## Saturday, October 22, 2011

## Wednesday, October 12, 2011

### Synthesis English P6

**Try**

__as I might, I was not able to write an answer that felt right.__**No sooner**

__had his mother left by the front door than he sneaked into the house through the back door__.## Saturday, October 1, 2011

## Friday, September 30, 2011

### Decimal P6 2011 PSLE P2 Q

**A fruit stall was selling pear at 70 cents each and apples at 40 cents each. Sally bought some pears and Tom bought some apples. Sally spent $1.10 more than Tom but had 7 less fruits than him.**

**a) How many pears did Sally buy?**

**b) How much did Tom spend?**

**0.40 x 7 = $2.80**

**1.10 + 2.80 = $3.90**

**0.70 - 0.40 = $0.30**

**3.90**

**÷ 0.30 = 13 pears**

**a) It was 13 pears.**

**13 + 7 = 20**

**20 x 0.40 = $8**

**b) It was $8.**

**---------------------------------------**

**Alternative solution**

**---------------------------**

**0.70 x 7 = $4.90**

**4.90 + 1.10 = $6**

**0.70 - 0.40 = 0.30**

**6 ÷ 0.30 = 20**

**20 - 7 = 13 pears**

**a) It was 13 pears.**

**20 x 0.40 = $8**

**b) It was $8.**

Labels:
M Decimal P6,
M Decimal PSLE 2011,
M PSLE 2011

### PSLE 2011 Incomplete questions and answers

**Paper 1**

**-----------**

**Q13) Question on 2 Circles**

**Ans:**

**66 cm**

**Q14) Which column A, B, C or D should 432 be?**

**Ans: Column A (Ans: 1)?? Remainder 3 --> Column C (Ans: 3)**

**Q) Eight right-angled triangles and square?**

**Ans: 17 cm**

The dotted line area is 289?

Square root 289 =

The dotted line area is 289?

Square root 289 =

__17 cm__

**Q) Parallelogram and rhombus**

**Ans: 42 degrees**

**Q) How many pupils bought 3 books?**

**Ans: 22 pupils**

**28) Question on rice**

**Ans:**

**2.4 kg**

**Paper 2**

**-----------**

**Q6) 36/120 x 100%**

**Ans: 30%?? 20%??**

**Q13)**

**Ans: 66**

**Q) Tiles?**

**Ans: a) 5/9; b) 180m2**

### Whole Number P6 2011 PSLE P1 Q17

**A school was holding an event and tickets were sold to the teachers and pupils. Each teacher had to pay $20 each while each pupil had to pay $8 each. 1/4 of the tickets were bought by the teachers and the rest bought by the pupils. The total cost of tickets bought by the pupils was $416 more than the total cost of the tickets bought by the teachers. What was the total cost of all the tickets sold?**

**1 x 20 = 20**

**3 x 8 = 24**

**24 – 20 = 4 u --> 416**

**44**

**44 u --> ----- x 416 = $4 576**

**4**

**It was $4 576.**

### Fraction P6 2011 PSLE P2 Q18

**Faizal had a sum of money. He spent 1/4 of his money on a wallet and 2/5 of the remainder on a book. After that, his parents gave him $120. Finally, the ratio of the amount of money he had in the end to the amount of money he had at first was 5 : 4. What was the sum of money Faizal had at first?**

**1 3**

**1 - --- = ----**

**4 4**

**2 3**

**1 - --- = ----**

**5 5**

**3 3 9**

**--- x ---- = ----**

**5 4 20**

**9**

**---- + $120 --> 5 u**

**20**

**1 --> 4 u**

**9 9**

**---- --> ---- x 4 u = 1.8 u**

**20 20**

**5 u - 1.8 u --> $120**

**3.2 u --> $120**

**4**

**4 u --> ----- x 120 = $150**

**3.2**

**It was $150.**

**--------------------------------------------------------------------------**

**Alternative solution**

**------------------------**

**\<---------------- 4 p --------------->|**

|<----------- 5 p ----------->|

5 p --> 9 u + 120

4 p --> 20 u

5

5 p --> ---- x 20 u = 25 u

4

25 u --> 9 u + 120

16 u --> 120

20

20 u --> ---- x 120 = $150

16

It was $150.

**[ | | | | ]****[ | | | | ]****[ | | | |]****[ | | | | ]****[ | | ][ | | ]****[ | | ][ | | ]****[ | | ][ $120 ]**|<----------- 5 p ----------->|

5 p --> 9 u + 120

4 p --> 20 u

5

5 p --> ---- x 20 u = 25 u

4

25 u --> 9 u + 120

16 u --> 120

20

20 u --> ---- x 120 = $150

16

It was $150.

Labels:
M Fraction P6,
M Fraction P6 PSLE 2011,
M PSLE 2011

### Whole Number P6 2011 PSLE

**The chairs in a hall were arranged in rows of 9 chairs each. For a concert to be held in the hall, Alex bought another 6 chairs and rearranged the chairs into rows of 7 chairs each. After the rearrangment, he found that he had 12 additional rows. How many chairs were there in the hall for the concert?**

**12 x 7 = 84**

**84 - 6 = 78**

**9 - 7 = 2**

**78 ÷ 2 = 39 rows originally**

**39 x 9 = 351**

**351 + 6 = 357**

**chairs**

**It was 357 chairs.**

**-----------------------------------------**

**Alternative solution**

**----------------------------**

**9 x 1 u -->**

**7 x 1 p - 6**

**{1 u -- number of rows at the start; 1 p -- number of rows in the end}**

**9 u --> 7 p - 6**

**1 u --> 1 p - 12**

**7 u --> 7 p - 7 x 12 = 7 p - 84**

**2 u --> 84 - 6 = 78**

**1 u --> 78 ÷ 2 = 39**

**39 x 9 = 351**

**351 + 6 = 357**

**It was 357 chairs.**

### Fraction 2011 PSLE

**Mr Lee has 185 more chicken pies than tuna pies. After he sold 3/5 of the chicken pies and half of the tuna pies there were 146 pies left. How many pies were sold?**

**5 C - 2 T --> 185**

**2 C + 1 T --> 146**

**4 C + 2 T --> 2 x 146 = 292**

**9 C --> 292 + 185 = 477**

**1 C --> 477 ÷ 9 = 53**

**1 T --> 146 - 2 x 53 = 40**

**3 C --> 3 x 53 = 159**

**159 + 40 = 199**

**It was 199 pies.**

Labels:
M Fraction P6,
M Fraction P6 PSLE 2011,
M PSLE 2011

### Speed P6 2011 PSLE

**Alex and Bob were running round a 400 m**

**circular track. Alex ran at a speed of 190 m/min while Bob ran at a speed 25 m/min slower than Alex. When Alex ran****300 m**

**more than Bob, how many complete rounds had he run?**

**25 m --> 1 min**

**300**

**300 m --> ----- x 1 = 12 min**

**25**

**190 x 12 = 2280 m**

**2280 ÷ 400 = 5.7**

**≈ 5 complete rounds**

**It was 5 complete rounds.**

Labels:
M PSLE 2011,
M Speed P6,
M Speed PSLE 2011

### Average 2011 PSLE

The average of A, B and C is 5y. C has 2 y more than B and A has y more than B.

a) Find B. Give your answer in terms of y.

b) If y = 5, what is B?

a) Find B. Give your answer in terms of y.

b) If y = 5, what is B?

**A [][ 2 y ] )****B [] ) 5 y x 3 = 15 y****C [][ y ] )****3 u --> 15 y - 2 y - y = 12 y****1 u --> 12 y ÷ 3 = 4 y****a) It was 4 y.****4 x 5 = 20****b) It was 20.**
Labels:
M Average P6,
M Average PSLE 2011,
M PSLE 2011

### Whole Number P6 2011 PSLE P1 Q15

**Sally has a book which has 525 pages. From Monday to Thursday she reads 15 pages per day and Friday to Sunday she reads 30 pages per day. What is the least number of days she needs to finish reading the whole book?**

**Friday to Sunday Ã 30 x 3 = 90**

**Monday to Thursday Ã 15 x 4 = 60**

**1 set (7 days) --> 90 + 60 = 150**

**525 ÷ 150 = 3 sets remainder 75 pages**

**75 ÷ 30 = 2 r 15 days**

**{So can start on Thursday, Friday or Saturday}**

**3 x 7 = 21**

**21 + 3 = 24 days**

**It is 24 days.**

## Thursday, September 29, 2011

## Wednesday, September 28, 2011

### Challenging P6 2011 Nanyang SA2 P2 Q14

**(a) 16, 17, 18, 19, 20, 21**

**1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10**

**= (1 + 10)/2 x 10 = 55**

**{Aveage x Number of numbers}**

**{Average = Sum of first and last numbers divided by 2}**

**(b) It is 55**

**1 + 2 + 3 + ..... + 99 + 100**

**= (1 + 100)/2 x 100 = 5050**

**5050 - 99 = 4951**

**c) It is 4951.**

### Percentage P6 2011 Nanyang SA2 P2 Q17

17. Packet A, Packet B and Packet C each contained some salt. At first, there were 200 g more salt in Packet A than Packet B. Packet C had 3/4 of the amount of salt in Packet A. After 1/8 of the amount of salt in Packet A was transferred to Packet B, there was 82.15 g of salt in Packet B. How many percent less salt were there in Packet C than Packet A

Answer given: 25%

**at first?**[5 marks]**{Should be be at the end instead of at first?}**Answer given: 25%

**1 - 3/4 = 1/4****1/4 x 100% = 25%****It was 25%.**### Ratio P6 2011 Nanyang SA2 P2 Q18

18. In a cinema, the ratio of the number of girls to the number of boys was 3 : 2. The ratio of the number of women to the number of boys was 5 : 4. The ratio of the number of girls to the number of men was 2 : 5. During the movie, 6 women and 27 men left the cinema. The ratio of the number of women to the number of men then became 1 : 2.

(a) Express the number of women as a fraction of the number of men at first. Leave your answer in its simplest form.

(b) How many children were there in the cinema?

Answer given: (a) 1/3 and (b) 30

(a) Express the number of women as a fraction of the number of men at first. Leave your answer in its simplest form.

(b) How many children were there in the cinema?

Answer given: (a) 1/3 and (b) 30

**x 2**

**3 : 2 = 6 : 4****5 : 4**

**x 3****2 : 5 = 6 : 15****5 /15 = 1/3****a) It was 1/3.****W M W x 2**

**----------------------------****5****: 15 10 {Use to 5 : 15 instead of 1 : 3}****- 6 - 27 - 12****----------------------------****1 : 2 2****----------------------------****15 u – 27**

**Ã**

**10 u – 12**

**5 u**

**Ã**

**27 – 12 = 15**

**1 u**

**Ã**

**15/5 = 3**

**10 u**

**Ã**

**10 x 3 = 30**

**b) It was 30 children.**

### Volume P6 Nanyang 2011 SA2 P2 Q15

15. A rectangular tank measuring 3 m by 3 m by 1.5 m was 1/3 filled with water. A tap was turned on to fill up with water at a rate of 18 l/min. Every 2 minutes after the tap was turned on, 6 l of water was poured from a pail into the tank. How long did it take for the rectangular tank to be completely filled with water? Leave your answer as a mixed number in its simplest form. [4 marks]

Answer given: 428 2/3 min

Answer given: 428 2/3 min

**2/3 x 300 x 300 x150 =9 000 000 cm3 =**9 000 litres

**18 x 2 6 36 6**

**|---------|-----|----------|------|-----**

2 min 0 2 min 0

2 min 0 2 min 0

**1 cycle (2 min) Ã 18 x 2 + 6 =**42 litres

**9 000 litres Ã 9000/42 x 2 ≈ 214 cycles**

**9 000 - 214 x 42 =**12 litres

**12/18 = 2/3 min**

**214 x 2 = 428 = min**

**428 + 2/3 = 428 2/3 min**

**It was 428 2/3 min.**

## Tuesday, September 27, 2011

## Monday, September 26, 2011

## Monday, September 19, 2011

### Fraction P6 Nan Hua 2011 SA2 P2 Q14

A train has a capacity of 154 seats. Tickets for seats are sold at $8 and $12. There are 1/5 more $8-seats than $12-seats on the train. During a trip, the amount collected from the sales of $8 tickets was twice the amount collected from the $12 tickets. The total amount collected was $540. How many $8-seats were not taken during the trip?

**Note: Those in red are not necessary for the actual workings.****$8 $12 Total****------------------------------------------------------****Number of seats 6 u : 5 u 154****Amount collect 2 p : 1 p $540****------------------------------------------------------****11 u --> 154****1 u --> 154 ÷ 11 = 14****6 u --> 6 x 14 = 84****3 p --> 540****1 p --> 540 ÷ 3 = 180****2 p --> 2 x 180 = 360****360 ÷ 8 = 45****84 - 45 = 39 $8 tickets****It was 39 $8 tickets not taken up.**## Monday, August 29, 2011

### Ratio P5 Question

Mr Tang has some 20-cent and 50-cent coins.

The ratio of the value of the 20-cent coins to the value of the 50-cent coins is 7 : 6.

Find the ratio of the number of 20-cent coins to the number of 50-cent coins.

[Ans: 35 : 12]

The ratio of the value of the 20-cent coins to the value of the 50-cent coins is 7 : 6.

Find the ratio of the number of 20-cent coins to the number of 50-cent coins.

[Ans: 35 : 12]

### Decimal P5 Question

Box A contained 1.36 kg of sand, box B contained 0.6 kg of sand, box C contained 1.68 kg of sand and box D contained 1.54 kg of sand.After some sand was transferred from box C to box A and from box D to box B, boxes A and B had the same amount of sand and box C had 5 times as much sand as box D.

(a) How much sand was transferred from box D to box B? [Ans: 1.315 kg]

(b) How much sand was transferred from box C to box A? {Ans: 0.555 kg]

(a) How much sand was transferred from box D to box B? [Ans: 1.315 kg]

(b) How much sand was transferred from box C to box A? {Ans: 0.555 kg]

### Fraction P5 Question

William had $6 and Xena had $40 at first.William save 90 cents a day and Xena saved 40 cents a day.

(a) How long did it take William to save $18? [20 days]

(b) How long did it take for William's total money to be 1 1/2 times of Xena's total money? [Ans: 180 days]

(a) How long did it take William to save $18? [20 days]

(b) How long did it take for William's total money to be 1 1/2 times of Xena's total money? [Ans: 180 days]

### Fraction P5 Question

Amy saved 5/8 of her salary every month and she spent the rest.

Ben saved 3/7 of his salary every month and he spent the rest which amounted to $600.

Amy took 1 1/6 years less than Ben to save $12600.

(a) What was Ben's monthly salary? [Ans: $1050]

(b) What was Amy's monthly salary? [Ans: $1440]

Ben saved 3/7 of his salary every month and he spent the rest which amounted to $600.

Amy took 1 1/6 years less than Ben to save $12600.

(a) What was Ben's monthly salary? [Ans: $1050]

(b) What was Amy's monthly salary? [Ans: $1440]

## Monday, August 8, 2011

## Tuesday, July 26, 2011

### Ratio P5

The ratio of the amount of money Jenny had to the amount of money Siti had was 3:4. The next day, their parent gave each of them some money. Siti received twice as much as Jenny. The ratio then became 5:8. If both girls had a total of $70 at first, how much did Siti receive?

J [][][] [][]

S [][][][] [][][][]

7 u --> $70

4 u --> 4/7 x 70 = $40

Siti received $40.

J [][][] [][]

S [][][][] [][][][]

7 u --> $70

4 u --> 4/7 x 70 = $40

Siti received $40.

## Tuesday, July 19, 2011

## Monday, June 27, 2011

## Sunday, June 26, 2011

### Fraction P6 2010 SA1 Rosyth Q18

18. There were 156 more pupils in the playground than in the library. 1/5 of the pupils in the library were girls and 5/6 of the pupils in the playground were boys. If there were 17 more girls in the playground than in the library, find the total number of pupils in the two places. [5]

## Monday, May 30, 2011

### ??

Ali has $300. He lost 1/3 of it and ends up with $200. To have the $300 again, he needs to win $100 which is ½ of the $200. 1/3 is known as the Losing Fraction (LF) and ½ is known as the Winning Fraction (WF). ½ times 1/3 = 1/6. 1/6 is the product of the LF and WF, known as the PLW. Find the LF and the WF if the PLW is 81/400.

81 = 81 x 1

= 27 x 3

= 9 x 9

400 = 400 x 1

= 200 x 2

= 100 x 4

= 80 x 5

= 50 x 8

= 40 x 10

= 25 x 16

LF = a/b

WF = c/d

a/b = c/d (1 - a/b)

a d = c (b - a)

Using the above factors, trial and error,

a = 9, b = 25, c = 9 and =16

LF = 9/25 and WF = 9/16

81 = 81 x 1

= 27 x 3

= 9 x 9

**(a and c)**400 = 400 x 1

= 200 x 2

= 100 x 4

= 80 x 5

= 50 x 8

= 40 x 10

= 25 x 16

**(b and d)**LF = a/b

WF = c/d

a/b = c/d (1 - a/b)

a d = c (b - a)

Using the above factors, trial and error,

a = 9, b = 25, c = 9 and =16

LF = 9/25 and WF = 9/16

## Monday, May 23, 2011

### Fraction P6 2010 SA1 Rosyth P2 Q18

There were 156 more pupils in the playground than in the library. 1/5 of the pupils in the library were girls and 5/6 of the pupils in the playground were boys. If there were 17 more girls in the playground than in the library, find the total number of pupils in the two places.

**You may start with****a) There were 156 more pupils in the playground than in the library, or****b) there were 17 more girls in the playground than in the library****1/5 of the pupils in the library were girls --> 5 units in library with 1 unit girls****5/6 of the pupils in the playground were boys --> 6 UNITS in playground, with 1 UNIT girls****Note: unit and UNIT are not the same****a)****There were 156 more pupils in the playground than in the library****Draw 6 UNITS for playground + 156 [divided in 6 parts]****Draw 6 UNITS for library, but with 1 UNIT divided into 5 parts****P [ ][ ][ ][ ][ ][ ][][][][][][]****L [ ][ ][ ][ ][ ][||||]<---156--->****156 ÷ 6 = 26****Compare the girls in the playground and library****26****[ ][ ]****[ ][|****17****26 - 17 = 9****1 u --> 9 x 5 = 45 Compare the 6 UNITS of playground with 6 UNITS of libary****6 u --> 6 x 45 = 170****270 + 156 + 270 = 696 pupils****There were 696 pupils.****Alternative solution (b)****----------------------------****there were 17 more girls in the playground than in the library****[ ][17]****[ ]****[][17] [][17] [][17] [][17] [] [17] [][17]****[] [] [] [] [] <------------156------------>****6 u + 17 x 6 --> 5 u + 156****1 u --> 156 - 102 = 54****5 u --> 5 x 54 = 270****270 + 270 + 156 = 696 pupils****There were 696 pupils.**## Monday, January 3, 2011

### Graph PSLE 2010 P2 Q15

Chris filled a tank with water using two taps. He turned on Tap A first and after 4 minutes, he also turned on Tap B. Both taps were turned off at the same time when the tank was completely filled without overflowing.

The graph below shows the amount of water in the tank over 16 minutes.

10 - 4 = 6

30/6 = 5

5/4 = 1.25

5 - 1.25 = 3.75 litres

Alternative method

----------------------

10 - 4 = 6

6/4 x 5 = 7.5

35 - 5 - 7.5 = 22.5

22.5/6 = 3.75 litres

b) In one minutes, 3.75 litres of water flowed from Tap B.

The graph below shows the amount of water in the tank over 16 minutes.

(a) What fraction of the tank was filled 4 minutes after Tap A was turned on? Express your answer in the simplest form.

(b) In one minute, how many litres of water flowed from Tap B?

5/35 = 1/7

a) 1/7 of the tank was filled 4 minutes after Tap A was turned on.

35 - 5 = 30

10 - 4 = 6

30/6 = 5

5/4 = 1.25

5 - 1.25 = 3.75 litres

Alternative method

----------------------

10 - 4 = 6

6/4 x 5 = 7.5

35 - 5 - 7.5 = 22.5

22.5/6 = 3.75 litres

b) In one minutes, 3.75 litres of water flowed from Tap B.

### Volume PSLE 2010 P2 Q18

Diagram given - Tank A, 60 cm by 10 cm by 40 cm, with a tap above it, was empty.

Diagram given - Tank B, 50 cm by 20 cm by 36 cm, with a tap above it, was filled with water.

At first, Tank A was empty and one third of Tank B was filled with water. Both taps were turned on at the same time and water from both taps flowed at the same rate of 1.2 litres per minute.

How long did it take for the height of the water to be the same in both tanks?

(1 litre = 1000 cm³)

1/3 x 36 = 12

60 x 10 x H --> 50 x 20 x (H - 12)

1000 H - 600 H --> 12 000

H --> 12 000 / 400 = 30

60 x 10 x 30 = 18 000

18 000 / 1 200 = 15 minutes

It took 15 minutes.

Alternative method

----------------------

60 x 10 : 50 x 20 = 3 : 5

2 u --> 1/3 x 36 = 12 cm

5 u --> 5/2 x 12 = 30 cm

60 x 10 x 30 ÷ 1200 = 15 cm

It took 15 minutes.

Diagram given - Tank B, 50 cm by 20 cm by 36 cm, with a tap above it, was filled with water.

At first, Tank A was empty and one third of Tank B was filled with water. Both taps were turned on at the same time and water from both taps flowed at the same rate of 1.2 litres per minute.

How long did it take for the height of the water to be the same in both tanks?

(1 litre = 1000 cm³)

1/3 x 36 = 12

60 x 10 x H --> 50 x 20 x (H - 12)

1000 H - 600 H --> 12 000

H --> 12 000 / 400 = 30

60 x 10 x 30 = 18 000

18 000 / 1 200 = 15 minutes

It took 15 minutes.

Alternative method

----------------------

60 x 10 : 50 x 20 = 3 : 5

2 u --> 1/3 x 36 = 12 cm

5 u --> 5/2 x 12 = 30 cm

60 x 10 x 30 ÷ 1200 = 15 cm

It took 15 minutes.

### Perimeter PSLE 2010 P1 Q28

The shaded figure below is formed using 3 squares and 3 equilateral triangles. The length of the straight line AB is 15 cm. Find the perimeter of the shaded figure.

15 x 3 = 45

15 x 2 = 30

45 + 30 = 75 cm

Alternative method

----------------------

15 x 5 = 75 cm

15 x 3 = 45

**Squares**15 x 2 = 30

**Triangles**45 + 30 = 75 cm

Alternative method

----------------------

15 x 5 = 75 cm

### Speed PSLE 2010 P1 Q27

Chun and Devi started jogging from the same place in opposite directions along a straight path. They jogged for 40 minutes. At the end of the jog, they were 7 km apart. Chun's average speed was 6 km/h.

What was Devi's average speed?

6 x 40/60 = 4

7 - 4 = 3

3 x 60/40 = 4.5 km/h or 3/4 x 6 = 4.5 km/h

Alternative method

----------------------

7 ÷ 40/60 = 7 x 60/40 = 10.5

10.5 - 6 = 4.5 km/h

What was Devi's average speed?

6 x 40/60 = 4

7 - 4 = 3

3 x 60/40 = 4.5 km/h or 3/4 x 6 = 4.5 km/h

Alternative method

----------------------

7 ÷ 40/60 = 7 x 60/40 = 10.5

**Combined speed**10.5 - 6 = 4.5 km/h

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