Question 20 - A-Level Maths

Edexcel D1 2021 October — Question 20

Exam Board	Edexcel
Module	D1 (Decision Mathematics 1)
Year	2021
Session	October
Topic	Permutations & Arrangements
Type	Assignment/allocation matching problems

20
23
17
15
22
19
25
13
28
32 A lower bound for the number of bins required is 4

Determine the range of possible values of $n$. You must make your method clear.
(3)
Carry out a quick sort to produce a list of the numbers in descending order. You should show the result of each pass and identify your pivots clearly.
(4) When the first-fit bin packing algorithm is applied to the original list of numbers, the following allocation is achieved. \end{table}
\includegraphics[max width=\textwidth, alt={}]{d409aaae-811d-4eca-b118-efc927885f97-14_1193_1586_1270_185}
Shortest path from A to J: $\_\_\_\_$
Length of shortest path from A to J: $\_\_\_\_$ \section*{2.
$\_\_\_\_$} \section*{3.}
A B C D E F G H
A - 36 38 40 23 39 38 35
B 36 - 35 36 35 34 41 38
C 38 35 - 39 25 32 40 40
D 40 36 39 - 37 37 26 33
E 23 35 25 37 - 42 24 43
F 39 34 32 37 42 - 45 38
G 38 41 40 26 24 45 - 40
H 35 38 40 33 43 38 40 -

A B C D E F G H
A - 36 38 40 23 39 38 35
B 36 - 35 36 35 34 41 38
C 38 35 - 39 25 32 40 40
D 40 36 39 - 37 37 26 33
E 23 35 25 37 - 42 24 43
F 39 34 32 37 42 - 45 38
G 38 41 40 26 24 45 - 40
H 35 38 40 33 43 38 40 -

A B C D E F G H
A - 36 38 40 23 39 38 35
B 36 - 35 36 35 34 41 38
C 38 35 - 39 25 32 40 40
D 40 36 39 - 37 37 26 33
E 23 35 25 37 - 42 24 43
F 39 34 32 37 42 - 45 38
G 38 41 40 26 24 45 - 40
H 35 38 40 33 43 38 40 -

A B C D E F G H
A - 36 38 40 23 39 38 35
B 36 - 35 36 35 34 41 38
C 38 35 - 39 25 32 40 40
D 40 36 39 - 37 37 26 33
E 23 35 25 37 - 42 24 43
F 39 34 32 37 42 - 45 38
G 38 41 40 26 24 45 - 40
H 35 38 40 33 43 38 40 -
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d409aaae-811d-4eca-b118-efc927885f97-22_755_1157_246_404} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure}
Activity
Immediately
preceding
activities
A
B
C
D
E

Activity
Immediately
preceding
activities
F
G
H
I
J

Activity
Immediately
preceding
activities
K
L
M
$$v = \ldots \quad x = \ldots \quad y = \ldots$$ \includegraphics[max width=\textwidth, alt={}, center]{d409aaae-811d-4eca-b118-efc927885f97-23_2255_56_315_37}
\includegraphics[max width=\textwidth, alt={}]{d409aaae-811d-4eca-b118-efc927885f97-23_1153_1338_303_310}
\section*{Grid 2} 5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d409aaae-811d-4eca-b118-efc927885f97-24_591_1433_255_260} \captionsetup{labelformat=empty} \caption{Figure 3
[0pt] [The total weight of the network is 166]}
\end{figure} 6.
\includegraphics[max width=\textwidth, alt={}]{d409aaae-811d-4eca-b118-efc927885f97-26_1287_1645_301_162}
\section*{Diagram 1} 7. $\begin{array} { l l l l l l l l l l l } 14 & 20 & 23 & 17 & 15 & 22 & 19 & 25 & 13 & 28 & 32 \end{array}$

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Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q20

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-

	A	B	C	D	E	F	G	H
A	-	36	38	40	23	39	38	35
B	36	-	35	36	35	34	41	38
C	38	35	-	39	25	32	40	40
D	40	36	39	-	37	37	26	33
E	23	35	25	37	-	42	24	43
F	39	34	32	37	42	-	45	38
G	38	41	40	26	24	45	-	40
H	35	38	40	33	43	38	40	-