GANSBAAI ACADEMIA
INVESTIGATION
March 2014
Total: 55
Time: 2 x 45 min
MATHEMATICS
Grade 10
EXAMINATOR
MODERATOR
L. Havenga
L. Mostert
memo
TASK 1
Number of triangles
Number of matches
Perimeter
[13]
1
3
3

2
5
4

3
7
5

4
9
6

7
15
9
20
41
22

n
2n+1
n+2

(½ x 12=6)
a)
Double  the number of triangles and add 1. 
(2)
b)
Number of matches needed for 25 triangles:
(25 x 2) + 1.= 51 
(2)
Number of triangles formed with 75 matches:
2n + 1 = 75

=> 2n = 74

=> n = 37

(3)
c)
1
TASK 2
Number of squares
Number of matches
Perimeter
[6]
1
4
4

2
7
6

3
10
8

4
13
10

7
22
16
20
41
42

n
3n+1
2n+2

(½ x 12=6)
TASK 3
[34]
1. PENTAGON
Broken up, the pattern is:

Number of pentagons
Number of matches
Perimeter
1
5
9

2
9
8

3
13
11

4
17
14

7
29
23

20
81
62

(2)
n
4n+1
3n+2

(½ x 14=7)
2. HEXAGONS

Number of hexagons
Number of matches
Perimeter
1
6
6

2
11
10

3
16
14

4
21
18

7
36
30

20
101
82

(2)
n
5n+1
4n+2

(½ x 14=7)
3. OCTAGONS

Number of octagons
Number of matches
Perimeter
1
8
8

2
15
14

3
22
20

4
29
26

7
50
44

20
141
122

(2)
n
7n+1
6n+2

(½ x 14=7)
2
c)
Number of sides of polygon
Number of matches for n polygons
3
2n+1

4
3n+1

5
4n+1

6
5n+1

8
7n+1

(5)
Number of sides (of polygon) MINUS 1, multiply with number of polygons PLUS 1
(Number of sides – 1) x number of polygons + 1

TASK 4
(2)
[2]
m  ( s  1)n  1
OR
m  n( s  1)  1
OR
m  sn  n  1

(2)
TOTAL: 55
3