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

Solve equations and inequalities in the real and complex number systems, using algebraic and graphical methods 
SAQA US ID UNIT STANDARD TITLE
243827  Solve equations and inequalities in the real and complex number systems, using algebraic and graphical methods 
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  4 
REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER
Passed the End Date -
Status was "Registered" 		 2007-09-12  2010-09-12  SAQA 0172/07 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2011-09-12   2014-09-12  

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 rigorous understanding of algebra and a more comprehensive set of algebraic manipulation skills thereby laying a valuable foundation for the algebraic manipulations.

A person credited with this unit standard is able to:
  • Determine the real and complex roots of polynomial equations.
  • Draw and work with absolute value graphs.
  • Solve simple absolute value equations.
  • Solve rational equations and inequalities.

    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 
    It is assumed that learners working in this unit are competent in Mathematics at NQF Level 2 or equivalent. 

    UNIT STANDARD RANGE 
    N/A 

    Specific Outcomes and Assessment Criteria: 

    SPECIFIC OUTCOME 1 
    Draw and work with absolute value graphs. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    The absolute value function is defined algebraically and represented graphically. 

    ASSESSMENT CRITERION 2 
    Absolute value graphs of the form (See the formula shown in the MS Word document) are drawn, given the equation of the function. 

    ASSESSMENT CRITERION 3 
    The equation of the absolute value function is determined in the form (See formula shown in the MS Word document) given the necessary information on the graph of the function. 

    ASSESSMENT CRITERION 4 
    Absolute value graphs of other pre-requisite functions are drawn by inference. 
    ASSESSMENT CRITERION RANGE 
    Includes, but is not limited to, (See the formula shown in the MS Word document) and (See the formula shown in the MS Word document).
     

    ASSESSMENT CRITERION 5 
    Absolute value graphs, in conjunction with other algebraic graphs, are analysed to identify significant points. 
    ASSESSMENT CRITERION RANGE 
    Includes determining specific points on the graph, points of intersection of graphs, vertical and horizontal distances between points on the graphs).
     

    SPECIFIC OUTCOME 2 
    Solve simple absolute value equations. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Absolute value equations of the form (See the formula shown in the MS Word document) are solved using algebraic methods. 

    ASSESSMENT CRITERION 2 
    Verification of the algebraic solution of absolute value equations using graphical methods. 

    SPECIFIC OUTCOME 3 
    Solve rational equations and inequalities. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Multi-term rational equations are solved using algebraic methods. 
    ASSESSMENT CRITERION RANGE 
    Solutions are written in the form (See the formula shown in the MS Word document) where appropriate.
     

    ASSESSMENT CRITERION 2 
    Rational inequalities are solved using algebraic methods. 
    ASSESSMENT CRITERION RANGE 
    Includes logical argument, number lines and graphical methods.
     

    SPECIFIC OUTCOME 4 
    Determine the real and complex roots of polynomial equations. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Quadratic equations are solved using factorisation or the quadratic formula. 
    ASSESSMENT CRITERION RANGE 
    Solutions are written in the form (See the formula shown in the MS Word document) where appropriate.
     

    ASSESSMENT CRITERION 2 
    Cubic equations are solved using factorisation or the factor theorem. 
    ASSESSMENT CRITERION RANGE 
    Solutions are written in the form (See the formula shown in the MS Word document) where appropriate.
     


    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 
    Learners can identify, interpret and manipulate various algebraic statements, equations and inequalities with the purpose of representing and then finding simplifications or solutions:
  • Evaluate solutions to algebraic equations and identify the accompanying field to which they belong.
  • Solve equations up to degree three (the roots may be real or complex.).
  • Solve absolute value equations algebraically and graphically.
  • Solve rational equations and inequalities.
  • Draw absolute value graphs of the form (See the formula shown in the MS Word document).
  • Find the equation of the absolute value function given the graph.
  • Draw the absolute value graph of other pre-requisite functions by inference.
  • Interpret the absolute value graphs to determine specific points on the graph.
  • Solve absolute value equations of the form (See the formula shown in the MS Word document).
  • Solve multi-term rational equations using algebraic methods.
  • Solve rational inequalities using methods most suited to the learning style of the learner. 
    		•

    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:
  • Solving a variety of mathematical problems requiring graphs, trigonometry and differentiation. 
    		•

    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:
  • Interpret information in order to develop a corresponding mathematical model of the context. 
    		•

    UNIT STANDARD CCFO COMMUNICATING 
    Communicating effectively using visual, mathematical and/or language skills in the modes of oral and/or written persuasion when:
  • Use everyday language and mathematical language and symbols to describe processes, theorems and in solving mathematical problems. 
    		•

    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 

    UNIT STANDARD NOTES 
    N/A 

    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.
     
    NONE 


    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.