O-LevelMathematicsVectors and transformations4024/11 · May/June 2023 · Q276 Marks
OABC is a parallelogram. OA = 2a and OC = 3c. M is the midpoint of BC. T is the point on OB such that OT : TB = 2 : 1.
- (a)Find OB in terms of a and c.[1]
- (b)(i)Express, as simply as possible, in terms of a and c AM[1]
- (b)(ii)Express, as simply as possible, in terms of a and c AT.[2]
- (c)Show that ATM is a straight line.[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 2023). The mark or mark type is shown in brackets.
- [1] 2a + 3c final answer
- [1] 3c - a final answer
- [2] 2c - (2/3)a or (6c - 2a)/3 final answer
- [2] dep on correct AM and AT B1 for AM = (3/2)AT oe and AM is parallel to AT and both go through A so ATM is a straight line OR TM = c - (1/3)a and AT = 2TM and AT is parallel to TM and both go through T so ATM is a straight line
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