Topic outline

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    IGCSE Mathematics Resource Plus overview
    • Vectors and transformations
      Vectors
      • Further materials

      show/hide  Video transcript
      This unit of work is Vectors.

      Learners often struggle with the difference between vector and scalar quantities. They can also be confused with Vector notation.

      This unit will help to develop learners conceptual understanding of vectors and give them the opportunity to apply their understanding to complex multi-step problems.

      For instance learners will understand how vectors can be used to describe the translation of shapes by plotting the translation of each of the individual points.

      Extended learners will apply vectors to real life problems including finding the magnitude and direction of a vector. They will also solve problems in Vector Geometry.

      This unit of work is just one of several approaches that you could take when teaching this topic and you should aim to adapt the resources to match ability level of your learners as well as your school context.

    • Vectors



    • In this unit of work, are going to formalise work learners have already completed on transformations, securing links to different areas of mathematics, specifically Pythagoras theorem and trigonometry.

      We will extend learners’ understanding by exploring practical situations including real life problems and Vector Geometry. For example we will demonstrate how you can use vectors to describe the translation of shapes by plotting the translation of each of the individual points.

      Extended learners will apply vectors to real life problems including finding the magnitude and direction of a vector. They will also solve problems in Vector Geometry.

      Learners can have difficulty understanding the difference between vector and scalar quantities and will often struggle to understand that vectors need a direction as well as a magnitude. Some think that the magnitude of a component is equal to the magnitude of the vector, and others know the “rule” that components are shorter than the vector but have problems identifying the magnitude of the components graphically.

      They can confuse the language of vectors for example speed and velocity which are often used incorrectly in the media and online, and they can also be confused by the different notation used for vectors. For this reason it is important to be rigorous when using the language of vectors and scalars in the classroom.

      This unit of work is just one of several approaches that you could take when teaching this topic, and you should aim to adapt the resources to match ability level of your learners, as well as your school context.


    • Lesson resources




    • Lesson 3 video


      show/hide  Video transcript
      As we have already seen a vector has magnitude (size) and direction. When looking at a vector diagram the length of the line shows its magnitude and the arrow represents the direction of the vector.

      We're going to start by looking at how you add vectors. We can add two vectors by joining them end on end.

      Here you can see two vectors a and b.

      To add vector b to vector a you join the tail of vector b to the head of vector a.

      The result is a vector that joins the tail of vector a to the head of vector b. This is called the resultant vector a + b.

      Think about two non-parallel vectors, a and b. Then a plus b is the translation of a followed by the translation of b.

      You should be able to see from the diagram that it doesn't matter which order you add them, you will get the same result.

      So a plus b is exactly the same as b plus a.

      This tells us that vector addition, like ordinary numerical addition is commutative, in other words the order doesn't matter.

      You can add vectors with or without the use of a diagram for example if you want to add two vectors p and q you can add the horizontal components and then the vertical components.

      This will give you the vector five-two. Five to the right and two up.

      You can always check your results using a diagram.

      You can also subtract vectors.

      a - b is defined as the translation of a followed by the translation of minus b.

      To subtract vector b from vector a you join the tail of vector -b to the head of vector a.

      The resultant vector a - b joins the tail of vector a to the head of vector b.

      You can see that the resultant vector a minus b can be considered either as a minus b or as minus b plus a.

      You can also subtract vectors with or without the use of a diagram by subtracting components.

      First subtract the horizontal components and then the vertical components.

      In this example the resultant vector is one eight - one to the right and eight up.

      This can be pictured on a diagram as follows.


    • Interactive tools

    • show/hide  How can these tools be used?
      These resources are for use with any digital display in your classroom - including a projector, interactive whiteboard or any form of screen sharing technology. When selected, they fill the current available display. The resource is then ready for presentation and annotation.

      As part of your ongoing Resource Plus subscription, we plan to include additional tools. We'd love to know your thoughts and ideas for further development.

      • Graph A4 4mm axes

      • Graph A4 4mm axes

      • Graph A4 4mm


    • Test Maker - Vectors past paper questions


    • testmaker-img_tcm149-505892.jpg

    • Test Maker is an online service that makes it easy for you to create high-quality, customised test papers for your learners using Cambridge questions.

      Test Maker is currently available for Cambridge IGCSE Mathematics 0580 and Cambridge IGCSE Additional Mathematics 0606 syllabuses, but although the grading differs for Cambridge IGCSE (9-1) syllabuses, the questions are valid for equivalent Cambridge IGCSE (9-1) and O Level syllabuses.

      Test Maker is available to all Cambridge schools through the Extra Services section of the School Support Hub.