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

Use and apply matrices and graphs to organise information and solve problems 
SAQA US ID UNIT STANDARD TITLE
243838  Use and apply matrices and graphs to organise information and solve 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  2 
REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER
Passed the End Date -
Status was "Reregistered" 		 2018-07-01  2023-06-30  SAQA 06120/18 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2026-06-30   2029-06-30  

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 will enable students to represent numerical data in a rectangular array and perform the simple operations on a matrix. The unit will also enable students to define and classify graphs.

A person credited with this unit standard is able to:
  • Arrange numbers in a matrix and perform matrix operations to facilitate problem solving.
  • Solve systems of linear equations by diagonalisation or determining the inverse matrix.
  • Define different types of graphs and associated properties.
  • Identify and use walks, paths and circuits in graphs.

    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 
    A working knowledge of the solution of simultaneous equations in two variables and representation of two dimensional geometrical figures, NQF Level 2. 

    UNIT STANDARD RANGE 
    N/A 

    Specific Outcomes and Assessment Criteria: 

    SPECIFIC OUTCOME 1 
    Arrange numbers in a matrix and perform matrix operations to facilitate problem solving. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    The matrix is used as a suitable summary of information to facilitate solving of problems. 

    ASSESSMENT CRITERION 2 
    Dimensions of a matrix are used to test the feasibility of matrix operations. 

    ASSESSMENT CRITERION 3 
    A matrix is multiplied by a scalar to alter the matrix elements by an enlargement factor. 

    ASSESSMENT CRITERION 4 
    Compatible matrices are added or multiplied to solve problems. 

    SPECIFIC OUTCOME 2 
    Solve systems of linear equations by diagonalisation or determining the inverse matrix. 
    OUTCOME RANGE 
    Systems of linear equations are in two variables. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    A system of simultaneous linear equations is summarised in a matrix. 

    ASSESSMENT CRITERION 2 
    Simultaneous equations are solved by diagonalisation through row reduction. 

    ASSESSMENT CRITERION 3 
    The inverse of a 2 x 2 matrix is found using (See the formula shown in the MS Word document). 

    ASSESSMENT CRITERION 4 
    The inverse matrix is used to solve systems of linear equations. 

    SPECIFIC OUTCOME 3 
    Define different types of graphs and associated properties. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Graph Theory terminology is used to classify graphs according to their properties. 
    ASSESSMENT CRITERION RANGE 
    Terminology includes but is not limited to vertex, edge, simple, regular, connected and tree.
     

    ASSESSMENT CRITERION 2 
    The degree of vertices of a graph are found to describe graphs. 

    ASSESSMENT CRITERION 3 
    A graph is drawn given the specifications of the vertices. 

    ASSESSMENT CRITERION 4 
    Isomorphic graphs are identified by spatial interpretation of drawn graphs. 

    SPECIFIC OUTCOME 4 
    Identify and use walks, paths and circuits in graphs. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Walks, paths and circuits are defined to classify aspects of graphs. 

    ASSESSMENT CRITERION 2 
    Eulerian paths or circuits are identified in graphs to inform problem solving in networks. 

    ASSESSMENT CRITERION 3 
    Hamiltonian circuits are identified in graphs to inform problem solving in networks. 

    ASSESSMENT CRITERION 4 
    Algorithms are used to test the nature of the paths and circuits in the graph. 
    ASSESSMENT CRITERION RANGE 
    Algorithms used include Euler's, Fleury's and Dirac's algorithms.
     


    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 
  • Arrange numbers in a suitable rectangular array or matrix.
  • Addition and multiplication of compatible matrices and multiplication by a scalar.
  • The solution of systems of linear equations in two variables by the method of diagonalisation.
  • Finding the inverse of 2 x 2 matrices by a sequence of row transformation (See the formula shown in the MS Word document).
  • Use the inverse matrix to solve systems of linear equations.
  • Define simple, regular and connected graphs, their vertices, edges and the degree of vertices.
  • Identify isomorphic graphs.
  • Define walks, paths, circuits (including Eulerian and Hamiltonian). 
    		•

    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 and matrices. 
    		•

    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 (graph) 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:
  • Represent information in a matrix. 
    		•

    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  64829   National Certificate: Lifting Machine Operations  Level 3  NQF Level 03  Passed the End Date -
    Status was "Reregistered"     		 2023-06-30  TETA 


    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. Cathy Hill Solutions (Pty) Ltd 
    2. Dee's Training (PTY) LTD 
    3. Diversity technology Training Institute 
    4. DQ Staffing Solutions 
    5. Edu Wize Group Pty Ltd 
    6. Excellect 209 (PTY) LTD 
    7. Excellect 209 PTY LTD 
    8. Learning Exchange Pty (Ltd) 
    9. Mediro Training Academy 
    10. Mphatlalatsane Learning Resources 
    11. Phephani Learnerships cc 
    12. Quantum Leap College Pty Ltd 
    13. Safety Haz Training (PTY) Ltd 
    14. Staffing Logistics 
    15. The Skills Authority 


    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.