Mathematics > MARK SCHEME > OCR GCE Further Mathematics A Y534/01: Discrete Mathematics Advanced Subsidiary GCE Mark Scheme for  (All)

OCR GCE Further Mathematics A Y534/01: Discrete Mathematics Advanced Subsidiary GCE Mark Scheme for Autumn 2021

Document Content and Description Below

Mark Scheme October 2021 Question Answer Marks AO Guidance 1 (a) 5 partitions into a set of size 1 and a set of size 4 B1 1.1 5 where smaller set has size 1 or 5C1 = 5 {X | X, X, X, X} 10 partitio... ns into a set of size 2 and a set of size 3 B1 2.5 10 where smaller set has size 2, with an explanation of why it is 10 {X, X | X, X, X} because there are 5C2 choices for the set of size 2 (note the totalof 15 is given in the question) e.g. 5C2 = 10 or (5×4) ÷ 2 = 10 or 4 + 3 + 2 + 1 = 10 Alternative solution {A}, {B, C, D, E} {B}, {A, C, D, E} B1 List (or any equivalent) that has exactly 5 distinct cases where {C}, {A, B, D, E} {E}, {A, B, C, D} {D}, {A, B, C, E} smaller set has size 1 May just list one set, e.g. {A}, {B}, {C}, {D}, {E} {A, B}, {C, D, E} {A, C}, {B, D, E} List (or any equivalent) that has 10 distinct cases sets where smaller {A, D}, {B. C. E} {B, C}, {A, D, E} {B, E}, {A, C, D} {C, E}, {A, B, D} {A, E}, {B, C, D} {B, D}, {A, C, E} {C, D}, {A, B, E} {D, E}, {A, B, C} B1 set has size 2 May just list one set, e.g. {A, B}, {A, C} {A, D}, {A, E}, {B, C}, {B, D}, {B, E}, {C, D}, {C, E}, {D, E} [2] 1 (b) Partitions into sets of sizes 1, 1 and 3 M1 1.1 Considering cases where set sizes are 1, 1, 3 5 × 4 ÷ 2 = 10 partitions of this type A1 2.1 Explanationof why there are 10 of these e.g. 5C3 = 10 or 5 × 4 ÷ 2 = 10 or a list of the cases Partitions into sets of sizes 1, 2 and 2 M1 1.1 Considering cases where set sizes are 1, 2, 2 5 × (4C2 ÷ 2) = 5 × 3 = 15 partitions of this type A1 2.1 Explainingwhy there are 15 of these e.g a relevant calculation or list of cases [4] 1 (c) 10 partitions into sets of sizes 1, 1, 1, 2 M1 2.1 Trying to dealwith the cases when there are more than 3 subsets 1 partition into sets of sizes 1, 1, 1, 1, 1 May be implied from answer 51 15 + 25 + 10 + 1 = 51 A1 1.1 51 [2] 1 (d) Number line is split into 6 pieces B1 2.1 6 pieces But there are 8 numbers B1 2.2a Using pigeonhole, or explainingwhy there must be at least one piece Hence result by the pigeonhole principle with two or more numbers [2]Y534/01 Mark Scheme October 2021 Question Answer Marks AO Guidance 2 (a) (i) Next-fit method M1 A1 [2] 1.1 1.1 Bins 1 and 2 correct All correct 2 (a) (ii) First-fit method M1 A1 [2] 1.1 1.1 Bins 1 and 2 correct All correct 2 (a) (iii) 23 18 15 12 8 7 5 First-fit decreasingmethod M1 A1 [2] 1.1 1.1 Ordered list may be seen Bins 1 and 2 correct All correct 2 (b) With ‘online’ lists the items are presented one at a time and the whole list is not known untilthe end. With next-fit and first-fit the items are placed in the order they appear in the list, so these methods can be used ‘offline’ or ‘online’. However, for first-fit decreasingthe whole list needs to be known before it can be sorted, so first-fit decreasing can only be used for an ‘offline’ list. B1 B1 [2] 1.2 2.3 Evidence of understandingwhat ‘online’ means Evidence of realising that ffd cannot be used with an online list (or implied from an appropriate statement aboutnext-fit andfirst-fit) Bin 1 12 Bin 2 23 Bin 3 15 Bin 4 18 8 Bin 5 7 5 Bin 1 12 15 Bin 2 23 7 Bin 3 18 8 Bin 4 5 Bin 5 Bin 1 23 7 Bin 2 18 12 Bin 3 15 8 5 Bin 4 Bin 5Y534/01 Mark Scheme October 2021 Question Answer Marks AO Guidance 2 (c) 88 ÷ 4 = 22, so M is at least 22 But it is not possible to fill 4 bins of capacity22 Since 22 – 18 = 4 which is less than 5 So the 23 would have to be split as 4 and 19 And then there is no 3 to go with the 19 M = 23 is possible e.g. 23 – x and x, 18 + 5, 15 + 8, 12 + 7 Hence, least M is 23 M1 A1 B1 [3] 1.1 2.4 2.2a Identifyingthat M must be at least 22 Showing that M = 22 is not possible Fully correct explanation Showing that M = 23 is possible 3 (a) ABXE B1 [1] 1.1 3 (b) M1 A1 M1 A1 [4] 1.1 1.1 1.1 1.1 AB = 0.6, AC = 1.1 AD = 2.7, AE = 2.8 DF = 0.6, EF = 0.7 BF = 2.7, CF = 2.5 AF = 3.3 or ft from other valu [Show More]

Last updated: 1 year ago

Preview 1 out of 10 pages

Add to cart

Instant download

Reviews( 0 )

$10.00

Add to cart

Instant download

Can't find what you want? Try our AI powered Search

OR

REQUEST DOCUMENT
49
0

Document information


Connected school, study & course


About the document


Uploaded On

Jun 29, 2022

Number of pages

10

Written in

Seller


seller-icon
SupremeDocs

Member since 2 years

25 Documents Sold


Additional information

This document has been written for:

Uploaded

Jun 29, 2022

Downloads

 0

Views

 49

Document Keyword Tags

Recommended For You

Get more on MARK SCHEME »

$10.00
What is Browsegrades

In Browsegrades, a student can earn by offering help to other student. Students can help other students with materials by upploading their notes and earn money.

We are here to help

We're available through e-mail, Twitter, Facebook, and live chat.
 FAQ
 Questions? Leave a message!

Follow us on
 Twitter

Copyright © Browsegrades · High quality services·