Further Pure Mathematics FP2 (6668)

Practice paper B mark scheme

Question number / Scheme / Marks
1. / (a) / / M1 A1 (2)
(b) / / M1
= / M1
= 1 – () / A1 cso(3)
(5 marks)
2. / (a) (i) / |x + (y – 2)i| = 2|x + (y + i)| / M1
x2 + (y – 2)2 = 4(x2 + (y + 1)2)
so 3x2 + 3y2 + 12y = 0 any correct form; 3 terms; isw / A1 (2)
(ii) /
(0, -2) / Sketch circle / B1
Centre (0,–2) / B1
r = 2 or touches axis / B1 (3)
(b) / w = 3(z – 7 + 11i) / B1
= 3z – 21 + 33i / B1 (2)
(7 marks)
3. / Attempt form / M1
I.F. = , = / M1, A1
 or / M1ft
i.e. / M1 A1
y = / A1cao (7)
(7 marks)
4. / (a) / ,
, / M1
,
, / A1
,
, / A1
(three terms are sufficient to establish method) / M1
/ A1 (5)
(b) / Substitute x = 1 / B1
/ M1A1cao (3)
(8 marks)
5. / (a) / (cos  + i sin )5 = cos 5 + i sin 5 / M1
(cos  + i sin )5 =
cos5 + 5 cos4(i sin ) + 10 cos3(i sin )2
+ 10 cos2(i sin )3 + 5 cos  (i sin )+ (i sin )5 / M1 A1
cos 5 = cos5 – 10 cos3 sin + 5 cos  sin4 / M1
= cos5 – 10 cos3 (1 – cos2) +
5 cos (1 – 2cos2 + cos4) / M1
= 16 cos5 – 20 cos3 + 5 cos  () / A1cso (6)
(b) / cos 5 = –1 (or 1, or 0) / M1
5 = (2n 1)180 =(2n 1)36 / A1
x = cos  = –1, – 0.309, 0.809 / M1 A1 (4)
(10 marks)
6. / (a) / y = (x – 2)(x – 4)

8
6
2 3 4
y = 6 – 2x / Line crosses axes / B1
Curve shape / B1
Axes contacts:
6, 8 / B1
3, 2, 4 / B1 (4)
(b) / 6 – 2x = (x – 2)(x – 4) and –6 + 2x = (x – 2)(x – 4) / M1 M1
x2 – 4x + 2 = 0 x2 – 8x + 14 = 0 either / M1
= 2 – 2 = 4 – 2 / A1 A1 (5)
(c) / 2 – 2 < x < 4 – 2 / M1A1 (2)
(11 marks)
7. / (a) / , / M1 A1
x2– 2x+ (2 + 9x2)vx = x5 / M1
/ A1
Given result () / A1cso (5)
(b) / CF: / M1 A1
Appropriate form for PI: (or ax2 + bx + c) / M1
Complete method to find  and  / M1
/ M1A1ft (6)
(c) / y = Ax sin 3x + Bx sin 3x + – / B1ft (1)
(12 marks)
8. / (a) (i) / / B1 (1)
(ii) / , = 0 / M1A1, M1
(Proceed to ) / M1
, () / A1 A1 cso(6)
(b) / / M1 A1
/ M1 A1
/ M1 A1
() / M1 A1cso(8)
(15 marks)

GCE Further Pure Mathematics and Decision Mathematics mock paper mark schemes – UA0195821