Alevel_C1C2

13
Exam-style mark scheme
Sequences and series
Question Scheme Marks
Number
1. (a) 4, 2, 1, 1 2
A1 (1)
(b)
10
41 ( − ( 05 . ) )
S 10 = = 7. 9922 (4 dp.)
1−
0.
5
M1 A1 (2)
(c) S ∞ =
2
= 8
1−
0.
5
M1 A1
S∞ S10 0. 0078
A1 (3)
6
2. (a) d = 5 ÷
5
− =
3
−
1
3
M1 A1 (2)
(b)
5
,
5
− A2 (2)
81 243
( )
−
(c) S ∞ = 5 ÷ 1 −
1
=
3
15
4
2 3 4
or 3.75 M1 A1 (2)
6
3. (a) 16 + 32x + 24x + 8x + x A3 (3)
2 3 4 2
(b) ( 1 + 2x)( 16 + 32x + 24x + 8x + x ) ≈ 16 + 64x + 88x
a = 16, b = 64, c = 88 A3 (3)
6
−
( ) n
( )
2
1
4. (a) 1− = 1− × + ( )
n
× −
2 2 2 2
+ ... M1 A1
nn ( − 1)
∴ = 9
8
B1
2
n − n − 72 = 0
B1
( n − 9)( n + 8)
= 0
Since n is a positive, therefore n = 9 A1 (5)
(b) Coefficient of x 3 : nn ( 1 )( n 2 )
6
5. (a)
− − ×
1
( − )
2
3
=
−
21
2
M1 A1 (2)
8 × 7 2
a = 448, a =±4 M1 A2 (3)
2
2 2 3 3
(b) 1 + 8ax + 28a x + 56a x + ... M3
Let x = 0.1, then
B1
8
( 1 + 4 × 0. 1) ≈ 1 + 32 × 0. 1 + 448 × 0. 01 + 3584 × 0.
001 = 12.264 M1 A1 (6)
8
(c) Percentage error: (.) 1 4 − 12 . 264
× 100 = 17%
8
(nearest integer)
(.) 14
M1 A1 (2)
11
7
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Core C2