OPM1501
Assignment 3
Due 7 July 2025
, Question 1: Patterns and Flow Diagrams
1.1 Pattern Analysis
The table below identifies whether each number set constitutes a pattern and explains the
reasoning process.
Number Pattern or
Description
Set Not
1, 3, 5, 7, 9, b) The sequence increases by a constant difference of 2 (3 − 1 = 2, 5 − 3
a) Pattern
… = 2, etc.), indicating an arithmetic sequence with the rule a_n = 2n - 1
d) The differences between terms are inconsistent (3 − 2 = 1, 4 − 3 = 1,
2, 3, 4, 4, 6, c) Not a
4 − 4 = 0, 6 − 4 = 2, etc.), showing no consistent rule or predictable
5, 8, … Pattern
sequence.
f) The sequence does not follow a clear arithmetic or geometric rule.
9, 18, 729, e) Not a
For example, 18 ÷ 9 = 2, but 729 ÷ 18 = 40.5, and subsequent terms do
6569, … Pattern
not align with a consistent pattern.
h) The differences are 8 − 7 = 1, 10 − 8 = 2, 12 − 10 = 2, 14 − 12 = 2,
7, 8, 10, 12, suggesting an arithmetic sequence after the first term, with a possible
g) Pattern
14, … rule a_n = 2n + 5 for n \geq 2
.
j) The differences are 28 − 14 = 14, 34 − 28 = 6, 41 − 34 = 7, 48 − 41 =
14, 28, 34,
i) Pattern 7, indicating an arithmetic sequence after the first term, with a
41, 48, …
possible rule a_n = 7n + 7 for n \geq 2
Table 1: Analysis of Number Sets for Patterns
,1.2 and 1.3 Flow Diagrams
Note: The problem statement references flow diagrams for Questions 1.2 and 1.3 but does
not provide the diagrams. Assuming these are sequences continuing from Question 1.1, we
hypothesize that the flow diagrams require extending the patterns identified in the table.
Without specific diagrams, we provide hypothetical extensions for two sequences marked
as patterns (e.g., 1,3,5,7,9,...
and 7,8,10,12,14,...) to the next term.
• For 1,3,5,7,9,...: The rule is an = 2n − 1. The 6th term (n = 6) is:
a6 = 2 × 6 − 1 = 11
Answer: (f) - 11
• For 7,8,10,12,14,...: Assuming the arithmetic pattern continues with a difference of 2
after the first term, the 6th term is:
a6 = 14 + 2 = 16
Answer: (d) - 16
, OPM1501
Assignment 3
Due 7 July 2025
Question 2: Transformations of ∆PQR
Given points:
• P(4;3)
• Q(0;1)
• R(−1;3)
1.1. Reflection on the x-axis
Concept: When a point (x,y) is reflected on the x-axis, its new coordinates become (x,−y).
Calculations:
• P(4,3) → P′(4,−3)
• Q(0,1) → Q′(0,−1)
• R(−1,3) → R′(−1,−3)
New points: P′(4,−3), Q′(0,−1), R′(−1,−3)
Diagram:
1
Assignment 3
Due 7 July 2025
, Question 1: Patterns and Flow Diagrams
1.1 Pattern Analysis
The table below identifies whether each number set constitutes a pattern and explains the
reasoning process.
Number Pattern or
Description
Set Not
1, 3, 5, 7, 9, b) The sequence increases by a constant difference of 2 (3 − 1 = 2, 5 − 3
a) Pattern
… = 2, etc.), indicating an arithmetic sequence with the rule a_n = 2n - 1
d) The differences between terms are inconsistent (3 − 2 = 1, 4 − 3 = 1,
2, 3, 4, 4, 6, c) Not a
4 − 4 = 0, 6 − 4 = 2, etc.), showing no consistent rule or predictable
5, 8, … Pattern
sequence.
f) The sequence does not follow a clear arithmetic or geometric rule.
9, 18, 729, e) Not a
For example, 18 ÷ 9 = 2, but 729 ÷ 18 = 40.5, and subsequent terms do
6569, … Pattern
not align with a consistent pattern.
h) The differences are 8 − 7 = 1, 10 − 8 = 2, 12 − 10 = 2, 14 − 12 = 2,
7, 8, 10, 12, suggesting an arithmetic sequence after the first term, with a possible
g) Pattern
14, … rule a_n = 2n + 5 for n \geq 2
.
j) The differences are 28 − 14 = 14, 34 − 28 = 6, 41 − 34 = 7, 48 − 41 =
14, 28, 34,
i) Pattern 7, indicating an arithmetic sequence after the first term, with a
41, 48, …
possible rule a_n = 7n + 7 for n \geq 2
Table 1: Analysis of Number Sets for Patterns
,1.2 and 1.3 Flow Diagrams
Note: The problem statement references flow diagrams for Questions 1.2 and 1.3 but does
not provide the diagrams. Assuming these are sequences continuing from Question 1.1, we
hypothesize that the flow diagrams require extending the patterns identified in the table.
Without specific diagrams, we provide hypothetical extensions for two sequences marked
as patterns (e.g., 1,3,5,7,9,...
and 7,8,10,12,14,...) to the next term.
• For 1,3,5,7,9,...: The rule is an = 2n − 1. The 6th term (n = 6) is:
a6 = 2 × 6 − 1 = 11
Answer: (f) - 11
• For 7,8,10,12,14,...: Assuming the arithmetic pattern continues with a difference of 2
after the first term, the 6th term is:
a6 = 14 + 2 = 16
Answer: (d) - 16
, OPM1501
Assignment 3
Due 7 July 2025
Question 2: Transformations of ∆PQR
Given points:
• P(4;3)
• Q(0;1)
• R(−1;3)
1.1. Reflection on the x-axis
Concept: When a point (x,y) is reflected on the x-axis, its new coordinates become (x,−y).
Calculations:
• P(4,3) → P′(4,−3)
• Q(0,1) → Q′(0,−1)
• R(−1,3) → R′(−1,−3)
New points: P′(4,−3), Q′(0,−1), R′(−1,−3)
Diagram:
1
