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SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED UNIT STANDARD: 

Find the derivatives and antiderivatives of a range of sample functions and apply these to problems involving curve sketching, areas under curves, maxima and minima and rates of change 
SAQA US ID UNIT STANDARD TITLE
7482  Find the derivatives and antiderivatives of a range of sample functions and apply these to problems involving curve sketching, areas under curves, maxima and minima and rates of change 
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:

Determine the derivatives and antiderivatives of polynomial and other suitable functions;
Express the relationships involved between a function, its derivative and antiderivative in terms of numerical, graphical, verbal and symbolic approaches;
Sketch the graphs of a range of functions;
Analyse and represent mathematical and contextual situations using derivatives and antiderivatives;
Use mathematical models involving derivatives and antiderivatives to 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 Unit Standard Math 3002A. 

UNIT STANDARD RANGE 
This unit standard includes the requirement to:

Use basic rules of differentiation to differentiate polynomial and other simple functions.
Determine the antiderivatives of suitable functions.
Use differentiation to determine maxima and minima.
Sketch the graphs of suitable functions.
Determine the area under a curve in simple cases.
Determine instantaneous rates of change. 

Specific Outcomes and Assessment Criteria: 

SPECIFIC OUTCOME 1 
Determine antiderivatives and area under curves using rules. 
OUTCOME RANGE 
This outcome includes the following requirement:
  • Use the definition of an antiderivative.
  • Establish the rules by differentiation
  • Assume the rule to determine the area A between the graph of a function f, the x-axis and coordinates at a and b. 

  • ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    1. Antiderivatives are determined by using the rules correctly. 
    ASSESSMENT CRITERION NOTES 
    3.1 The coordinates and nature of stationary points are determined correctly by appropriate use of differential calculus.

    3.2 The sketches, in which all the required information is used correctly, are drawn clearly and represent the functions correctly. 
    ASSESSMENT CRITERION RANGE 
    This outcome includes the requirement to:

    Determine intervals over which a function is increasing or decreasing;
    Determine position of stationary points;
    Determine the nature of stationary points using either the first or second derivative of the function in question;
    Determine the values of x-intercepts for cases where the relevant equation can be solved by the use of the quadratic formulae or by factorisation using the factor theorem if necessary;
    Describe the behaviour of the function value.
     

    ASSESSMENT CRITERION 2 
    2. Areas are determined correctly by splitting over two or more intervals when the graph crosses the x-axis. 

    SPECIFIC OUTCOME 2 
    Determine maximum and minimum values of a function over an interval. 
    OUTCOME RANGE 
    This outcome includes the requirement to:
  • Work with both the absolute and relative values
  • Use only the functions for which the derivatives can be found as in Unit Standard Math 3002A. 

  • ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    1. Both absolute and relative values are taken into account when determining maximum or minimum value over an interval. 

    ASSESSMENT CRITERION 2 
    2. Maximum and minimum values are reported correctly. 

    SPECIFIC OUTCOME 3 
    Use calculus methods to sketch the curves of polynomial functions. 
    OUTCOME RANGE 
    This outcome includes the requirement to:
  • Determine intervals over which a function is increasing or decreasing
  • Determine position of stationary points
  • Determine the nature of stationary points using either the first or second derivative of the function in question
  • Determine the values of x-intercepts for cases where the relevant equation can be solved by the use of the quadratic formulae or by factorization using the factor theorem if necessary
  • Describe the behaviour of the function value 

  • ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    1. The coordinates and nature of stationary points are determined correctly by appropriate use of differential calculus. 

    ASSESSMENT CRITERION 2 
    2. The sketches, in which all the required information is used correctly, are drawn clearly and represent the functions correctly. 

    SPECIFIC OUTCOME 4 
    Apply calculus methods to solve practical problems. 
    OUTCOME RANGE 
    This outcome includes the requirement to:
  • Solve optimisation problems involving maxima and minima
  • Solve problems in which areas need to be determined
  • Apply knowledge of differentiation and antidifferentiation to solve problems involving rates
  • Model the problems using calculus methods
  • Verify the results of the calculus modeling by referring to the practical context. 

  • ASSESSMENT CRITERIA
     

    ASSESSMENT CRITERION 1 
    1. Calculus knowledge is applied correctly in modelling the practical problem. 

    ASSESSMENT CRITERION 2 
    2. Relevant mathematics is used to solve the model. 

    ASSESSMENT CRITERION 3 
    3. The results of solving the model are verified in the practical context 


    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 option 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 by means 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.

    Differentiation.
    Antidifferentiation.
    The increasing, decreasing or stationary nature of a function at a point. 


    Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
  • Identify and solve a variety of problems using critical and creative thinking:
    Solving a variety of problems based on differentiation and antidifferentiation 

  • UNIT STANDARD CCFO COLLECTING 
  • Collect, analyse, organise and critically evaluate information:
    Interpret information in order develop a corresponding mathematical model of the context 

  • UNIT STANDARD CCFO COMMUNICATING 
  • Communicate effectively:
    Use everyday language and mathematical language and symbols to describe processes and in solving problems. 

  • 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  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  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  21792   National Diploma: Contact Centre Management  Level 5  NQF Level 05  Passed the End Date -
    Status was "Reregistered" 
    2020-07-30  SERVICES 


    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. ELSENBURG AGRICULTURAL COLLEGE 
    4. NWK Beperk 
    5. RCL Foods-Sugar & Milling (MP) 
    6. Sekhukhune FET College - Central Office 
    7. Senwes Beperk 
    8. Suidwes Beleggings Eiendoms Beperk 
    9. 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.