1. A rectangular tank with dimensions 130 cm by 100 cm by 210 cm was
30% filled with water. 8 identical pails of water, completely filled,
were scooped out from it and this resulted in a drop of the water level
to 38 cm. The remaining amount of water was transferred into a
cubical tank containing 39b of water. The water was then drained
out through a tap at the bottom of the cubical tank at 13b per minute.
(a) What is the capacity of each pail? (2m)
(b) How long did it take to drain the water from the cubical tank completely? (3m)
2. At Carpark P, the number of lorries to that of vans was in the ratio 3 : 7.
At Carpark Q, the number of lorries to that of vans was in the ratio 8 : 9.
When 40% more lorries from an industrial park entered Carpark P, and
20% of the vans at Carpark Q moved to Carpark P, there were 76 fewer
lorries at Carpark P than at Carpark Q. How many vehicles were there
altogether at the two carparks finally? (5m)
3. A bullet train took 5 hours to travel from Patient Town to Honest Town while
an electric train took 4 hours longer to travel from Honest Town to Patient
Town. Both trains set off at the same time and moved towards each other.
Two hours later, they were 255 km apart. What was the speed of the electric
train? (4m)
4. Korey's allowance to Skyler's allowance was in the ratio 10 : 11. Both of
them spent an equal amount. Then Korey’s remaining allowance was 7/9
of Skyler's remaining allowance. What percentage of Skyler's allowance
did she spend? Leave your answer correct to 2 decimal places. (4m)
5. Mrs Ker had a bag of brown sugar. After she used some of the brown sugar,
she had 2/3 of the brown sugar left. Then she distributed 1/4 of what she
had left equally between her neighbours, Mrs Dee and Mrs Bheem. Finally,
Mrs Ker had 437.5 g of brown sugar more than Mrs Bheem. How much
brown sugar did Mrs Ker use? Leave your answer in g. (4m)
6. Shop A sold a party dress for $600. This was 20% more than the price of a similar dress in Shop B. During a sale, both shops offered the same percentage discount on the dress. Mrs Goh bought the dress from Shop B and found that she had paid $70 less than the discounted price in Shop A.
a) Find the price of the dress in Shop B before the sale. (2m)
b) What was the percentage discount given during the sale? (3m)
7. A fruit seller had some oranges, pears and durians. After selling some of them, there were 6 pears for every 5 oranges left and 7 oranges for every 3 durians left. He sold 168 oranges. He had 456 pears and oranges left. The number of pears sold was the same as the number of durians sold.
a) How many oranges had he at first? (2m)
b) If the number of pears was twice the number of durians at first, what was the
total number of pears and durians sold? (3m)
8. Tom and Gary ran in a race. When Gary had completed the run in 20 minutes, Tom had only run 5/8 of the distance.
Tom’s average speed for the race was 75 m/min less than Gary’s.
(a) Find the distance of the race. (2m)
(b) What was Tom’s speed in m/min? (3m)
9. After spending part of his salary on transport and 4/7 of the remainder on food, Ali saved $840.
a) If his salary was $2100, what fraction of his salary did he spend on transport? (2m)
b) If he had the same salary and he had to spend the same amount on transport, what fraction of his salary could he spend on food to save 3/5 of his salary? (2m)
10. Minghua and his sister had 25 stickers altogether at first. After their mother had given them some more stickers, Minghua had 5 times the number of stickers he had before and his sister had 3 times the number of stickers she had before. They had a total of 95 stickers in the end. How many stickers did their mother give each of them?
Ans: Minghua:________________(2m)
Sister:________________(2m)
Friday, October 2, 2009
Nominating Sulin Wong for the Junior Kindness Award
I am writing in with delight to nominate Sulin Wong, a pupil of Punggol School for the Junior Kindness Award (1m).
Last Monday, 7 July 2008, which was Youth Day, a school holiday (1m), I was on Bus 851 (1m) with my mother. As it was at the peak hour at 5.30 pm (1m), the bus was very crowded (1m). At the bus-stop opposite Ganghou Mall, an elderly woman boarded the bus bound for the Punggol Interchange. On seeing the elderly's plight in getting a seat, my mother and I witnessed before us a Samaritan at work. Sulin Wong, who was also on board, readily rose from her seat and offered it to the old lady (1m).
Not only did her act of kindness touch the heart of the old lady who was generous with her praises, it also taught all who were at the scene how Singapore can be a more pleasant and gracious society through simple but selfless gestures.
Sulin Wong's act is exemplary and her kindness definitely deserves to be recognised.
Harry Tan
Passenger of Bus 851
I am writing in with delight to nominate Sulin Wong, a pupil of Punggol School for the Junior Kindness Award (1m).
Last Monday, 7 July 2008, which was Youth Day, a school holiday (1m), I was on Bus 851 (1m) with my mother. As it was at the peak hour at 5.30 pm (1m), the bus was very crowded (1m). At the bus-stop opposite Ganghou Mall, an elderly woman boarded the bus bound for the Punggol Interchange. On seeing the elderly's plight in getting a seat, my mother and I witnessed before us a Samaritan at work. Sulin Wong, who was also on board, readily rose from her seat and offered it to the old lady (1m).
Not only did her act of kindness touch the heart of the old lady who was generous with her praises, it also taught all who were at the scene how Singapore can be a more pleasant and gracious society through simple but selfless gestures.
Sulin Wong's act is exemplary and her kindness definitely deserves to be recognised.
Harry Tan
Passenger of Bus 851
Wednesday, September 30, 2009
Maths Problems 1 October 09
1. Elaine’s mom gave her money to buy some markers of the same price.
If she bought 8 such markers, she would have $8 left over.
If she bought 12 such markers, she would have $6 short.
(a) How much money did Elaine’s mom give her?
(b) How many markers could she buy if her mom were to give her another $14?
2.
A librarian counted the number of adults in the library and found that 2/5 of the number of women was equal to 2 times the number of men. When another 12 men entered the library and 45 women left the library, the ratio of the number of women to the number of men became 5 : 2.
(a) What was the ratio of the number of women at first to the number of men at first? Give your answer in its simplest form.
(b) Find the number of women in the library at first.
3.
Cinema admission tickets for children were priced at $8 each. There were 20 more boys than girls in the cinema for the first movie. For the second movie, the number of boys decreased by 10% but the number of girls increased by 5%. If there were 408 children at the second movie, how much money was collected from the sales of admission tickets for the first movie?
4.
A van travelled from Town A to Town B at an average speed of 55 km/h. A car started its journey from Town B to Town A at the same time as the van, travelling at an average speed of 90 km/h. The two vehicles passed each other 70 km from the middle of the whole journey. Find the distance between the two towns.
5. At first, 25% of Kumar’s money was the same as 33 1/3% of Lily’s money.
Lily’s father gave her $80 later, while Kumar spent $325.
In the end, Lily had 2 1/2 times as much money as Kumar.
(a) How much money did Kumar have at first?
(b) How much money did Lily have in the end?
If she bought 8 such markers, she would have $8 left over.
If she bought 12 such markers, she would have $6 short.
(a) How much money did Elaine’s mom give her?
(b) How many markers could she buy if her mom were to give her another $14?
2.
A librarian counted the number of adults in the library and found that 2/5 of the number of women was equal to 2 times the number of men. When another 12 men entered the library and 45 women left the library, the ratio of the number of women to the number of men became 5 : 2.
(a) What was the ratio of the number of women at first to the number of men at first? Give your answer in its simplest form.
(b) Find the number of women in the library at first.
3.
Cinema admission tickets for children were priced at $8 each. There were 20 more boys than girls in the cinema for the first movie. For the second movie, the number of boys decreased by 10% but the number of girls increased by 5%. If there were 408 children at the second movie, how much money was collected from the sales of admission tickets for the first movie?
4.
A van travelled from Town A to Town B at an average speed of 55 km/h. A car started its journey from Town B to Town A at the same time as the van, travelling at an average speed of 90 km/h. The two vehicles passed each other 70 km from the middle of the whole journey. Find the distance between the two towns.
5. At first, 25% of Kumar’s money was the same as 33 1/3% of Lily’s money.
Lily’s father gave her $80 later, while Kumar spent $325.
In the end, Lily had 2 1/2 times as much money as Kumar.
(a) How much money did Kumar have at first?
(b) How much money did Lily have in the end?
Tuesday, September 29, 2009
Picture writing by Jin Hao (unedited)
Johnny and Ravi were both police officers. It was their first day at work and they were patrolling the neighbourhood at Bedok.
“Headquarters told us that there has been a lot of vandalism done by school children,” said Ravi.
“So, that means we have to watch out for any vandals,” said Johnny.
As they turned around the bend of the carpark and were about to leave the carpark to patrol other carparks, they saw a group of boys. The boys were in their teens, and were holding spray cans in different colours. A grin appeared on each of their faces as they started defacing the walls on the void deck.
Johnny and Ravi then knew that they had to step in and take control. Stepping out of their police car, the two men walked towards the boys.
The policemen placed a hand on one of the boy’s shoulder. The boys spun around. The grin on his face was gone and there was only utter shock when he saw both men.
The three terrified boys were under the stern eyes of both men. As Ravi turned his back around to call for assistance, one of the boys took out a sharp knife.
Immediately, the boy charged forward and tried to stab Ravi. Johnny saw what was happening. Without thinking of his own safety, Johnny ran forward and gave the boy with the knife a flying kick.
Shouting for Ravi to keep an eye on the other two boys, Johnny quickly handcuffed the boy he had kicked. The boy turned around and grinned. Slowly Johnny realized that blood was on the boy’s knife. He fell to the floor, with a deep pool of blood surrounding him.
Ravi bent down to check on his partner. The other two boys took the opportunity and ran away. Ravi felt like punching the boy, but he took control of himself. He forced the boy into the patrol car.
Carefully lifting up his partner, he requested for an ambulance.
“Johnny ! You are going to be all right ! You hear me ! You are going to make it ! “ Ravi shouted.
Johnny was admitted to the operating room. Hours later, the doctor came out, shaking his head. Johnny did not make it.
The other two boys were caught and the three were sentenced to four years in the boy’s home. As they were too young, they could not be hanged. The boy who killed Johnny was given six strokes of the cane.
Till now, Ravi always remembers Johnny. His one and only partner.
“Headquarters told us that there has been a lot of vandalism done by school children,” said Ravi.
“So, that means we have to watch out for any vandals,” said Johnny.
As they turned around the bend of the carpark and were about to leave the carpark to patrol other carparks, they saw a group of boys. The boys were in their teens, and were holding spray cans in different colours. A grin appeared on each of their faces as they started defacing the walls on the void deck.
Johnny and Ravi then knew that they had to step in and take control. Stepping out of their police car, the two men walked towards the boys.
The policemen placed a hand on one of the boy’s shoulder. The boys spun around. The grin on his face was gone and there was only utter shock when he saw both men.
The three terrified boys were under the stern eyes of both men. As Ravi turned his back around to call for assistance, one of the boys took out a sharp knife.
Immediately, the boy charged forward and tried to stab Ravi. Johnny saw what was happening. Without thinking of his own safety, Johnny ran forward and gave the boy with the knife a flying kick.
Shouting for Ravi to keep an eye on the other two boys, Johnny quickly handcuffed the boy he had kicked. The boy turned around and grinned. Slowly Johnny realized that blood was on the boy’s knife. He fell to the floor, with a deep pool of blood surrounding him.
Ravi bent down to check on his partner. The other two boys took the opportunity and ran away. Ravi felt like punching the boy, but he took control of himself. He forced the boy into the patrol car.
Carefully lifting up his partner, he requested for an ambulance.
“Johnny ! You are going to be all right ! You hear me ! You are going to make it ! “ Ravi shouted.
Johnny was admitted to the operating room. Hours later, the doctor came out, shaking his head. Johnny did not make it.
The other two boys were caught and the three were sentenced to four years in the boy’s home. As they were too young, they could not be hanged. The boy who killed Johnny was given six strokes of the cane.
Till now, Ravi always remembers Johnny. His one and only partner.
Maths Problems 29 Sep 2009
1. Shoes and belts are sold in Mr K's shop. The ratio of the price of the shoes to the price of the belts is 5 : 2. The price of each belt is $22. Mr K sold 1/4 of the items in his shop on Sunday and collected $1056. 1/3 of the items sold were belts.
a) How many belts were sold on Sunday?
b) If the number of belts left is 3 times as many as the number of shoes left, how much would Mr K colllect if he sold all the remaining shoes and belts in his shop?
2. There were some white and black marbles in a bag. When 20 black marbles are removed, the total number of marbles in the bag left was 7 times the number of black marbles left.
When 50 white marbles were removed, the total number of marbles in the bag left was 5 times the number of black marbles. Find the total number of marbles.
a) How many belts were sold on Sunday?
b) If the number of belts left is 3 times as many as the number of shoes left, how much would Mr K colllect if he sold all the remaining shoes and belts in his shop?
2. There were some white and black marbles in a bag. When 20 black marbles are removed, the total number of marbles in the bag left was 7 times the number of black marbles left.
When 50 white marbles were removed, the total number of marbles in the bag left was 5 times the number of black marbles. Find the total number of marbles.
Monday, September 28, 2009
CW by Meng Yu
l was always a responsible class monitress and a good student in the teacher's eyes and l also get along well with my classmates.But there was once,l had disappointed my teacher and lost her trust in the end.
That day,l sat on my usual seat in the canteen while l was eating.My best friend,Tinghui came to me,her expression was full of anxiety and worries.
"l thought you were supposed to be in Mrs Tan's office,helping her carrry books?"l asked wandering why she was so anxious.
"Um...You did not tell anyone about it right?"She asked,looking around.
l nodded and looked her suspiciously,wandering what she could have done.
"Well,you must promise me no tto tell the teacher about it,"she paused,scanning around,"l accidentally spilt Mrs Tan's coffee on her work,accidentally,"She accented the word 'accidentally'.
"Oh!"l choked,"you are going to get it from her if she knows that!" She quickly covered my mouth and put one finger on her mouth.
"You are going to help me,aren't you?You are my best friend right?l'm sure the teacher will ask all of us who have seen this incident or something like that,you just need to keep quiet and sit there,okay?"She whispered in my ear.
"If you are going to let the cat out of the bag,l am not going to talk to you forever,not a single word!"She warned me.
l sat there,still like a statue.Still thnking through what she had told me.l was not used to lie to people but she was my best friend and l could not betary her.That was the most difficult decisionl have ever had to make.Between friendship and honesty,l needed to choose either one,but both were important to me.l sighed and decided to put them a side,and see what would happen next.
True enough,Mrs Tan was frustrated but she wanted the person to own up.Maybe,l thought,she would give the person a chance.A sweat rolled down my cheek and l realised that l was nervous,very nervous.l saw Tinghui blink at me and put a finger on her lips.l knew she wanted me to keep quiet.
"This is nothing big.Just be quiet.The teacher will not know.Just shut mouth."l told myself in my heart while l felt butterflies in my stomach.
"If no one is going to own up,l am going to find out on my own."Mrs Tan announced and stormed out of the classroom.
Soon,the students were murmuring about this incident and Tinghui smiled at me.l did not feel happy or relieved but just guilty.
"Shh...."As soon as we heard the teacher's footsteps,we kept very quiet.
"You have been to my office right?Tinghui."Mrs Tan asked,arms arcoss her chest. All of us turned to her and some were murmuring under their breathe.Shocked,Tinghui stood up and nodded.
"You come to me,"Mrs Tan said.
l felt more nervous,afraid that Tinghui would say anything related to me.l tried to calm myself down.After a few minutes,l was also called by the teacher and l knew that was the end of me .Standing in front of Mrs Tan, l prepared for the worst.She did not shout or scream at me,that made me relieved.But,all she said was,"l am really disappointed in you."
That's when l felt the real pain,the thing which was so important.l had lost it,the trust.
That day,l sat on my usual seat in the canteen while l was eating.My best friend,Tinghui came to me,her expression was full of anxiety and worries.
"l thought you were supposed to be in Mrs Tan's office,helping her carrry books?"l asked wandering why she was so anxious.
"Um...You did not tell anyone about it right?"She asked,looking around.
l nodded and looked her suspiciously,wandering what she could have done.
"Well,you must promise me no tto tell the teacher about it,"she paused,scanning around,"l accidentally spilt Mrs Tan's coffee on her work,accidentally,"She accented the word 'accidentally'.
"Oh!"l choked,"you are going to get it from her if she knows that!" She quickly covered my mouth and put one finger on her mouth.
"You are going to help me,aren't you?You are my best friend right?l'm sure the teacher will ask all of us who have seen this incident or something like that,you just need to keep quiet and sit there,okay?"She whispered in my ear.
"If you are going to let the cat out of the bag,l am not going to talk to you forever,not a single word!"She warned me.
l sat there,still like a statue.Still thnking through what she had told me.l was not used to lie to people but she was my best friend and l could not betary her.That was the most difficult decisionl have ever had to make.Between friendship and honesty,l needed to choose either one,but both were important to me.l sighed and decided to put them a side,and see what would happen next.
True enough,Mrs Tan was frustrated but she wanted the person to own up.Maybe,l thought,she would give the person a chance.A sweat rolled down my cheek and l realised that l was nervous,very nervous.l saw Tinghui blink at me and put a finger on her lips.l knew she wanted me to keep quiet.
"This is nothing big.Just be quiet.The teacher will not know.Just shut mouth."l told myself in my heart while l felt butterflies in my stomach.
"If no one is going to own up,l am going to find out on my own."Mrs Tan announced and stormed out of the classroom.
Soon,the students were murmuring about this incident and Tinghui smiled at me.l did not feel happy or relieved but just guilty.
"Shh...."As soon as we heard the teacher's footsteps,we kept very quiet.
"You have been to my office right?Tinghui."Mrs Tan asked,arms arcoss her chest. All of us turned to her and some were murmuring under their breathe.Shocked,Tinghui stood up and nodded.
"You come to me,"Mrs Tan said.
l felt more nervous,afraid that Tinghui would say anything related to me.l tried to calm myself down.After a few minutes,l was also called by the teacher and l knew that was the end of me .Standing in front of Mrs Tan, l prepared for the worst.She did not shout or scream at me,that made me relieved.But,all she said was,"l am really disappointed in you."
That's when l felt the real pain,the thing which was so important.l had lost it,the trust.
Picture writing by Belinda (unedited)
The void deck was utterly quiet. It was quiet, so quiet till you could hear a pin drop. It was four in the afternoon when most adults would be working and most students would be doing their homework or revising. However, the silence was broken when thundering footsteps could be heard. Three boys appeared, panting. The trio looked all around them, as if they were making sure that not a single soul was in sight.
The three boys, Bala, Alan and Wei Ming threw their bags on the concrete floor. Their hair was unkempt and their uniforms were tucked out. Next, they pulled out a stack of CDs from their bags they had stolen just now from a shop.
“We’re going to earn big bucks when we sell these CDs to our classmates!” Bala said with a mischievous gleam in his eyes as he sat down on the cool, concrete floor.
“Yeah,” Alan agreed. “Think of what we can buy with all those money!” Alan added, as a slow, silly smile started spreading on his face.
“Also, the shopkeeper was such a fool. I swear he didn’t even realise that we entered the shop. He really knows how to take care of his shop by talking on the phone all day!” Wei Ming sniggered.
Next, Wei Ming reached to his bag and pulled out a pack of cigarettes and a lighter. He laughed when he saw the looks of shock on Bala’s and Alan’s faces. Wei Ming lit up a cigarette and started smoking. Bala’s eyes nearly popped out of their sockets while Alan stood rooted at the same spot, gaping with obvious disbelief.
“C’mon, don’t look so shocked. I stole this pack of cigarettes from my older brother. Want to try?” Wei Ming offered.
Bala was the first one to recover from his shock. Without thinking twice, he reached for a cigarette from the pack and copied how Wei Ming had lit up the cigarette and stuck it into his mouth. However, Alan remained hesitant.
“What… what if somebody saw us? Anyway, we… we’re underage!” Alan stammered nervously.
“Chill, there’s no one at all. Come on, don’t be a chicken! Just take one and try!” Wei Ming snapped, annoyed.
“But… but…” Alan started to say, but was silenced by Wei Ming’s icy glare. Shrugging, Alan reached for a cigarette. However, Alan’s face turned as pale as a sheet of paper, like he’d seen a ghost. Alan pointed a trembling finger behind Wei Ming and Bala. Puzzled, Wei Ming and Bala turned around and got the shock of their lives!
The cigarette in Wei Ming’s mouth dropped on the concrete floor. They were face-to-face with two burly policemen! Wei Ming drew in a sharp breath as Bala shifted uncomfortably. Alan’s lips quivered. “Smoking, eh? You three are underage!” Once of the policemen shook his head.
With that, the trio hung their heads in shame. Apparently, someone had caught sight of them smoking and reported it to the police. The two policemen questioned the trio. They had no choice but to surrender. Wei Ming handed the pack of cigarettes and lighter to the policemen while the other two, Alan and Bala gave the stack of CDs to the policemen and explained how they had stolen them.
The two policemen shook their heads again. “You three have to follow us to the station!” the other policeman boomed.
Hobson’s choice, the trio picked their bags up and followed the policemen. They knew they were in hot soup and they braced themselves to face the music.
The three boys, Bala, Alan and Wei Ming threw their bags on the concrete floor. Their hair was unkempt and their uniforms were tucked out. Next, they pulled out a stack of CDs from their bags they had stolen just now from a shop.
“We’re going to earn big bucks when we sell these CDs to our classmates!” Bala said with a mischievous gleam in his eyes as he sat down on the cool, concrete floor.
“Yeah,” Alan agreed. “Think of what we can buy with all those money!” Alan added, as a slow, silly smile started spreading on his face.
“Also, the shopkeeper was such a fool. I swear he didn’t even realise that we entered the shop. He really knows how to take care of his shop by talking on the phone all day!” Wei Ming sniggered.
Next, Wei Ming reached to his bag and pulled out a pack of cigarettes and a lighter. He laughed when he saw the looks of shock on Bala’s and Alan’s faces. Wei Ming lit up a cigarette and started smoking. Bala’s eyes nearly popped out of their sockets while Alan stood rooted at the same spot, gaping with obvious disbelief.
“C’mon, don’t look so shocked. I stole this pack of cigarettes from my older brother. Want to try?” Wei Ming offered.
Bala was the first one to recover from his shock. Without thinking twice, he reached for a cigarette from the pack and copied how Wei Ming had lit up the cigarette and stuck it into his mouth. However, Alan remained hesitant.
“What… what if somebody saw us? Anyway, we… we’re underage!” Alan stammered nervously.
“Chill, there’s no one at all. Come on, don’t be a chicken! Just take one and try!” Wei Ming snapped, annoyed.
“But… but…” Alan started to say, but was silenced by Wei Ming’s icy glare. Shrugging, Alan reached for a cigarette. However, Alan’s face turned as pale as a sheet of paper, like he’d seen a ghost. Alan pointed a trembling finger behind Wei Ming and Bala. Puzzled, Wei Ming and Bala turned around and got the shock of their lives!
The cigarette in Wei Ming’s mouth dropped on the concrete floor. They were face-to-face with two burly policemen! Wei Ming drew in a sharp breath as Bala shifted uncomfortably. Alan’s lips quivered. “Smoking, eh? You three are underage!” Once of the policemen shook his head.
With that, the trio hung their heads in shame. Apparently, someone had caught sight of them smoking and reported it to the police. The two policemen questioned the trio. They had no choice but to surrender. Wei Ming handed the pack of cigarettes and lighter to the policemen while the other two, Alan and Bala gave the stack of CDs to the policemen and explained how they had stolen them.
The two policemen shook their heads again. “You three have to follow us to the station!” the other policeman boomed.
Hobson’s choice, the trio picked their bags up and followed the policemen. They knew they were in hot soup and they braced themselves to face the music.
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