Knowledge organisers

Transformations and vectors: Cambridge IGCSE Maths (0580) knowledge organiser

Everything to know about transformations and vectors on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Translation: Slides a shape without turning it; described by a column vector.
Enlargement: Changes the size by a scale factor from a centre of enlargement.
Column vector: Shows a movement: the top number across, the bottom number up.
Magnitude: The length of a vector: √(x² + y²).

Key formulas

Vectors: add and subtract column vectors component by component; \(k\binom xy=\binom{kx}{ky}\)
Magnitude; position vectors	\(\left\|\binom xy\right\|=\sqrt{x^2+y^2},\) \(\overrightarrow{AB}=\mathbf b-\mathbf a\)

Worked example

a = (3, −1) and b = (2, 5), as column vectors. Find 2a − b and its magnitude.

2a = (6, −2)
2a − b = (6 − 2, −2 − 5) = (4, −7)
|2a − b| = √(16 + 49)

Answer: 2a − b = (4, −7), magnitude √65 = 8.06 (3 s.f.)

Common mistakes

Describing a transformation without all its details, such as the centre, angle and direction of a rotation
Reading a column vector the wrong way round: the top number is across

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

Reflect shapes in given lines and rotate them about a centre through multiples of 90°, describing each transformation fully.
Enlarge shapes by fractional and negative scale factors from a given centre, and describe such enlargements fully.
Recognise and fully describe single transformations, giving the mirror line, centre and angle, column vector or scale factor and centre as needed.
Calculate the magnitude of a column vector using Pythagoras' theorem, giving answers exactly as surds or to a set accuracy.
Express vectors in terms of given vectors such as a and b by following routes through a diagram, including points dividing lines in a ratio.
Reflect shapes in the lines y = x and y = −x, and describe such reflections fully, including within combined transformations.

The printable sheet

Transformations and vectors knowledge organiser for Cambridge IGCSE Maths (0580): one A4 page of key definitions, formulas, a worked example and common mistakes — Transformations and vectors knowledge organiser (Cambridge IGCSE Maths (0580)), A4. Download the PDF.

Revise it next

Other Cambridge IGCSE Maths (0580) topics: Number · Algebra and graphs · Coordinate geometry · Geometry · Mensuration · Trigonometry · Probability · Statistics · All Cambridge IGCSE Maths (0580) organisers