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These are the Transum resources related to the statement: "Pupils should be taught to apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; {use vectors to construct geometric arguments and proofs}".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Vector Maze Use vectors to navigate through a maze by the shortest distance.
- Vector Cops Help the cops catch the robbers by finding the vectors that will end the chase.
- Vectors Video Learn about addition and subtraction of vectors and multiplication of a vector by a scalar.
- Vectors An online exercise on addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic representations of vectors.
- Parallel Vectors Collect together in groups the vectors that are parallel to each other.

Here are some exam-style questions on this statement:

- "
*Find \(4a - b\) as a column vector.*" ... more - "
*Calculate the vector \(3a - 2b\) if the vectors \(a\) and \(b\) are:*" ... more - "
*OABC is a parallelogram with O as origin. The position vector of A is \(a\) and the position vector of C is \(c\).*" ... more - "
*(a) Shape \(A\) is translated to shape \(B\) using the vector \( \begin{pmatrix}m\\n\\ \end{pmatrix}\). What are the values of \(m\) and \(n\)?*" ... more - "
*ABCD is a quadrilateral. The points E, F, G and H are the midpoints of the sides of this quadrilateral.*" ... more - "
*ABCDOE is a regular hexagon with O as origin. The position vector of A is \(a\) and the position vector of B is \(b\).*" ... more - "
*Consider a triangle ABC where M is the midpoint of AB and F is the point on BC where BF:FC = 3:4.*" ... more - "
*In the parallelogram OABC two of the sides can be represented by vectors \(a\) and \(c\).*" ... more - "
*ABCD is a quadrilateral*" ... more - "
*(a) If A is the point (3,5) write down the position vector of A.*" ... more - "
*In the diagram above (not drawn to scale) \(X\) is the point on \(AB\) such that \(AX:XB = 9:4\).*" ... more - "
*Consider two perpendicular vectors \(p\) and \(q\).*" ... more - "
*Two points \(A\) and \(B\) have coordinates (1 , 3 , 6) and (8 , 7 , 10) respectively.*" ... more

Here is an Advanced Starter on this statement:

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Geometry Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of a formal mathematical science emerging in the West as early 6th Century BC. See also the topics of Angles, Area, Bearings, Circles, Enlargements, Mensuration, Pythagoras, Shape, Shape (3D), Symmetry, Transformations and Trigonometry.
- Vectors Vectors usually first make an appearance when pupils learn about transformations. A translation is best described with a vector written as a two by one matrix. Following that pupils learn how vectors can be used to prove geometric relationships in simple line diagrams. Ultimately vectors are studied as a major topic for A Level and International Baccalaureate courses where vectors in three dimensions are included.You can think of a vector as what is needed to 'carry' the point A to the point B. The Latin word vector means â€˜carrierâ€™ and was first used by 18th century astronomers investigating planet rotation around the Sun.

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