Challenging

Challenging

Challenging

Challenging

Challenging

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.

Area P6 2011 PSLE Q

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.

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 = 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 --------------->|
[ | | | | ]  [ | | | | ]  [ | | | |]  [ | | | | ]
       [ | | ][ | | ] [ | | ][ | | ][ | | ][   $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.

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.

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.

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 [][   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.

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 à 30 x 3 = 90

Monday to Thursday à 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.

Speed P6

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 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

          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  à 10 u – 12

5 u à 27 – 12 = 15

1 u à 15/5 = 3

10 u à 10 x 3 = 30

b) It was 30 children.

Area P6 2011 Nanyang P2 Q11

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

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

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

9 000  litres  à  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.

Area P6 2011 Nanyang P2 Q8

Ratio P6 Rosyth 2011 SA2 P2 Q11

Volume P6

Speed P6 Ang Mo Kio 2011 SA2 P2 Q47

Volume P6 Ang Mo Kio 2011 SA2 P2 Q46

Area P6 Ang Mo Kio 2011 SA2 P2 Q44

Speed P6 Mee Toh 2011 SA2 P2 Q18

Volume P6 Mee Toh 2011 SA2 P2 Q17

Whole Number P6 Mee Toh 2011 SA2 P2 Q16

Fraction P6 Mee Toh 2011 SA2 P2 Q13

Speed P6 2011 Nanyang P2 Q10

Volume P6 CHIJ 2011 SA2 P2 Q18

Fraction P6 CHIJ 2011 SA2 P1 Q10

Fraction P6

Volume P6 MGS 2011 SA2 P2 Q13

Speed P6 Nanyang 2011 SA2 P2 Q10

Angle P6 Rosyth 2011 SA2 P2 Q10

Area P6 Rosyth 2011 SA2 P1 Q11

Whole Number P6 Nan Hua 2011 SA2 P2 Q18

Challenging P6 Nan Hua 2011 SA2 P2 Q11

Volume P6 Nan Hua 2011 SA2 P2 Q16

Speed P6 Nan Hua 2011 SA2 P2 Q15

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.

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]

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]

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]

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]

Percentage P6 2010 SA2 Rosyth Paper 2 Q10

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.

Ratio P6

Ratio P6

Speed P6

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]

??

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   
(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

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.

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.

(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.