Level 5 · Mathematics M5.6

Vectors and matrices

Use vectors for position and direction, and matrices to move shapes and solve equations.

Planned. This book is not written yet. Below is its plan, which a teacher can already use.

You are ready for this book if

You can translate a shape on a grid by a column vector.

The plan

  1. M5.6.1 Vectors: size and direction
    • Add and subtract vectors, and multiply them by a number
    • Find the length and direction of a vector
  2. M5.6.2 Vectors in geometry
    • Use vectors to prove that two lines are parallel
    • Find the point that divides a line in the ratio 2 : 3
  3. M5.6.3 Vectors in 3D
    • Use i, j and k to write vectors in 3D
    • Find the distance between two points in 3D
  4. M5.6.4 The scalar product
    • Find the angle between two vectors with the scalar product
    • Show that two vectors are perpendicular
  5. M5.6.5 Lines in vector form
    • Write the equation of a line as r = a + tb
    • Find where two lines meet, or show that they never meet
  6. M5.6.6 Matrices
    • Add and multiply matrices
    • Show that AB is often not equal to BA
  7. M5.6.7 Matrices that move shapes
    • Find the matrix for a rotation, reflection or enlargement
    • Use the determinant to find how an area changes
  8. M5.6.8 Inverse matrices and equations
    • Find the inverse of a 2 by 2 matrix
    • Solve two simultaneous equations with an inverse matrix

For parents and teachers

Level 5 fits learners who can already: read a textbook. use functions and graphs. In many schools that is about 17 to 20, but start wherever the learner is.

Strand: Shape and space. Written and drawn by attnom. Free to read, print and share.