Topic Test 1 Mark Scheme
Sequences - Higher
Q Answer Mark Comments
1 17 – 2n B1
2 152 B1
B1 one correct term
Two terms from the sequence or
3 10n + 1 B2 lists at least the first three terms
ie two from 11, 21, 31, 41, ... from both sequences
ie 5, 7, 9, ... and 1, 6, 11, ...
a×1+b=a+b
4(a) and B1
b×1+a=a+b
2a + b or 3b + a M1
4(b)
2a + b = 3b + a so a = 2b A1
Substitutes n = 1, 2, 3 etc into Values are 11, 5, 1, 0.5, 0.28 for first 5
M1
5 formula for at least three terms terms
A1
6(a) 32(3 + 1) = 9 × 4 B1
102(10 + 1) or
M1
6(b) 100 × 11
1100 A1
AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registere
England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.
Q Answer Mark Comments
oe
eg If n is odd then n2(n + 1) is
Full explanation odd × odd × even = even
If n is odd then n2 is odd and n + 1 is and
even
If n is even then n2(n + 1) is
and even × even × odd = even
6(c) B2
If n is even then n2 is even and n + 1 B1 Partial explanation
is odd
eg If n is odd then n2 is odd and
and n + 1 is even
odd × even = even or
If n is even then n2(n + 1) is
even × even × odd = even
AQA Education (AQA) is a registered charity
umber
(n 1073334) and a company limited by guarantee registered i 2 of 3
England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.
Q Answer Mark Comments
7(a) 113 and 159 B2 B1 one correct term
Alternative method 1
14 22 30
First and second differences correct M1
8 8
their 8 2
Correctly subtracts n from the
2 M1 5 7 9 (11 13 15)
given sequence
2n M1dep
4n2 + 2n + 3 A1 oe
Alternative method 2
Any three of
a+b+c=9
Allow one error but all equations must
4a + 2b + c = 23 M1
be in a, b and c
9a + 3b + c = 45
16a + 4b + c = 75
Eliminates one variable to obtain a
pair of equations in two variables M1
7(b) eg 3a + b = 14 and 5a + b = 22
Eliminates one variable correctly
M1dep Allow one error
eg a= 4
4n2 + 2n + 3 A1 oe
Alternative method 3
Sets up table of differences
n 0 1 2 3 4
M1
c 3 9 23 45 75
a+b 6 14 22 30
2a 8 8 8
Extends table back to n = 0 M1
Identifies rows as 2a, a + b and c A1
4n2 + 2n + 3 A1 oe
AQA Education (AQA) is a registered charity
umber
(n 1073334) and a company limited by guarantee registered i 3 of 3
England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.
