Mathematics · Oct / Nov 2021 · Paper 51 · Question 4
YMA01
As printed in the paper
The question as text
4. The position vector, r metres, of a particle P at time t seconds, relative to a fixed origin O, is given by r = (t – 3)i + (1 – 2t)j
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
4(a)[3]
r
= −−
i
3
j
1
3
tan
θ = ±
or
±
3
1
162O or 198O nearest degree
4(b)[5]
(
t
−
3)
2
+
(1 2 )
−
t
2
=
2.5
4
t
2
8
t
3
0
5
t
2
10
t
3.75
0
−
+
=
(
−
+
=
)
1
or 3
t =
isw
2
2
Notes for question 4
4(a)
B1 cao
M1 for any trig ratio of a relevant angle from their r
(trig ratio could be implied by a relevant angle)
(cosine could come from use of the scalar product of their r with j)
A1 cao
4(b)
M1 oe
DM1, dependent on first M1, for simplifying to a 3 term quadratic or to a
form from use of completing the square.
A1 correct quadratic
M(A)1 for t = 0.5
A1 for t =1.5
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