Title:* Comprehensive MTE1501 Memorandum, for Intermediate, Phase Teachers

MODULE CODE: MIP1502



MEMORANDUM



ASSIGNMENT 3




18/07/2025

, QUESTION 1


1.1.1.1 First Differences for Each Pattern

Small triangles: 4 - 1 = 3, 9 - 4 = 5, 16 - 9 = 7, 25 - 16 = 9, 36 - 25 = 11 → First
differences: 3, 5, 7, 9, 11

Black triangles: 3 - 1 = 2, 5 - 3 = 2, 7 - 5 = 2, 9 - 7 = 2, 11 - 9 = 2 → First differences: 2,
2, 2, 2

Grey triangles: 1 - 0 = 1, 3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4 → First differences: 1, 2, 3, 4

White triangles: 1 - 0 = 1, 3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4 → First differences: 1, 2, 3, 4


1.1.1.2 Classify Each Pattern

Small triangles: Quadratic (second differences are constant)

Black triangles: Linear (first differences are constant)

Grey triangles: Quadratic

White triangles: Quadratic


1.1.1.3 Justify Small and Black Patterns

Small triangles: The values are perfect squares (1, 4, 9, 16…), meaning the second
differences are constant, which identifies a quadratic pattern.

Black triangles: The increase is by a fixed value (+2 each time), showing a constant
rate of change, which confirms it is a linear pattern.


1.1.2.1 Describe Grey and White Growth Patterns

Grey triangles: The number of new triangles added grows by 1 more each time (e.g.,
+1, +2, +3...).


1.1.2.2 Flow Diagrams