A-LevelFurther MathematicsMatrices9231/12 · May/June 2021 · Q414 Marks
The matrix M represents the sequence of two transformations in the x-y plane given by a rotation of 60° anticlockwise about the origin followed by a one-way stretch in the x-direction, scale factor d (d ≠ 0).
- (a)Find M in terms of d.[4]
- (b)The unit square in the x-y plane is transformed by M onto a parallelogram of area ½d² units². Show that d = 2.[2]
- (c)The matrix N is such that MN = [[1, 1], [½, ½]]. Find N.[3]
- (d)Find the equations of the invariant lines, through the origin, of the transformation in the x-y plane represented by MN.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [B1] Rotation 60° anticlockwise about the origin.
- [B1] One-way stretch in the x-direction, scale factor d.
- [M1 A1] Correct order.
- [M1] Uses value of det M.
- [A1] AG
- [B1 FT] Inverse of their M.
- [M1] Multiplies on the left by the inverse of their M.
- [A1] CAO
- [B1] Transforms (x, y) to (X, Y).
- [M1 A1] Uses y = mx and Y = mX.
- [A1]
- [A1] WWW
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