MIP1502
ASSIGNMENT 3 (ANSWERS) YEAR MODULE
DUE DATE: 18 JULY 2025
Written Assignment Submission Guidelines:
Please ensure that your assignment is submitted electronically through the myUnisa platform no
later than July 2025. Kindly note that fax or email submissions will not be accepted.
NB: Assignment submitted to the lecturer(s) through email will not be considered.
QUESTION 1
COMPLETE TABLE
Diagram (n) 1 2 3 4 5 6 7 8 9 10
Small triangles 1 4 9 16 25 36 49 64 81 100
Black triangles 1 3 5 7 9 11 13 15 17 19
Grey triangles 0 1 3 6 10 15 21 28 36 45
White triangles 0 0 1 3 6 10 15 21 28 36
1.1.1 Analysis of Patterns
1.1.1.1 First differences between consecutive terms
Small triangles:
4–1=3
9–4=5
16 – 9 = 7
25 – 16 = 9
,36 – 25 = 11
49 – 36 = 13
64 – 49 = 15
81 – 64 = 17
100 – 81 = 19
First differences: 3, 5, 7, 9, 11, 13, 15, 17, 19
Black triangles:
3–1=2
5–3=2
7–5=2
9–7=2
11 – 9 = 2
13 – 11 = 2
15 – 13 = 2
17 – 15 = 2
19 – 17 = 2
First differences: all 2
Grey triangles:
1–0=1
3–1=2
6–3=3
10 – 6 = 4
15 – 10 = 5
21 – 15 = 6
28 – 21 = 7
36 – 28 = 8
45 – 36 = 9
First differences: 1, 2, 3, 4, 5, 6, 7, 8, 9
, White triangles:
0–0=0
1–0=1
3–1=2
6–3=3
10 – 6 = 4
15 – 10 = 5
21 – 15 = 6
28 – 21 = 7
36 – 28 = 8
First differences: 0, 1, 2, 3, 4, 5, 6, 7, 8
1.1.1.2 Classification as linear or quadratic
• Small triangles: First differences not constant, but second differences (difference of first
differences) are constant (2). Therefore quadratic.
• Black triangles: First differences constant (2). Therefore linear.
• Grey triangles: First differences increase by 1 each time. Second differences are constant
(1). Therefore quadratic.
• White triangles: First differences increase by 1 each time (after first zero). Second
differences constant (1). Therefore quadratic.
1.1.1.3 Mathematical justification for classification
Black triangles: First differences are constant (2). A constant first difference means a linear
sequence because the pattern increases by the same amount each time (slope is constant).
ASSIGNMENT 3 (ANSWERS) YEAR MODULE
DUE DATE: 18 JULY 2025
Written Assignment Submission Guidelines:
Please ensure that your assignment is submitted electronically through the myUnisa platform no
later than July 2025. Kindly note that fax or email submissions will not be accepted.
NB: Assignment submitted to the lecturer(s) through email will not be considered.
QUESTION 1
COMPLETE TABLE
Diagram (n) 1 2 3 4 5 6 7 8 9 10
Small triangles 1 4 9 16 25 36 49 64 81 100
Black triangles 1 3 5 7 9 11 13 15 17 19
Grey triangles 0 1 3 6 10 15 21 28 36 45
White triangles 0 0 1 3 6 10 15 21 28 36
1.1.1 Analysis of Patterns
1.1.1.1 First differences between consecutive terms
Small triangles:
4–1=3
9–4=5
16 – 9 = 7
25 – 16 = 9
,36 – 25 = 11
49 – 36 = 13
64 – 49 = 15
81 – 64 = 17
100 – 81 = 19
First differences: 3, 5, 7, 9, 11, 13, 15, 17, 19
Black triangles:
3–1=2
5–3=2
7–5=2
9–7=2
11 – 9 = 2
13 – 11 = 2
15 – 13 = 2
17 – 15 = 2
19 – 17 = 2
First differences: all 2
Grey triangles:
1–0=1
3–1=2
6–3=3
10 – 6 = 4
15 – 10 = 5
21 – 15 = 6
28 – 21 = 7
36 – 28 = 8
45 – 36 = 9
First differences: 1, 2, 3, 4, 5, 6, 7, 8, 9
, White triangles:
0–0=0
1–0=1
3–1=2
6–3=3
10 – 6 = 4
15 – 10 = 5
21 – 15 = 6
28 – 21 = 7
36 – 28 = 8
First differences: 0, 1, 2, 3, 4, 5, 6, 7, 8
1.1.1.2 Classification as linear or quadratic
• Small triangles: First differences not constant, but second differences (difference of first
differences) are constant (2). Therefore quadratic.
• Black triangles: First differences constant (2). Therefore linear.
• Grey triangles: First differences increase by 1 each time. Second differences are constant
(1). Therefore quadratic.
• White triangles: First differences increase by 1 each time (after first zero). Second
differences constant (1). Therefore quadratic.
1.1.1.3 Mathematical justification for classification
Black triangles: First differences are constant (2). A constant first difference means a linear
sequence because the pattern increases by the same amount each time (slope is constant).
