Cambridge IGCSE Maths (0580) · Revision notes · Topic 7 of 9

Cambridge IGCSE Maths 0580 Transformations and Vectors Notes

Revision notes for topic 7, Transformations and vectors, of the Cambridge IGCSE Mathematics (0580) syllabus for exams from 2025 to 2030 (Cambridge says the 2028–2030 syllabus has no significant changes that affect teaching). Each of the 4 sub-topics lists what the syllabus asks, marked Core or Extended, with a short explanation and a worked example. Cover the answer and try each example first.

4 sub-topics
1 Core and Extended
3 Extended only

Core Core students (Papers 1 and 3) learn the Core statements. Extended Extended students (Papers 2 and 4) learn everything: the Core statements, the Extended additions and the Extended-only sub-topics. Papers 1 and 2 are non-calculator.

7.1 Transformations

Core C7.1 Extended E7.1

Recognise, describe and draw reflections, rotations (multiples of 90°), enlargements (positive and fractional scale factors) and translations (by a column vector)

Extended also: Reflections in lines such as y = x and y = -x, and enlargements with negative scale factors.

Same mathematics as Edexcel 4MA1.

0580 practice questions

8 questions written for 0580 in the Transformations and vectors practice: 7 Core and 1 Extended, 5 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Write down the image of each point after the translation.

(a) $(3, 2)$ translated by $(\begin{matrix} 4 \\ - 5 \end{matrix})$ (b) $(- 1, 6)$ translated by $(\begin{matrix} - 2 \\ 3 \end{matrix})$

Show the answer and mark scheme

B1 (a) (7, −3)
B1 (b) (−3, 9)

Answer: (a) $(7, - 3)$ (b) $(- 3, 9)$

Practice question (Extended, non-calculator, 4 marks):

$P$ is the point $(3, - 2)$ . Write down the image of $P$ after

(a) a reflection in the line $y = x$

(b) a reflection in the line $y = - x$

Show the answer and mark scheme

B1 (a) (−2, 3)
B1 (b) (2, −3)
M1 (c) vector from centre (2, −3), multiplied by −2 to give (−4, 6)
A1 (−3, 7)

Answer: (a) $(- 2, 3)$ (b) $(2, - 3)$ (c) $(- 3, 7)$

0580 questions: Transformations questions (Core and Extended, with worked answers)
Edexcel 4MA1 notes: Geometry and Trigonometry (all notes)
Practise (4MA1 questions, same mathematics): Transformations questions

7.2 Vectors in two dimensions

Extended only E7.2

Extended: Vector notation and column vectors; Add and subtract vectors and multiply a vector by a scalar.

Same mathematics as Edexcel 4MA1.

Revise it

A vector has size and direction. Add column vectors component by component; parallel vectors are multiples of each other.

Example: a = (3, −1), b = (1, 2). Find 2a + b.

Answer: (6, −2) + (1, 2) = (7, 0).

0580 practice questions

8 questions written for 0580 in the Transformations and vectors practice: 8 Extended, all non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Extended, non-calculator, 2 marks):

$a = (\begin{matrix} 5 \\ - 3 \end{matrix})$ and $b = (\begin{matrix} - 2 \\ 6 \end{matrix})$ .

Find (a) $a + b$ (b) $3 a$ .

Show the answer and mark scheme

B1 (a) (3, 3) as a column vector
B1 (b) (15, −9) as a column vector

Answer: (a) $(\begin{matrix} 3 \\ 3 \end{matrix})$ (b) $(\begin{matrix} 15 \\ - 9 \end{matrix})$

Practice question (Extended, non-calculator, 3 marks):

$a = (\begin{matrix} 4 \\ - 1 \end{matrix})$ and $b = (\begin{matrix} - 2 \\ 3 \end{matrix})$ .

Find the vector $c$ such that $2 a + c = 3 b$ .

Show the answer and mark scheme

M1 c = 3b − 2a
M1 (−6, 9) − (8, −2)
A1 (−14, 11)

Answer: $(\begin{matrix} - 14 \\ 11 \end{matrix})$

0580 questions: Vectors questions (Core and Extended, with worked answers)
Edexcel 4MA1 notes: Vectors
Practise (4MA1 questions, same mathematics): Vectors questions

7.3 Magnitude of a vector

Extended only E7.3

Extended: The magnitude of a column vector (x, y) is √(x² + y²).

Same mathematics as Edexcel 4MA1.

0580 practice questions

8 questions written for 0580 in the Transformations and vectors practice: 8 Extended, 5 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Extended, non-calculator, 2 marks):

Find the magnitude of $(\begin{matrix} 6 \\ 8 \end{matrix})$ .

Show the answer and mark scheme

M1 √(6² + 8²)
A1 10

Answer: $10$

Practice question (Extended, calculator, 4 marks):

The vector $(\begin{matrix} 2 t \\ t - 1 \end{matrix})$ has magnitude 5.

Find the two possible values of $t$ .

Show the answer and mark scheme

M1 (2t)² + (t − 1)² = 25
A1 5t² − 2t − 24 = 0
M1 (5t − 12)(t + 2) = 0
A1 t = 2.4 or t = −2

Answer: $t = 2.4$ or $t = - 2$

0580 questions: Vectors questions (Core and Extended, with worked answers)
Edexcel 4MA1 notes: Vectors
Practise (4MA1 questions, same mathematics): Vectors questions

7.4 Vector geometry

Extended only E7.4

Extended: Express vectors in terms of two others; position vectors; Use vectors to show lines are parallel or points are collinear.

Same mathematics as Edexcel 4MA1.

0580 practice questions

Practice question (Extended, non-calculator, 2 marks):

In triangle $O A B$ , $\vec{O A} = a$ and $\vec{O B} = b$ . The point $N$ is halfway along $O B$ .

Write down, in terms of $a$ and $b$ , (a) the vector from $B$ to $A$ (b) the vector from $A$ to $N$ .

Show the answer and mark scheme

B1 (a) a − b
B1 (b) −a + ½b

Answer: (a) $a - b$ (b) $- a + \frac{1}{2} b$

Practice question (Extended, non-calculator, 3 marks):

$\vec{O P} = 2 a + b$ , $\vec{O Q} = 5 a + 4 b$ and $\vec{O R} = a + b$ .

Show that $P Q$ is parallel to $O R$ and find the ratio of their lengths.

Show the answer and mark scheme

M1 PQ = OQ − OP
A1 3a + 3b
A1 = 3(a + b) = 3 OR, so parallel; PQ : OR = 3 : 1

Answer: $\vec{P Q} = 3 (a + b)$ , parallel to $O R$ , ratio $3 : 1$

0580 questions: Vectors questions (Core and Extended, with worked answers)
Edexcel 4MA1 notes: Vectors
Practise (4MA1 questions, same mathematics): Vectors questions

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Practise transformations and vectors

32 practice questions are written for 0580 on every sub-topic of this topic. For the 4 sub-topics that are the same mathematics in Edexcel 4MA1, the practice also has our 4MA1 Higher questions, which are Extended level. Core students: use the Core filter on the practice page; every sub-topic with Core content has questions written for 0580 Core. Practice is part of the IGCSE plan, with a free preview; these notes are free.

Transformations and vectors practice for 0580: the 32 questions written for 0580, tagged Core or Extended and non-calculator or calculator, with the Edexcel 4MA1 Higher questions for the sub-topics that are the same mathematics
Student hub: the Edexcel 4MA1 units (Unit 5, Unit 7), each question marked
Cambridge IGCSE Maths 0580 past papers: the 2025 specimen papers and past papers, with a timer
Formulas for transformations and vectors on the one-page 0580 formula sheet (free PDF), showing which are on the paper's formula list
Cambridge 0580 transformations and vectors questions by topic, Core and Extended, with worked answers

More on this topic

Knowledge organiser: Transformations and vectors on one page (printable)

Knowledge organiser: Transformations and vectors on one page (key facts, formulas and mistakes to avoid; printable PDF)

Questions about transformations and vectors

What is in Cambridge IGCSE 0580 transformations and vectors?

Topic 7 has 4 sub-topics: 7.1 Transformations; 7.2 Vectors in two dimensions; 7.3 Magnitude of a vector; 7.4 Vector geometry.

Which transformations and vectors sub-topics are Extended only?

7.2 Vectors in two dimensions; 7.3 Magnitude of a vector; 7.4 Vector geometry. Core students (Papers 1 and 3) do not need them.

Are these notes free?

Yes. Every note and worked example on these pages is free to read, with no sign-in.

Join free: practise transformations and vectors with marking →

Cambridge IGCSE Maths 0580 Transformations and Vectors Notes

7.1 Transformations

0580 practice questions

7.2 Vectors in two dimensions

Revise it

0580 practice questions

7.3 Magnitude of a vector

0580 practice questions

7.4 Vector geometry

0580 practice questions

Practise transformations and vectors

Try it now

Questions about transformations and vectors