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IGCSE Maths: Transformations and vectors

Topic 7 of the Cambridge IGCSE Mathematics (0580) syllabus: transformations of shapes, and vectors with their magnitude and geometry. Here is what each part asks, a practice question for each, and the mistakes that cost the most marks.

Practise transformations and vectors as a game

The 4 parts of the topic

Each part with one practice question, made by the same engine your child plays. Parts marked Extended are for the Extended paper only.

7.1 Transformations: recognise, describe and draw reflections, rotations, enlargements and translations

Shape A is reflected in the x-axis, and the image is then reflected in the line y = x.
Which SINGLE transformation takes A straight to the final image?

  1. Reflection in the y-axis
  2. Rotation of 180° about the origin
  3. Rotation of 90° anticlockwise about the origin
  4. Translation by (3, −2)
Show the answer

Rotation of 90° anticlockwise about the origin. (x, y) → (x, −y) → (−y, x): that is a quarter turn anticlockwise about the origin.

7.2 Vectors in two dimensions: a translation as a vector, add and subtract, multiply by a scalar Extended

a = (5, 5) b = (−5, −2)
Find a − b.

  1. (0, 3)
  2. (10, 7)
  3. (−10, −7)
  4. (7, 10)
Show the answer

(10, 7). Subtract the x parts and the y parts: (5 − −5, 5 − −2).

7.3 Magnitude of a vector Extended

Find the magnitude of the vector
(−5, −12).

  1. 7
  2. 17
  3. 15
  4. 13
Show the answer

13. √(5² + 12²) = √169 = 13. Squaring removes any minus signs.

7.4 Vector geometry Extended

p = a − b and q = −3a + 3b.
q = kp. Find k.

  1. 2
  2. -3
  3. -2
  4. 3
Show the answer

-3. Compare the a parts: −3 ÷ 1 = −3; the b parts give 3 ÷ −1 = −3 as well. So q = −3p: q is parallel to p, in the opposite direction.

The mistakes that cost the most marks

Huh Lab checks every wrong answer against known mistakes like these, and goes back to the step behind the one your child keeps making.

Adds the scale factor to the coordinates

Enlargement MULTIPLIES distances from the centre. Adding just slides the shape.

Rotates the wrong way round

Clockwise is the way the clock hands go. Put a finger on the centre and turn the shape that way.

Enlarges from the origin instead of the centre given

Distances are multiplied from the CENTRE of enlargement. Draw rays from it through each corner.

Checks only one part of a vector

Parallel needs the SAME multiplier for the a part and the b part. Check both.

Ignores the minus sign on the scale factor

A negative scale factor sends the image through the centre to the OTHER side, upside down.

Gives the y-coordinate first

Along the corridor, THEN up the stairs: x comes before y.

Reflects in the wrong direction

A reflection goes straight ACROSS the mirror line, never along it.

Loses the negative sign

Use a number line: below zero the numbers keep counting, in the other direction.

Other IGCSE Maths topics

Number17 parts Algebra and graphs13 parts Coordinate geometry7 parts Geometry8 parts Mensuration5 parts Trigonometry6 parts Probability4 parts Statistics7 parts

Practise it as a game

Short rounds on any topic, a new question every time, the exact mistake found, and a report to you after every session.

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