Mathematics · Oct / Nov 2022 · Paper 41 · Question 1
YMA01
As printed in the paper
The question as text
1. A curve C has parametric equations t −3 y = 1 t x = t + 2 t ∈ t > 3 Show that all points on C lie on the curve with Cartesian equation y = ax −1 bx where a and b are constants to be found. (3)
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
Attempts to get t in terms of x or y . E.g.
x
=
=
t
−
t
−
3
x
1
Forms a Cartesian equation and makes progress to making y the subject
x
−
1
1
y
=
+
2
y
=
+
2
E.g.
t
x
3
x
−
7
1
y
=
x
3
M1: For an attempt to get t or 1
t in terms of x or y.
Condone poor attempts here. It is the intention that is important
dM1: For a complete attempt to form an equation of the form
y
=
f( )
x
Look for
t in terms of x or y
y the subject.
t
3
x
1
1
x
=
=
t
− followed by
y
=
+
y
=
+
E.g.I.
2
2
t
−
3
x
1
t
3
x
x
−
1
1
1
E.g.II.
y
=
+
=
t
followed by
2
t
y
−
2
1
y
−
(
)
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