GANSBAAI ACADEMIA

MATHEMATICS
Grade 10 / /

INVESTIGATION

March 2014

Total: 55
Time: 2 x 45 min
EXAMINATOR
MODERATOR / L. Havenga
L. Mostert

memo

TASK 1[13]

Number of triangles / 1 / 2 / 3 / 4 / 7 / 20 / n
Number of matches / 3 / 5 / 7 / 9 / 15 / 41 / 2n+1
Perimeter / 3 / 4 / 5 / 6 / 9 / 22 / 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)

c)Number of triangles formed with 75 matches:

2n + 1 = 75

=> 2n = 74

=> n = 37(3)

TASK 2[6]

Number of squares / 1 / 2 / 3 / 4 / 7 / 20 / n
Number of matches / 4 / 7 / 10 / 13 / 22 / 41 / 3n+1
Perimeter / 4 / 6 / 8 / 10 / 16 / 42 / 2n+2
 /  /  /  /  / 

(½ x 12=6)

TASK 3[34]

1. PENTAGON

Broken up, the pattern is:

(2)

Number of pentagons / 1 / 2 / 3 / 4 / 7 / 20 / n
Number of matches / 5 / 9 / 13 / 17 / 29 / 81 / 4n+1
Perimeter / 9 / 8 / 11 / 14 / 23 / 62 / 3n+2
 /  /  /  /  /  / 

(½ x 14=7)

2. HEXAGONS

(2)

Number of hexagons / 1 / 2 / 3 / 4 / 7 / 20 / n
Number of matches / 6 / 11 / 16 / 21 / 36 / 101 / 5n+1
Perimeter / 6 / 10 / 14 / 18 / 30 / 82 / 4n+2
 /  /  /  /  /  / 

(½ x 14=7)

3. OCTAGONS

(2)

Number of octagons / 1 / 2 / 3 / 4 / 7 / 20 / n
Number of matches / 8 / 15 / 22 / 29 / 50 / 141 / 7n+1
Perimeter / 8 / 14 / 20 / 26 / 44 / 122 / 6n+2
 /  /  /  /  /  / 

(½ x 14=7)

c)

Number of sides of polygon / 3 / 4 / 5 / 6 / 8
Number of matches for n polygons / 2n+1 / 3n+1 / 4n+1 / 5n+1 / 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 (2)

TASK 4[2]

OR

OR

(2)

TOTAL: 55

1