ; b ax y + =
    2
    ax y = ; x
    a y = ;
    3
    ax y = ;
    x
    a y =
    ; sin x a y = x a y cos = ; ; tan x a y =
    Convert flexibly among various representations of the above functions.
  • Work with the laws and definitions that relate to the above functions.
  • Trigonometric functions are limited to:
    q sin = y ; q q tan ; cos = = y y for ] 360 ; 0 [ ? ? I q using the co-ordinate definitions.
  • Laws applying to exponents
  • Represent, interpret and solve problems mathematically that relate to these 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 generalizations of situations 
    OUTCOME RANGE 
    This outcome includes the requirement to:
  • deal with situations involving the range of functions specified in the main range statement
  • distinguish between patterns which apply to limited sets of data and generalizations which can apply to extended sets of data
  • develop generalizations 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.Generalizations are based on systematic investigations and adequate evidence. 

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

    ASSESSMENT CRITERION 3 
    3.Conjectures are supported by acceptable arguments and claims that generalizations are not possible are supported by coherent reasons. 

    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
  • Explore and express the behaviour of functions using a variety of approaches such as finding function values and solving equations
  • Identify, contrast and compare the features of the functions listed in the main range statement
  • Represent and interpret simple situations which are not expressed in terms of the standard basic functions 
    		•

    ASSESSMENT CRITERIA     

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

    ASSESSMENT CRITERION 2 
    2.Computations in dealing with functions are accurate. 

    ASSESSMENT CRITERION 3 
    3.The key features of the graphs of functions 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 
    Analyze and represent mathematical situations and structures using symbolic forms 
    OUTCOME RANGE 
    This outcome includes the requirement to:
  • Use expressions, functions, equations and inequalities to represent situations
  • Develop strategies for deciding whether symbolic representations are reasonable and interpret such results
  • Recognize equivalent forms of an expression, equation, function or relation
  • Solve systems of linear equations involving 2 equations in 2 variables. 
    		•

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    1.Situations are represented correctly and comprehensively 

    ASSESSMENT CRITERION 2 
    2.Representations are analyzed 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 context 
    OUTCOME RANGE 
    Represent and interpret simple situations which are not expressed in terms of the standard basic functions 

    ASSESSMENT CRITERIA     

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

    ASSESSMENT CRITERION 2 
    2.Representations are analyzed 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. 


    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.
  • Mathematical relations and functions
  • Representations of functions and relations. 
    		•


    Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
    Use mathematics:

    Use mathematics to analyze, describe and represent realistic and abstract situations and to solve problems. 

    UNIT STANDARD CCFO COLLECTING 
    Collect, analyze, organize and critically evaluate information:

    Gather, organize, 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. 

    UNIT STANDARD NOTES 
    This unit standard has expired and is in the process of being reviewed. It will be replaced in due course. 

    QUALIFICATIONS UTILISING THIS UNIT STANDARD: 
    NONE 


    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. College of Vocational Studies (Pty) Ltd 
    2. Colors Packhouse (Pty) Ltd 
    3. Hi-Veld Fruit Packers (Pty) Ltd 
    4. In House Media Instruction 
    5. Kromco (Pty) Limited 
    6. Mobile Agri Skills Development and Training NPC 
    7. NWK Beperk 
    8. Senwes Beperk 


    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.