6
ANSWER: E Let Q
then P because APQ is isosceles
∧ ∧
= =
y y
, ,
∆ QA C
A C B Alternate interior angles AQ BC
but A C B = 60 ABC is equilateral
Q A C = 60
∧ ∧
∧ ∧
=
∴ ||
D D
∆
∴ =
+ +
∴ =
− ∴ =
− 180
2 2
60 2
120 2
60
D D
D D
y x
y x
y x
11. The units digit of 2
2 2
2000 2001
2002
+ +
is A
B C
D E
2 4
6 8
ANSWER: B 2
2 2
2 1 2
2 2
7 2
2 2
4 8
2 16
2 4 8 6
2 2
2 6 7
42
2000 2001
2002 2000
2 2000
2 4
2000 4
2000
+ +
= + +
= ∈
= =
= =
= × =
. ,
, ;
; ;
; ; ; ,
, The number
N has only the following possibilities for its unit digit: 2
2 i.e.
and Since
for some this number has 6 as its unit digit.
Multiplying with 7, yields hence 2 as its unit digit.
1 3
x
n
x
n
7
12. The total number of different
triangles in the diagram, including
∆ ABC , is
A B
C D
E 21
42 63
84 105
ANSWER: C Count all the different triangles. Work with a plan, say from the smallest to
the biggest: e.g. only some of the triangle sizes
Top row triangles: X6
X5 X4
X3 X2
X1 Second row triangles:
X6 … etc.
X6 …
etc. up to
X1 If all the different triangles have been identified and calculated, you get 63
different triangles. B
C A
8
13. A 3-digit number has x as its units digit;
x −
1 as the tens digit and 1
2 x
as its hundreds digit. The number in terms of x is
A B
C D
E 5
1 7
1 111
1 61
10 5
2 1
x x
x x
x −
− −
− −
ANSWER: D 3
10 1
100 1
2 10
10 50 61
10 −
+ − +
= + − +
= −
digit number: x
x x
x x
x x
.
14. A company makes solid blocks with square bases.
The volume of this block is 640 cm
3
. Its height is 10 cm. The cost of painting all the faces of this
block at 15c per cm
2
is
A R64,00 B R67,20 C R70,40 D R73,60 E R60,20
ANSWER: B Volume: V
area of base area of base
area of base Area of base
length of base length of base
64
Surface area of block base area
base perimete
Cost: R
= ×
∴ =
× =
= =
× ∴
= × ∴ =
= × +
× ∴ = ×
+ ×
∴ = +
∴ = ∴
× =
h cm
cm cm
cm cm
cm l
l l
cm S
r h
S cm
S cm
S cm
c 640
10 640
10 64
8 2
2 64 32 10
128 320 448
448 15 67 20
3 3
2
2
2 2
2
: [
] [ ]
, 10 cm
9
15. In an alien language, jalez borg farn means “good maths skills”. Nurf klar
borg means “maths in harmony” and darko klar farn means “good in gold”.
What is “harmony gold” in this language?
A klar darko
B
borg nurf
C jalez klar
D
darko nurf
E
farn borg
ANSWER: D a
jalez borg farn good maths skills
b Nurf klar borg
maths in harmony c
darko klar farn good in gold
From a and b: borg
maths From b and c:
klar in
nurf harmony
From a and c: farn
good Hence
darko gold
Also, from all the above, the sentences are translated in reverse order, e.g. the last word in the alien language becomes the first word in English.
“harmony gold”
darko nurf
10
PART C:
Each correct answer is worth 6 marks
16. As a result of poor attendance at soccer matches it was decided to decrease
