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A-LevelFurther MathematicsMatrices9231/12 · May/June 2024 · Q413 Marks

The matrix M is given by M = ( (1/2) (-√3/2) / (√3/2) (1/2) ) ( (14) (0) / (0) (1) )

  1. (a)The matrix M represents a sequence of two geometrical transformations in the x-y plane. Give full details of each transformation, and make clear the order in which they are applied.[4]
  2. (b)Write M⁻¹ as the product of two matrices, neither of which is I.[2]
  3. (c)Find the equations of the invariant lines, through the origin, of the transformation represented by M.[5]
  4. (d)The triangle ABC in the x-y plane is transformed by M onto triangle DEF. Given that the area of triangle DEF is 28 cm², find the area of triangle ABC.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [B1] [One way] stretch, rotation
  2. [B1] Stretch followed by rotation
  3. [B1] Stretch parallel to the x-axis, scale factor 14
  4. [B1] Rotation, π/3 [anticlockwise] about the origin.
  5. [B1] Both inverses correct.
  6. [B1] Correct order.
  7. [B1] M = ( (7) (-√3) / (7√3) (1/2) )
  8. [B1] Transforms (x / y) to (X / Y)
  9. [M1] Uses y = mx and Y = mX .
  10. [A1]
  11. [A1]
  12. [M1] Uses |DEF| = | det M|| ABC| .
  13. [A1] 2 cm² Allow with units missing.

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About this question

Topic
Matrices, A-Level Further Mathematics (syllabus 9231). Structured question, 13 marks.
Source
A-Level Further Mathematics, May/June 2024 Paper 1 Variant 2, question 4.

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