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AQA GCSE Maths Assessment Pack
Chapter 17 (marks available: 22)
1 Two consecutive numbers are n and n + 1.
n + (n + 1) = 2n + 1
2n + 1 is not divisible by 2 and therefore is not even.
This is true for any value of n, so the challenge is not fair.
2 5n − 6
3 a
Pattern number
1
2
3
4
5
Number of tiles
4
7
10
13
16
b 3n + 1 tiles
4 Any suitable fraction u such that u + (u + 1) is not a fraction, e.g. u = ½, so u + (u + 1) = ½ + 1½ = 2.
5 a −75, −108, −147
b −3n2
6 Ashanti is wrong because when a is negative, a3 is negative and a2 is positive, so a3 < a2. Also, when
a = 0 or 1, a3 = a2; a3 will be less than a2 when a is a fraction.
7 (3n − 4)2 = (3n − 4)(3n − 4)
= 9n2 − 12n − 12n + 16
= 9n2 − 24n + 16
= 8n2 + n2 − 18n − 6n + 9 + 7
= (n2 − 6n + 9) + (8n2 − 18n + 7)
= (n − 3)2 + (4n − 7)(2n − 1)
8 Two consecutive numbers are n and n + 1.
Two consecutive square numbers are therefore n2 and (n + 1)2 = n2 + 2n + 1.
One more than the sum two consecutive square numbers is then n2 + n2 + 2n + 1 + 1 = 2n2 + 2n + 2 =
2(n2 + n + 1).
2(n2 + n + 1) is divisible by 2 and is therefore even for any value of n.
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