AS LEVEL FURTHER MATHEMATICS A: Actual June 2025 PAST PAPER 1: Discrete
Mathematics. All Assessment Questions & Mark Scheme [OCR Y534/01]
Exam Resource Summary
The AS Level Further Mathematics A June 2025 Paper Y534/01: Discrete Mathematics
(OCR) – All Assessment Questions & Mark Scheme document combines the full official
examination paper with its complete mark scheme, providing a structured and detailed revision
resource. This paper assesses students’ understanding of key discrete mathematics concepts,
including graph theory, algorithms, network flows, linear programming, critical path
analysis, and game theory. It evaluates both procedural fluency and problem-solving ability,
requiring students to apply mathematical reasoning to model and solve real-world discrete
problems. The merged format presents each question alongside its corresponding marking criteria,
giving students clear visibility of examiner expectations, mark distribution, and step-by-step
solution structure. This resource is essential for focused revision, self-assessment, and
strengthening analytical and modelling skills, making it a key tool for preparation for the May
2026 OCR AS Level Further Mathematics A Paper Y534/01: Discrete Mathematics
examination.
Turn over
, 2
1 A builder has some pieces of wood that are 6 m in length. The builder needs to cut smaller pieces
to use in a project. The lengths of the smaller pieces required are shown below.
2.5 m 2m 4.5 m 3m 1.5 m 3.5 m 2m
(a) Use the first-fit decreasing algorithm to determine the smallest number of 6 m lengths of
wood needed to cut the seven smaller pieces. [3]
(b) First-fit decreasing is a heuristic algorithm. Explain what this means. [1]
The first-fit decreasing algorithm is order O(n2).
(c) It takes a computer 3.2 seconds to solve an allocation problem involving 200 items of data
using the first-fit decreasing algorithm. Calculate approximately how long it would take to
solve an allocation problem involving 1000 items of data. [2]
2 A student has six cards numbered from 1– 6. The cards are shown below.
1 2 3 4 5 6
(a) The student chooses four cards at random.
Use the Pigeonhole Principle to explain why they must have at least two cards whose
numbers add to seven. [2]
(b) The student now chooses two cards and places them side by side to form a two-digit number.
(i) Determine the number of different two-digit numbers that the student can make. [2]
(ii) Determine the number of different even two-digit numbers that the student can make. [2]
© OCR 2025 Y534/01 Jun25
, 3
3 The table shows the lengths in km of footpaths between six places, A to F, in a town.
A B C D E F
A – 5 3 5 8 10
B 5 – 6 2 7 5
C 3 6 – 1 10 8
D 5 2 1 – 9 4
E 8 7 10 9 – 3
F 10 5 8 4 3 –
(a) Apply the tabular form of Prim’s algorithm, starting at A, to the copy of the table in the
Printed Answer Booklet to construct a minimum spanning tree for the six places in the
town. You should state the order in which the arcs are added to the tree.
Draw the minimum spanning tree and find its weight. [4]
(b) Sam needs to walk from A to F.
Give an example of a question Sam could ask which leads to an enumeration problem. [1]
(c) Use an appropriate algorithm to find the shortest route from A to F. You must state its length.
[4]
© OCR 2025 Y534/01 Jun25 Turn over
, 4
4 Ryan and Casey play a game.
They can each choose to play one of three options.
Ryan can play options A, B and C and Casey can play options X, Y and Z.
The scores for each player for each combination of choices are shown in the pay-off matrices
below:
Scores for Ryan
Casey’s
Options
X Y Z
Ryan’s A 1 4 3
Options B 5 3 4
C 3 1 3
Scores for Casey
Casey’s
Options
X Y Z
Ryan’s A 5 2 3
Options B 1 3 2
C 3 5 3
© OCR 2025 Y534/01 Jun25
Mathematics. All Assessment Questions & Mark Scheme [OCR Y534/01]
Exam Resource Summary
The AS Level Further Mathematics A June 2025 Paper Y534/01: Discrete Mathematics
(OCR) – All Assessment Questions & Mark Scheme document combines the full official
examination paper with its complete mark scheme, providing a structured and detailed revision
resource. This paper assesses students’ understanding of key discrete mathematics concepts,
including graph theory, algorithms, network flows, linear programming, critical path
analysis, and game theory. It evaluates both procedural fluency and problem-solving ability,
requiring students to apply mathematical reasoning to model and solve real-world discrete
problems. The merged format presents each question alongside its corresponding marking criteria,
giving students clear visibility of examiner expectations, mark distribution, and step-by-step
solution structure. This resource is essential for focused revision, self-assessment, and
strengthening analytical and modelling skills, making it a key tool for preparation for the May
2026 OCR AS Level Further Mathematics A Paper Y534/01: Discrete Mathematics
examination.
Turn over
, 2
1 A builder has some pieces of wood that are 6 m in length. The builder needs to cut smaller pieces
to use in a project. The lengths of the smaller pieces required are shown below.
2.5 m 2m 4.5 m 3m 1.5 m 3.5 m 2m
(a) Use the first-fit decreasing algorithm to determine the smallest number of 6 m lengths of
wood needed to cut the seven smaller pieces. [3]
(b) First-fit decreasing is a heuristic algorithm. Explain what this means. [1]
The first-fit decreasing algorithm is order O(n2).
(c) It takes a computer 3.2 seconds to solve an allocation problem involving 200 items of data
using the first-fit decreasing algorithm. Calculate approximately how long it would take to
solve an allocation problem involving 1000 items of data. [2]
2 A student has six cards numbered from 1– 6. The cards are shown below.
1 2 3 4 5 6
(a) The student chooses four cards at random.
Use the Pigeonhole Principle to explain why they must have at least two cards whose
numbers add to seven. [2]
(b) The student now chooses two cards and places them side by side to form a two-digit number.
(i) Determine the number of different two-digit numbers that the student can make. [2]
(ii) Determine the number of different even two-digit numbers that the student can make. [2]
© OCR 2025 Y534/01 Jun25
, 3
3 The table shows the lengths in km of footpaths between six places, A to F, in a town.
A B C D E F
A – 5 3 5 8 10
B 5 – 6 2 7 5
C 3 6 – 1 10 8
D 5 2 1 – 9 4
E 8 7 10 9 – 3
F 10 5 8 4 3 –
(a) Apply the tabular form of Prim’s algorithm, starting at A, to the copy of the table in the
Printed Answer Booklet to construct a minimum spanning tree for the six places in the
town. You should state the order in which the arcs are added to the tree.
Draw the minimum spanning tree and find its weight. [4]
(b) Sam needs to walk from A to F.
Give an example of a question Sam could ask which leads to an enumeration problem. [1]
(c) Use an appropriate algorithm to find the shortest route from A to F. You must state its length.
[4]
© OCR 2025 Y534/01 Jun25 Turn over
, 4
4 Ryan and Casey play a game.
They can each choose to play one of three options.
Ryan can play options A, B and C and Casey can play options X, Y and Z.
The scores for each player for each combination of choices are shown in the pay-off matrices
below:
Scores for Ryan
Casey’s
Options
X Y Z
Ryan’s A 1 4 3
Options B 5 3 4
C 3 1 3
Scores for Casey
Casey’s
Options
X Y Z
Ryan’s A 5 2 3
Options B 1 3 2
C 3 5 3
© OCR 2025 Y534/01 Jun25
