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Answer Scheme (Paper 3)
1
Sub (1) into (2):
For 2 distinct roots, M1
M1
M1
M1A1
5
2(a)
B1
B1
2
2(b) M1
A1
M1
A1
A1
5
1
3 M1
A1
M1
A1
4
4
M1M1
M1
M1
A1
5
5
M1
M1
M1
M1
M1
8
2
M1
A1
A1
6 Let
M1
M1
M1M1
A1
M1
A1
7
3
7 M1
A1
M1
A1
M1
A1
M1
A1
8
8(i) By the property of circle, the perpendicular bisector of chord passes through centre of circle. Therefore, the perpendicular bisector of chord AB passes through C.
B11
8(ii)
The coordinates of C are .
M1
M1
M1
A1
4
4
y
x
4
2
43
1
0
1
2
cbxay sin
1cos2 xy3
y
x
4
2
43
1
0
1
cbxay sin
8(iii) Radius = Equation of circle:
M1
A1
2
9(a)
When ,
The gradient of the normal at is undefined.The equation of the normal is .
M1
A1
2
9(b)
M1
M1
M1
M1
A1
5
10(a) Possible values of Value of and
B0.5,B0.5B0.5,B0.5
2
5
10(b)Award 2 marks for correct graph drawn (with labels).
Number of solutions = 3
M1
B2
B1
4
11(i) M2
A1
3
11(ii) M1
M1
M1
M1
5
6
A1
12
1 2 3
0.5
1
1.5
2
xy
y
Award 1 point for each of the following:
M1
M1
8
1.19 1.74 2.07 2.28 2.40
1.19 0.87 0.69 0.57 0.48
7
(i)
(ii)
Correct labelling of the graph, x-axis and y-axis Appropriate use of scale and plotting of all points Drawing of best fit line
gradient
y-intercept
From the graph, when .
M3
A1
A1
A1
8