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