GRADET
SnIREDASSESSMENT 20
IB
PAPER 2: PROBLEM.SOLVING
PARTTWO
@O -5O MINUTES)
N,rut{g:
INSTRUCTIONS:
PART TWO: NON'ROUTINE PROBLEM.SOLVING
.
This part of the paper is out of 40.
o
A calculator may be used.
.
Answer ONlYj_question from each section in the space provided. lf you
answer 2 questions in the same section, cross out the one you do not want
to be marked. Othenruise the first one will be marked.
.
All working out must be shown.
SEcTIoN
A
B
c
D
E
YOUR
MARK
Page 1 of 9
F
G
H
TOTAL
SECTION A
1.
While visiting his uncle's farm, Robert saw some chickens and some sheep. He counted 52 legs
all together, but only 18 heads. How many chickens and how many sheep did he see?
2.
Two snails were climbing out of a hole 6m deep.
Z.L. In each hour, the first snail spent the first 30 minutes climbing up 3m and the last 30 minutes
sliding back lm, while it rested. How long did it take this snail to reach the top?
2.2 Thesecond snail could only manage to climb 2m in 30 minutes, and in the next 30 minutes it also
slid back 1m. How long did it take this snailto reach the top?
Page 2 of 9
SECTION B
1.
Joan was offered a job during the six-week school holidays and was able
to choose how she
would be paid.
Method 1: Paid fortnightly, so that she would get R140 the first fortnight and would receive a rise of
R40 each fortnight following.
Method 2: Paid weekly, so that she would get R70 the first week and then be given a rise of R10 each
succeeding week.
None of the money paid was invested at any stage before the end of the 6 week period, so no interest
was earned. Which method should Joan accept? How much more should Joan receive each fortnight,
by method 1, to earn the same as by method 2?
2. Mr Lucky won a targe amount of amount in a lottery. He put I of the amount in the bank and
g.u"
I of the rest to his son.
He spent
the remaining amount on a holiday. lf his holiday cost
R9 000, how much did he win?
Page 3 of 9
sEciloN c
1.
When my ball is dropped from a certain height, it rebounds to
1.1 lf it is dropped from 20m, calculate
L.2
I
of that height.
the height it will reach after 3 bounces. (Answer in
metres.)
From what height would the ball have to be dropped to reach a height of 27m after 3
bounces?
2"
The train
depart-from Pofadder every hour, on the hour. Four people wish to catch the 14:00
train.
she
Bob,s watch is 5 minutes slow but he thinks it is 5 minutes fast. Martina's is 5 minutes fast but
thinks it is 5 minutes slow. Thobile's is 10 minutes slow but she thinks it is 5 minutes slow.
Ngubekaya's is 5 minutes fast but he thinks at is 15 minutes fast. They all live exactly 9 minutes'
walking distance of the train's platform.
lf they all ptan to board the train one minute before its departure, who and how many will be there in
time to do so?
Page 4 of 9
SECTION D
1. How many rectangles may be seen in this diagram?
a
b
S
k
v
W
z
V
c
p
t
i
two digits. No digit used can be a multiple of four.
How many different numbers can be formed, if 0 may not be used for the first digit?
Z.Z
How many times woutd a 1 appear if all the numbers from 1 to 101 were written down?
A number comprises
Page 5 of 9
o
SECTION
t.
E
Nyasha shopped at a nearby centre. When she arrived, she thought she had
too little cash, so
she drew R200 at an ATM. ln the first shop her pet paper-muncher ate half her money before
she spent R30. ln the second shop her pet devourer again ate half her money before she spent
R40. Then her mischievous pet chomped half her remaining money, in the
third shop, before she
again spent R30. Then she had no money left.
1.1. How much money had she when she set out, from home, for the centre?
L.2. What value of money had the paper-eater eaten?
Z.
A bus starts from the station fully loaded. At the first stop,
people get on. At the next stop,
I
passengers get off and
I of the
12
of the new total get off and 4 people get on. There are now 30
passengers on the bus. How many passengers started the trip?
Page 6 of 9
SECTION
F
l-
Z feOtu ary 2O22 is
1.1.
1.2.
1.3.
noughts or even numbers.
f n relation to 21212022,
When was the previous time that this happened
Which was the previous odd date (before 212120221, when allthe digits were odd?
Which will be the next odd date?
2.L.
2.2.
thirds of the number of girls.
What is the ratio of young people to adults at the theatre?
lf there are 450 people in the theatre, how rnany are adults?
written 21212022. This is called an even date because all the digits are
tttrettreatreasyounggir|s.Thenumberofyoungboysistwo
Page 7 of 9
Section
L.
G
How many three-digit numbers can be formed, if each digit of the three-digit numbers must be
greater than the digit to its left? Zero, nine and eight may not be used.
MroomraceinwhichJanecrossedthefinishinglinejustasCaro|ine
reached the 90m mark.
first race by 10m, she decided to start the second race 10m behind the
starting line, to make the race fair. Caroline started on the starting line once more. lf both girls
ran at the same rate as in the first race, who won the second race?
2.2. ln the third race, Caroline started 10m ahead of the starting line. Jane started on the starting
line. Again, assuming that both girls run at the same rate, who is the winner of this race?
2.1.
Since Jane won the
Page 8 of 9
SECTION H
1.
On Monday, Samhaa had five times as many Rand as Lamisah. On Tuesday they each earned
R300 more. Samhaa then had twice as many Rand as Lamisah. On Wednesday, Samhaa spent the
same number of Rand as Lamisah and so then had three times as many Rand as Lamisah. How
many Rand did Samhaa have at the end of Wednesday?
2.
the same mass as Sl jiggles. 2 woggles and 6 jiggles have the same
mass as 3 wiggles. 5 woggles and 10 wiggles a have the same mass as 195 iiggles. lf a iiggle has a
mass of 4 kg, what is the mass of a woggle and what is the mass of a wiggle?
3 woggles and 3 wiggles have
Page 9 of 9