O-LevelMathematicsVectors and transformations4024/22 · May/June 2023 · Q108 Marks
(a) F is the point (6, 1), G is the point (–2, 4) and GH = (-3 8). Calculate |FH|. (b) [Figure 10.1] OA = a, OB = b and AC = kb. X is the point on OC such that OX = mOC.
- (a)F is the point (6, 1), G is the point (–2, 4) and GH = (-3 8). Calculate |FH|.[3]
- (b)(i)Write OX in terms of m, k, a and b.[2]
- (b)(ii)BX = (3/5)a - (1/2)b. Find the value of k.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [3] Scheme 1:
- B1 for FH = (-9 -5) oe
- M1 for their(-9)² + their(-5)²
- 10.3 or 10.29 to 10.30
- Scheme 2:
- B1 for [H =] (-3, –4) or [OH =] (-3 4)
- M1 for (6 – their(–3))² + (1 – their(–4))² oe
- [2] B1 for answer ma + ...b or ...a + mkb
- or OC = a + kb
- m (a + kb) or ma + mkb oe
- After 0 scored, SC1 for answer -ma - mkb oe
- [3] B2 for (3/5)a – (1/2)b = –b + ma + mkb oe
- or B1 for BX = BO + OX soi or OX = OB + BX soi
- 5/6
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