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MOCK EXAM MARKSCHEME AS Unit 1: Pure Mathematics A

This exam is based on 2018 Legacy WJEC C1 and C2 papers

Time allowed 2 ½ hours Total Marks Available 121

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13. Given that n is an even number, prove that 9𝑛2 + 6𝑛 has a factor of 12. [3]

If n is an even number, then n can be written as 2m

n = 2m

Now, 9n2 + 6n = 9(2m)2 + 6(2m) M1

= 36m2 + 12m

=12(3m2 + m) A1

Hence 12 must be a factor of 9n2 + 6n if n is an even number. A1

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15. The points A, B and C have position vectors -2i + j, 2i + 5j and 6i + 3j respectively.

M is the midpoint of BC.

(a) Find the position vector of the point D such that 𝐵𝐶⃗⃗⃗⃗ ⃗ = 𝐴𝐷⃗⃗ ⃗⃗ ⃗. [3]

(b) Find the magnitude of 𝐴𝑀⃗⃗⃗⃗⃗⃗ . [3]

(a) 𝐵𝐶⃗⃗⃗⃗ ⃗ = 4i -2j = 𝐴𝐷⃗⃗ ⃗⃗ ⃗ B1

𝐴𝐷⃗⃗ ⃗⃗ ⃗ = 𝑂𝐷⃗⃗⃗⃗⃗⃗ − 𝑂𝐴⃗⃗ ⃗⃗ ⃗

4i -2j = 𝑂𝐷⃗⃗⃗⃗⃗⃗ − ( -2i + j ) M1

𝑂𝐷⃗⃗⃗⃗⃗⃗ = 2i – j A1

(b) 𝑂𝑀⃗⃗⃗⃗ ⃗⃗ = 4i + 4j B1

𝐴𝑀⃗⃗⃗⃗⃗⃗ = 𝑂𝑀⃗⃗ ⃗⃗ ⃗⃗ − 𝑂𝐴⃗⃗ ⃗⃗ ⃗ = 4i + 4j – ( -2i + j )

𝐴𝑀⃗⃗⃗⃗⃗⃗ = 6i + 3j M1

|𝐴𝑀⃗⃗⃗⃗ ⃗⃗ | = √62 + 32 = √45 = 3√5 A1

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