Cambridge
      TECHNICALS
       CAMBRIDGE TECHNICALS 
       IN ENGINEERING
       LEVEL 3 UNIT 1 – MATHEMATICS FOR 
       ENGINEERING
       DELIVERY GUIDE
       Version 1
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   ENGINEERING
                                 Introduction 3
                                 Key Terms                             4
                                 Misconceptions 7
                                 Suggested Activities: 
                                     Learning Outcome (LO1)            8
                                     Learning Outcome (LO2)            10
                                     Learning Outcome (LO3)            11
                                     Learning Outcome (LO4)            12
                                     Learning Outcome (LO5)            14 
                                     Learning Outcome (LO6)            15
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          INTRODUCTION
                                                                                                                                                                                                                                           ENGINEERING
          This Delivery Guide has been developed to provide practitioners with a variety of                             Foreword: Resources                                                                                                FOR
          creative and practical ideas to support the delivery of this qualification. The Guide                         There are a wide range of resources that may be useful in supporting the delivery of this                         TICS
          is a collection of lesson ideas with associated activities, which you may find helpful                        unit, some of which have been listed in the separate Resources Link resource available                            A
          as you plan your lessons.                                                                                     from http://www.ocr.org.uk/qualifications/cambridge-technicals-engineering-level-3/.                              THEM
                                                                                                                        These include reference text books, web-based tutorials, web-based video tutorials and                            A
          OCR has collaborated with current practitioners to ensure that the ideas put forward in                       worked and practice questions.                                                                                    M
          this Delivery Guide are practical, realistic and dynamic. The Guide is structured by learning 
          outcome so you can see how each activity helps you cover the requirements of this unit.                       Many resources will singularly cover the entire content of this unit, and for this reason 
          We appreciate that practitioners are knowledgeable in relation to what works for them                         specific resources have not been listed against each topic area.  Although there are 
          and their learners. Therefore, the resources we have produced should not restrict or                          many resources that cover mathematical concepts generically, some are dedicated to 
          impact on practitioners’ creativity to deliver excellent learning opportunities.                              the application of mathematics in the context of engineering.  Teachers and learners are 
                                                                                                                        encouraged to solve problems related to engineering where possible.
          Whether you are an experienced practitioner or new to the sector, we hope you find                            The following two books (which also include further web-based resources and which 
          something in this guide which will help you to deliver excellent learning opportunities.                      are available as paperback or e-book) are highly recommended:
          If you have any feedback on this Delivery Guide or suggestions for other resources you                        Bird, John (2014) ‘Basic Engineering Mathematics’ – Routledge, UK
          would like OCR to develop, please email resources.feedback@ocr.org.uk.                                        Bird, John (2014) ‘Engineering Mathematics’ – Routledge, UK
          Unit aim                                                                                                       Unit 1 Mathematics for engineering
                                                                                                                           LO1      Understand the application of algebra relevant to engineering problems
          Mathematics is one of the fundamental tools of the engineer. It underpins every branch of                        LO2      Be able to use geometry and graphs in the context of engineering 
          engineering and the calculations involved are needed to apply almost every engineering                                    problems
          skill.                                                                                                           LO3      Understand exponentials and logarithms related to engineering problems
          This unit will develop learners’ knowledge and understanding of the mathematical 
          techniques commonly used to solve a range of engineering problems.                                               LO4      Be able to use trigonometry in the context of engineering problems
          By completing this unit learners will develop an understanding of:                                               LO5      Understand calculus relevant to engineering problems
          •    algebra relevant to engineering problems                                                                             Be able to apply statistics and probability in the context of engineering 
          •    the use of geometry and graphs in the context of engineering problems                                       LO6      problems
          •    exponentials and logarithms related to engineering problems 
          •    the use of trigonometry in the context of engineering problems                                                                                                                                                              ENGINEERING
          •    calculus relevant to engineering problems                                                                Opportunities for Maths skills development                                                                         IN
          •    how statistics and probability are applied in the context of engineering problems 
                                                                                                                        This unit provides a range of activities entirely focussed on Mathematics for Engineering.  
           Please note                                                                                                                                                                                                                    TECHNICALS
                                                                                                                        The activities are not designed to replace you own subject knowledge and expertise in                              
           The timings for the suggested activities in this Delivery Guide DO NOT relate to the Guided                  deciding what is most appropriate for your learners.
           Learning Hours (GLHs) for each unit. 
           Assessment guidance can be found within the Unit document available from                                                                                                                                                       MBRIDGE
                                                                                                                                      Maths                                                                                                CA
           www.ocr.org.uk.                                                                                                                                                                                                                3
                                                                                                                                                                                                                                           
           The latest version of this Delivery Guide can be downloaded from the OCR website.                                                                                                                                              VEL
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         KEY TERMS
         UNIT 1 – MATHEMATICS FOR ENGINEERING                                                                                                                                                                           ENGINEERING
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          Explanations of the key terms used within this unit, in the context of this unit                                                                                                                             A
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          Key term                 Explanation                                                                                                                                                                         A
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          Algebra                  Algebra is an area of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
          Angles and radians       Converting from angle to radians: 360˚= 2 π radians  i.e. x radians = 180°x/π degrees;
          Arcs                     x degrees = πx/180° radians
                                   Arc length s = rθ where θ is in radians                                         2
          Binomial expression A binomial is a mathematical expression (a polynomial) with two terms eg 3x  +2 or 5x -1
          Circles - areas                                        2
                                   The area of a circle: area = πr              2          2   2
          Circles – co-ordinate  The co-ordinate equation of a circle: (x – a)  + (y – b)  = r
          equation
          Co-ordinate              Co-ordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system.
          geometry
          Curve sketching          Curve sketching is the sketching of mathematical functions in order to visualise their shape and is often used to determine solution(s).
          Definite integrals       A definite integral is an integral expressed as the difference between the values of the integral at specified upper and lower limits of the independent variable.
          Differentiation –                                                    ax
          exponentials and         Differentiation of expressions containing e  and ln ax
          logarithms                                                                                                                                                                                     n
          Differentiation –        The derivative is the instantaneous rate of change of a function with respect to one of its variables.  Simple functions are taken to contain terms of the formy = ax                ENGINEERING
          simple functions                                                                                                                                                                                              IN
          Differentiation          Differentiation of expressions containing the terms sine (sin) and cosine (cos).
          – trigonometric 
          function                                                                                                                                                                                                     TECHNICALS
                                                                                                                                                                                                                        
          Exponential              An exponential function is a function whose value is a constant raised to the power of the argument.  In this unit, it is taken to be of the form y = ex and y = e-x
          function                                                                                                                                                                                                     MBRIDGE
          Factorisation            Factorisation is the reverse of expanding brackets.  For example putting 2x² + x - 3 into the form (2x + 3)(x - 1)                                                                   CA
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