O-LevelMathematicsVectors and transformations4024/22 · May/June 2022 · Q89 Marks
The matrix A satisfies the following equation. (2 3; 5 2) - 3A = (5 3; -4 -1) Find A.
- (a)The matrix A satisfies the following equation. (2 3; 5 2) - 3A = (5 3; -4 -1) Find A.[2]
- (b)B=(4 -2; p 2) The determinant of B is 2. Find the value of p and hence write down B⁻¹.[3]
- (c)(i)[Figure with shapes A and B on a coordinate grid] The diagram shows shape A and shape B. Describe fully the single transformation that maps shape A onto shape B.[2]
- (c)(ii)The transformation represented by the matrix (-2 0; 0 -2) maps shape A onto shape C. Draw and label shape C.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [2] B1 for 2 or 3 correct elements in final answer (-1 0; 3 1) or (-3 0; 9 3) soi or (3 0; -9 -3) soi
- [3] B2 for p = -3 OR M1 for 2p - (4 × -2) = 2 oe B1 for 1/2 (2 2; -p 4) oe
- [2] B1 for translation or (-4; 3) with no further properties
- [2] B1 for three vertices correct or three correct pairs of coordinates soi
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