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Questions: Lockdown Pure Maths Test 51 Question Paper
This is the A-Level Pure Mathematics marking scheme from September 2020. It shows how marks are awarded, so you can mark your own answers to the matching question paper. See the question paper.
Upper $6{ }^{\text {th }}$
LOCKDOWN PURE MATHS TEST 49
Tuesday 22 September 2020
ANSWERS
30 MARKS
NB: If a numerical answer cannot be given exactly, and the accuracy required is not specified in the question, then in the case of an angle it should be given to the nearest degree, and in other cases it should be given correct to $\mathbf{2}$ significant figures.
1. Given that $a * b=\left\{\begin{array}{ll}a+b | \text { if } a+b<6 a+b-6 | \text { if } a+b \geq 6\end{array}\right.$, and it is defined on the set $\{0,1,2,3,4,5\}$.
(i) Construct the operation table for *.
[3]
$*$ | 0 | 1 | 2 | 3 | 4 | 5
0 | 0 | 1 | 2 | 3 | 4 | 5
1 | 1 | 2 | 3 | 4 | 5 | 0
2 | 2 | 3 | 4 | 5 | 0 | 1
3 | 3 | 4 | 5 | 0 | 1 | 2
4 | 4 | 5 | 0 | 1 | 2 | 3
5 | 5 | 0 | 1 | 2 | 3 | 4
(ii) Determine whether $*$ forms a group or not.
[4]
(a) Checking for closure:
There are no new elements in the Cayley table ∴ the set is closed under *.
(b) Checking for Associativity:
$x *(y * z) \equiv(x * y) * z$
Let $x=0, y=2$ and $z=5$
LHS
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