MIP1502 Assignment 3 |COMPULSORY| 2025 (721003) - DUE 18 July 2025

MIP1502
ASSIGNMENT 3 2025

UNIQUE NO. 721003
DUE DATE: 18 JULY 2025

,Mathematics for Intermediate II

QUESTION 1

1.1.1.1 First differences


Diagram Small Diff Black Diff Grey Diff White Diff

1 1 - 1 - 0 - 0 -

2 4 3 3 2 1 1 0 0

3 9 5 5 2 3 2 1 1

4 16 7 7 2 6 3 3 2

5 25 9 9 2 10 4 6 3

6 36 11 11 2 10 4


1.1.1.2 Classification

 Small: Quadratic (second differences constant)
 Black: Linear (first differences constant)
 Grey: Quadratic (second differences constant)
 White: Quadratic (second differences constant)

1.1.1.3 Mathematical Justification

 Black triangles: Constant first difference (2) → linear: Tn = 2n - 1
 Small triangles: First differences not constant, but second differences constant
→ quadratic: Tn = n^2

1.1.2.1 Pattern Growth Description

 Grey triangles: Increases as triangular numbers: +1, +2, +3, +4...
 White triangles: Grows by 0, 1, 2, 3, 4... same as grey but delayed by one step

1.1.2.2 Flow Diagrams

,  Grey Triangles: Tn = n(n - 1)/2

Input n → Multiply by (n - 1) → Divide by 2 → Output

 White Triangles: Tn = (n - 1)(n - 2)/2

Input n → Subtract 1 → Multiply by (n - 2) → Divide by 2 → Output

1.1.3.1 Rule for Black Triangles

 Pattern: 1, 3, 5, 7, 9, 11...
 Tn = 2n - 1
 Teaching: Show each added triangle is 2 more than previous. Use number line or
count-on strategy.

1.1.3.2 Rule for Grey Triangles

 Tn = n(n - 1)/2
 Misconception: Learners may think growth is additive instead of multiplicative.
 Remedy: Use dot-pattern models to visualize triangular numbers.

1.1.3.3 Rule for White Triangles

 Tn = (n - 1)(n - 2)/2

Proof: Grey at n - 1 = (n - 1)(n - 2)/2 = White at n Hence, proven.

1.1.4.1 Graph

 Plot (1-5) for:
o Small: y = n^2
o Black: y = 2n - 1
o Grey: y = n(n - 1)/2
 Label axes: x = diagram number, y = number of triangles