P6 - More Algebra

1. Find the value of the following when a=5, b=7 and c=2.
(a)3a-5bc
(b)4a x 5b
(c)6b-9c
(d)42c-3b+5a
(e)13bc-14ac
(f)89c-4bc
(g)24bc divided by 5a
(h) 134c+2c -7ab

2. Solve the following.
(a) p x pq
(b)15y+34y-34a
(c)2m+2n-3m+5n
(d)7r-3t+t-7r+2t-6r
(e)cdf divided by fdc
(f)ACB+ xyz
(g) bef+feb-4bfe
(h) 2a+7d-9a-7a+15d

P6 - Algebra

1. Simplify each of the following.
(a) 5a+3a-6a
(b) 3a-(5a-4a)
(c) 3a+4b-a-b
(d) 12a+5b-7a-14b-9a
(e) 5x+7y+3z-2x-4y+z
(f) 2p-5q+7r-4p+2q-3r
(g) 12xy-13xz+5yz-4xz
(h) 7abc-4bca+6cba-cba
(i) 3a-4a+5a-7a+4
(j) 5ab-1.5ab+0.75bc+0.25cb

2. Evaluate each of the following.
(a)3a-5a+4a
(b)12a+5b-7a-14b-9a
(c)12p-25q+7r-4p+12q-3r
(d)7abc-41bca+16cba-3cba
(e)a+b+c+2b-c+3c+a
(f) 2ab+3bc+5ac-5ba+2cb+5ab

P5 Problem Sums- to be handed in on 8th Jan 2010

1. Jane, Alice and Peter had a sum of money. After Jane spent ¼ of her money, Alice spent $80 of hers and Peter spent ½ of his money, they had an equal amount of money left. If they had a total of $1008 in the end, how much did each of them have at first?

2. There were 1518 boys and girls in a room. When 2/3 of the boys and 1/5 of the girls left the room, there were twice as many girls as boys remaining in the room.
(a) How many girls were there at first?
(b) How many boys were there at first?

3. Cleo wanted to buy 16 similar shirts but she was $8 short. If she had bought 7 such shirts instead, she would have $19 left.
(a) What was the cost of 2 such shirts?
(b) How much money did Cleo have?

4. Mrs Baker bought some flour. She used ¼ of it to bake 16 cherry pies and packed the rest equally into 9 bags. There were 250g more flour in 2 similar bags than what was used for a cherry pie. If all the flour was packed into 25 bags instead, how much flour would there be in each bag? (sorry, please change 16 cherry pies to 15 and 250g to 270g.)

5. Half of a number is 90 more than a fifth of the number. What is the number?

6. Tom is nine years younger than Gary who is 13 years old. How many years later will Tom be of half Gary’s age?

7. Sally and Sandy have a total age of 45. Sally is 15 years older than Sandy. What was their total age when Sandy was half as old as Sally?

8. Eugene is 15 years old. His sister is 3/5 of his age. His sister is 3/11 of their mother’s age.
(a) How much older is Eugene’s mother than Eugene?
(b) In how many years’ time will Eugene’s mother be twice his age?

9. Juliana and Patrick had some marbles. If Juliana gave Patrick 20 marbles, both of them would have an equal number of marbles. If Patrick gave Juliana 20 marbles, Juliana would have 3 times as many marbles as Patrick. Find the number of marbles that each of them had.

10. James is 8 years old. Last year, his father was four times as old as he was. In how many years’ will their combined age be 51?

11. A bag costs $24.50. the total cost of 2 bags and a wallet is $85. What is the total cost of 3 bags and 3 wallets?

12. Aaron bought 2 similar books and 3 similar rulers for $40.30. Sharon bought 3 such books and 5 such rulers for $61. What was the total cost of a book and a ruler?

P6 Problem Sums - to be handed in on 8th Jan 2010

1 Tammy and Sally shared some money in the ratio 4:3. If Tammy gave $150 to Sally, they would have the same amount of money. How much money did they have altogether?

2 The ratio of the number of teddy bears Mei Mei had to that of the number Jane had was 3:7. Jane had 24 more teddy bears than Mei Mei. Jane gave some teddy bears to Mei Mei and the ratio of Mei Mei’s teddy bears to Jane’s teddy bears became 5:7. How many teddy bears did Jane give to Mei Mei?

3 Last year, the ratio of the number of boys to the number of girls in the Speech and Drama Club was 1:2. This year, 170 members joined the club. There are now 5 times as many boys and 4 times as many girls as last year. How many members were there in the Speech and Drama Club last year?

4 Five friends met at a reunion dinner. Each friend hugged each of the other friends just once. How many hugs were exchanged in all?

5 There were 78 three-legged and four-legged stools in Carpenter Calvin’s storeroom. There were 259 legs in all. Find the number of three-legged stools and four-legged stools.

6 There are 250 bicycles and cars in the car park. There are a total of 936 wheels. How many cars and how many bicycles are there in the car park?

7 Mrs Li sold 18 watermelons and 26 honeydews. She collected $160 from the sale. The selling price of a honeydew is one-third that of the selling price of a watermelon. How much did Mrs Li sell for each honeydew and for each watermelon?

8 Bob and Carl have some sweets each. If Bob eats 5 sweets each day and Carl eats 10 sweets each day, Bob will have 46 sweets left when Carl finishes all of his. If Bob eats 10 sweets each day and Carl eats 5 sweets each day, Bob will have only 1 sweet left when Carl finishes all his sweets. How many sweets does each boy have?

9 Ming and Ling have some Mathematics problems to solve. If Ming can solve 6 questions each hour and Ling can solve only 3 each hour, Ling has 21 questions left when Ming completes his. If Ming can solve 4 questions each hour and Ling can solve 8 questions each hour, Ling has 3 questions left when Ming solves all his problems. How many Mathematics problems does each of them need to solve?

10 Sally and Sandy sell toys. If Sally sells 30 toys each week and Sandy sells 90 toys each week, Sally will have 237 toys left unsold when Sandy has sold all her toys. If Sandy sells only 15 toys each week and Sally still sells 30 toys each week, Sally will have 87 toys left unsold when Sandy has sold all of hers. How many toys does each of them have?

P4 Science - Matter

Matter is anything that has mass and occupies space.

A solid
- has a definite shape
- does not take the shape of the container it is put into
- has a definite volume
- cannot be compressed
- does not take the volume of the container it is put into.

A liquid
- does not have a definite shape
- takes the shape of the container it is put into
- has a definite volume
- cannot be compressed
- does not take the volume of the container it is put into.

A gas
- does not have a definite shape
- takes the shape of the container it is put into
- does not have a definite volume
- can be compressed
- takes the volume of the container it is put into.

Water boils at 100 degrees celsius , melts at 0 degrees celsius and freezes at 0 degrees celsius.
Impurities such as salt or sugar can increase the boiling point of water and lower the freezing and melting points of water. Therefore, sea water boils at a temperature above 100 degrees celsius.
When water boils, air in the water escapes in the form of air bubbles. As such, plants and animals cannot survive in boiled water as there is no air in boiled water.

1. What is matter?
2. Name 7 non-matter.
3. What are the 3 states of matter?
4 What are the properties of (a) solids?
(b) liquids?
(c) gases?
5. How is a solid different from a liquid?
6. How is a solid different from a gas?
7. How is a liquid different from a gas?
8. What is the boiling point of water?
9. What is the freezing point of water?
10. What is the change in state when water evaporates?
11. What is the change in state when ice melts?
12. What is the change in state when water freezes?
13. List 3 ways in which an ice cube is different from water vapour?
14. What is observed water boils?
15. Does pure water or sea water boil at a higher temperature?

P5/6 - Emotions

Fear
I stood rooted to the ground. My legs turned wobbly and I could not move even an inch. A cold chill ran through my body, sending beads of cold perspiration down my spine. With quivering lips, I muttered in an edgy voice, “What could that be?” Fear engulfed me. My heart thumped. I could feel it coming out from my mouth. I could no longer contain my cowardice and broke into tears.

Anger
I clenched my fists tightly, piercing each fingernail into my palms. I bit my lips and took a deep breath. It was of no use. The raging fury in me gushed out through my mouth, “Put that down!” I could no longer contain my temper. Anger engulfed me, taking away all composure I had. Nothing could put out the wild fire in my chest.

Joy
My eyes glittered in bliss. I was riding on cloud nine, making my way to the top of the world. I had never felt better. I was overwhelmed with euphoria. It was so much excitement that I could not contain my joy anymore. The smile on my face extended and I was grinning from ear to ear. I boasted in glee, “What else can I ask for?” Tears of joy welled up in my eyes.

Sorrow
I had not expected it. Sadness had taken over every part of me. It felt like a dagger stabbing right into my heart. Deep grief engulfed me. Tears of sorrow welled up in my eyes. I tried to hold back the beads of helplessness, but to no avail. Nothing else could seep into my dark world, except for, “Why?” There were no answers and only questions echoed in my vacuumed mind.

Embarrassment
I flushed. “Does anyone have a paper bag to spare?” I mumbled in complete embarrassment. How I wished that I could hide myself somewhere to save all this humiliation. Even if it were just a paper bag, it would suffice. Beads of cold perspiration gathered at my forehead. I had never felt worse. Little did I expect myself to be caught in such a situation.

Regret/Guilt
All I needed was a second chance to undo the wrong deed. “Look before you leap, child.” My mother’s advice fell on my deaf ears. My heart ached. It felt like I had just stabbed myself with a dagger. I had only myself to blame and no one would bother to nurse the aching heart of a wrongdoer. Tears of guilt and remorse trickled down my sunken cheeks. I truly regretted my foolish act.

P5/6- Comprehension Corrections (2)

61. He needed the cloth to wrap his legs in order to keep warm.
62. She stopped being a court lady after her husband was exiled.
63. She knew that if she had given birth to a boy, he would have been killed.
64. "Us" refers to the girl and her mother.
65. She requested for her daughter to worship Kannon faithfully,
66. He was impressed by her faith and wanted to do something for her.
67. He had to bow three times before each cut.
68. She had to cut her hair and take her vows.
69. The word is "exiled".
70. She was a filial girl.

P5 - Science

1. Why is the water cycle important?
2. Name 3 ways to reduce the use of water.
3. What are the 3 main causes of water pollution?
4. Is there a gain of heat or loss of heat in the following processes?
(a) condensation
(b) evaporation
(c) boiling
(d) freezing
(e) melting
5. What is the boiling point of water?
6. What is the freezing point of water?
7. What is the change in state when water evaporates?
8. What is the change in state when ice melts?
9. What is the change in state when water freezes?
10. List 3 ways in which an ice cube is different from water vapour?
11. What is observed when water boils?
12. Does pure water or sea water boil at a higher temperature?

P6 - Composition

“ Let’s go with them!” I turned around as these words rang in my ears. I wondered what was happening. I had just alighted from the school bus when I saw hordes of students running towards the school field. Curiosity got the better of me and I decided to follow the crowd.

Students let out stifled giggles. Teachers wore horrified faces. I was getting impatient and could wait no longer to know the cause of the commotion. I elbowed my way through the mass. “ Ha ha ha!” I let out convulsions of laughter upon sight of the centre of attraction. Mr Lim, our Head of Department of Physical Education, was lying on the tracks of the school field in a contorted manner.

The silence around me broke my laughter. All eyes turned from Mr. Lim to me. Only then did it dawn on me that I had been really rude. I flushed. “Does anyone have a paper bag to spare?” I mumbled in complete embarrassment. How I wished that I could hide myself somewhere to save all this humiliation! Even if it were just a paper bag, it would suffice. Beads of cold perspiration gathered at my forehead. I had never felt worse. Little did I expect myself to be caught in such a situation.

Most timely for me, the paramedics had just arrived. As they checked on Mr Lim, the vast sea of eyes gave these angels all their focus. I stepped backwards and stood amidst the crowd to avoid unnecessary attention. As I eavesdropped on the hushed whispers of the students around me, I managed to find out how Mr Lim was injured. While the paramedics were helping Mr Lim onto the stretcher, a fat boy, the culprit , was standing not too far away. The guilty look he wore signalled a confirmation that he was the one who had knocked Mr Lim down as he was training with the members of the “Fat Club” during the morning workout.

The crowd moved towards the assembly ground for the flag-raising ceremony and everyone seemed to have forgotten about me. “Phew!” The paramedics really saved me.

P5 - Difference Concept

1. Mrs Ong is 45 years old. Her niece is 30 years younger than she is. In how may years' time will Mrs Ong be twice as old as her niece?

2. There were 1240 pupils in School A and 20% more pupils in School B. When an equal number of pupils left each school, the ratio of the number of pupils in School B to that of School A became 5:4. How many pupils were there in School B in the end?

3. Ben's age is 1/3 that of Tom's. In 9 years' time, his age will be 2/3 that of Tom's. How old is Ben now?

4. The ratio of John's age to Ryan's age is 3:1 now. 25 years later, the ratio will become 4:3. How old is John now?

5. Mr Lim had 50% as much money as Mr Ibrahim. After they each spent $200 on a DVD player, Mr Lim had 1/3 as much money as Mr Ibrahim. Find the sum of money Mr Lim had at first.

6. There were 40% as many adults as children on a bus. After 8 children and 8 adults boarded the bus, there were twice as many children as adults. How many adults were on the bus at first?

P5 - Total Concept

1. Tom had 1/2 the number of marbles Ben had at first. After Ben gave 12 of his marbles to Tom, Tom had 2/3 the number of marbles Ben had. How many marbles did Tom have at first?

2. Van and Bob had some cards. After Bob gave 4/9 of his cards to Van, the ratio of the number of Bob's cards to the number of Van's cards became 10:17. What was the ratio of the number of Van's cards to the number of Bob's cards at first?

3. The ratio of Jane's money to Mary's money was 3:4 at first. After Jane gave Mary $24, the ratio of Jane's money to Mary's money became 1:2. What was the total amount of money they had altogether?

4. Mary and Henry shared a collection of stamps. Mary had 63% of the total number of stamps. If Mary gave 39 of her stamps to Henry, both of them would have the same number of stamps. How many stamps did Mary have?

5. The ratio of the number of seashells Beng had to the number of seashells Rose had was 8:5. After Beng gave Rose 12 of his seashells, both had an equal number of seashells. How many seashells did Rose have at first?

6. A, B and C bought a present for thei mother. A paid 1/3 of the total amount paid by B and C. B paid 1/5 of the total amount paid by A and C. If C paid $60 more than B did, how much did the present cost?

7. C and D had some savings each. If C gave D $120, both would have an equal amount of savings. If D gave C $120, C would have 3 times as much savings as D. How much did each of them have?

P5/6- Comprehension Corrections

61. The person to possess the plate of gold must love his fellow people.
62. They hoped that the priests would give them the plate of gold for their good deeds.
63. He dropped the plate of gold out of shock when it turned into lead.
64. The sentence is "But when he took it in his hands, it turned into worthless lead."
65. Four people were awarded the plate of gold in that two years.
66. They wanted to receive money from the claimants of the plate of gold.
67. The beggars failed to receive sympathy and pity.
68. The word is 'alms'.
69. "Them" refers to the beggars crowding outside the temple gate.
70. He was in poverty, could not see and was crippled.