Higher November 2023 Paper 4 Q2

OCRHigherCurrent spec3 marksProperties of Numbers

2 A prime number is a whole number that has exactly two factors.

(a) Explain why 1 is not a prime number. [1]

(b) \(a\) and \(b\) are prime numbers.

Write down the 6 factors of \(a^2b\). [2]

Mark scheme (a)

Answer	Marks	Part marks and guidance
it has only one factor	1		Accept any correct reason, see appendix If more than one statement mark the best as long as it is not contradicted or has an incorrect statement

Response	Mark
It’s a square number and square numbers are not prime	1 bod
Its only factor is 1	1
It does not have two factors only one	1
It can only be 1×1	1bod
It only has itself as a factor	1
It can only be divided by itself	1
Doesn’t have exactly 2 factors	0
It does not have two factors	0
It’s a square number	0
Its only multiples are 1 and itself	0
It only goes into itself	0
It only has one prime factor	0
There is only 1 ×1 = 1 there are no other factors to make 1 and it’s not a whole number (spoilt)	0
It does not have two factors that are not 1 or 0	0
It has the same factor	0
It does not have any factors	0

Mark scheme (b)

Answer	Marks	Part marks and guidance
1, \(a\), \(b\), \(ab\), \(a^2\), \(a^2b\)	2	B1 for at least 3 correct	Ignore repetitions Maximum of 6 values, if more than 6 apply choice Condone e.g. \(a \times a\), \(a \times b\)